From 4f8029bb3870388541ac8d6dcd84fc85fb4d11dc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:06:28 +0800
Subject: [PATCH 0001/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index acfacf31..f82d4556 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -11,3 +11,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/91.jpg" />
 </p>
+人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。

From de2ddbba8e700c9a1be1ba6d37bfae3b5fb358d8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:06:49 +0800
Subject: [PATCH 0002/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index f82d4556..e88d9666 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -12,3 +12,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/91.jpg" />
 </p>
 人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。
+
+算法背景和发展
+

From 5a75f46bfc1c73948f85f45679c1cdb89524d70f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:07:19 +0800
Subject: [PATCH 0003/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index e88d9666..87ae0460 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -15,3 +15,26 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法背景和发展
 
+20世纪40年代，人们开始对神经网络研究。
+
+1943 年，美国心理学家麦克洛奇（Mcculloch）和数学家皮兹（Pitts）提出了M-P模型，此模型比较简单，但是意义重大。在模型中，通过把神经元看作功能逻辑器件来实现算法，从此开创了神经网络模型的理论研究。
+
+1949心理学家赫布（Hebb）提出Hebb法则，为构造有学习功能的神经网络模型奠定了基础。
+
+1957 年，罗森勃拉特（Rosenblatt）以M-P 模型为基础，提出了感知器（Perceptron）模型；
+
+1959年，美国著名工程师威德罗（B.Widrow）和霍夫（M.Hoff）等人提出ADALINE网络模型，ADALINE网络模型是一种连续取值的自适应线性神经元网络模型，可以用于自适应系统。
+
+1972年，芬兰的KohonenT.教授，提出了自组织神经网络SOM(Self-Organizing feature map)。
+
+1976年，美国Grossberg教授提出了著名的自适应共振理论ART(Adaptive Resonance Theory)，其学习过程具有自组织和自稳定的特征。
+
+1982年，美国物理学家霍普菲尔德（Hopfield）提出了一种离散神经网络，即离散Hopfield网络，从而有力地推动了神经网络的研究；
+
+1984年，Hinton与年轻学者Sejnowski等合作提出了Boltzmann机模型；
+
+1986年，儒默哈特（D.E.Ru melhart）等人在多层神经网络模型的基础上，提出了多层神经网络权值修正的反向传播学习算法----BP算法（Error Back-Propagation）；
+
+1988年，Chua和Yang提出了细胞神经网络（CNN）模型；
+
+1994年，廖晓昕关于细胞神经网络的数学理论与基础的提出，带来了这个领域新的进展。通过拓广神经网络的激活函数类，给出了更一般的时滞细胞神经网络(DCNN)、Hopfield神经网络（HNN）、双向联想记忆网络（BAM）模型；

From 4d6f4d3ea59e2dbd3decac76c5c45076d5630fe1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:07:49 +0800
Subject: [PATCH 0004/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 87ae0460..7e3c7f02 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -13,7 +13,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。
 
-算法背景和发展
+
+算法发展的背景
 
 20世纪40年代，人们开始对神经网络研究。
 

From 5a7328b6b8b99569ac18e260beef5100404a2ff8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:09:47 +0800
Subject: [PATCH 0005/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 7e3c7f02..5e8b1a04 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -2,7 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### Hopfield神经网络
 
 人工神经网络 （Artificial Neural Network，ANN）简称神经网络(NN)，是基于生物学中神经网络的基本原理，在理解和抽象了人脑结构和外界刺激响应机制后，以网络拓扑知识为理论基础，模拟人脑的神经系统对复杂信息的处理机制的一种数学模型，根植于神经科学、数学、思维科学、人工智能、统计学、物理学、计算机科学以及工程科学的一门技术，通常用于解决分类和回归问题。具有并行分布的处理能力、高容错性、智能化和自学习等能力的特征，本质上是一个有大量简单元件相互连接而成的复杂网络，具有高度的非线性，能够进行复杂的逻辑操作和非线性关系实现的系统。
 
@@ -39,3 +38,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 1988年，Chua和Yang提出了细胞神经网络（CNN）模型；
 
 1994年，廖晓昕关于细胞神经网络的数学理论与基础的提出，带来了这个领域新的进展。通过拓广神经网络的激活函数类，给出了更一般的时滞细胞神经网络(DCNN)、Hopfield神经网络（HNN）、双向联想记忆网络（BAM）模型；
+
+#### Hopfield神经网络

From 5b614f5574eaca749328bf21baf8e4a3b2631c7d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:10:35 +0800
Subject: [PATCH 0006/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 5e8b1a04..96f19b04 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -40,3 +40,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 1994年，廖晓昕关于细胞神经网络的数学理论与基础的提出，带来了这个领域新的进展。通过拓广神经网络的激活函数类，给出了更一般的时滞细胞神经网络(DCNN)、Hopfield神经网络（HNN）、双向联想记忆网络（BAM）模型；
 
 #### Hopfield神经网络
+
+Hopfield提出了连续和离散的Hopfield神经网络模型，并采用全互联型神经网络尝试对非多项式复杂度的旅行商问题（Travelling Salesman Problem，TSP）进行了求解，促进神经网络的研究再次进入了蓬勃发展的时期
+
+Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大器等元件组成的模拟电路实现了对网络神经元的描述，把最优化问题的目标函数转换成Hopfield神经网络的能量函数，通过网络能量函数最小化来寻找对应问题的最优解．Hopfield网络是一种循环神经网络，从输出到输入有反馈连接，典型的Hopfield神经网络模型如图所示．
+<p align="center">
+<img width="300" align="center" src="../../images/92.jpg" />
+</p>

From a740a9487debba1c42ef861f4c4c4e048e4c0e8c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:11:11 +0800
Subject: [PATCH 0007/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 96f19b04..c36ee845 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -47,3 +47,4 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <p align="center">
 <img width="300" align="center" src="../../images/92.jpg" />
 </p>
+在图中每组运算放大器及其相关的电阻、电容组成的网络代表一个神经元。每个神经元有两组输入，一组是恒定的外部电流，另一组是来自其他运算放大器输出的正向或反向的反馈连接。假设第i个神经元的内部膜电位为Ui(i=1,2,…,n)，细胞膜的输入电容和传递电阻分别为Ci和Ri，神经元的输出电位为Vi，外部输入电流为Ii，并用电阻Rij(i，j=1,2,…,n)来模拟第i个和第j个神经元之间的突触特性。由基尔霍夫电流定律(Kirchhoff’s Cureent Law ,KCL)可知，放大器输入节点处的流入电流和流出电流保持平衡，亦即有下式成立：

From 4dbee9729c2c7b15f0008b04784e8260166052b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:14:02 +0800
Subject: [PATCH 0008/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index c36ee845..0a723042 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -48,3 +48,6 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <img width="300" align="center" src="../../images/92.jpg" />
 </p>
 在图中每组运算放大器及其相关的电阻、电容组成的网络代表一个神经元。每个神经元有两组输入，一组是恒定的外部电流，另一组是来自其他运算放大器输出的正向或反向的反馈连接。假设第i个神经元的内部膜电位为Ui(i=1,2,…,n)，细胞膜的输入电容和传递电阻分别为Ci和Ri，神经元的输出电位为Vi，外部输入电流为Ii，并用电阻Rij(i，j=1,2,…,n)来模拟第i个和第j个神经元之间的突触特性。由基尔霍夫电流定律(Kirchhoff’s Cureent Law ,KCL)可知，放大器输入节点处的流入电流和流出电流保持平衡，亦即有下式成立：
+<p align="center">
+<img width="300" align="center" src="../../images/93.jpg" />
+</p>

From 21be4c1c76e44969728d0eed5713afa2e40cff1e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:15:00 +0800
Subject: [PATCH 0009/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 0a723042..12227d2b 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -51,3 +51,8 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <p align="center">
 <img width="300" align="center" src="../../images/93.jpg" />
 </p>
+同时，每一个运算放大器模拟了神经元输入和输出之间的非线性特性，即有
+
+<p align="center">
+<img width="300" align="center" src="../../images/94.jpg" />
+</p>

From 82b5364c80020911d6f11ee183007a5dde1510df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:15:41 +0800
Subject: [PATCH 0010/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 12227d2b..1b44c7a9 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -56,3 +56,4 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <p align="center">
 <img width="300" align="center" src="../../images/94.jpg" />
 </p>
+其中，fi代表了第i个神经元的传递函数，并定义W=Rij-1 （i,j＝1,2,…,n）为网络的权系数矩阵．为证明连续型网络的稳定性，Hopfield定义了如下的能量函数：

From 8dd212e5db90a793719d56514b21da36ff9acb1f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:15:57 +0800
Subject: [PATCH 0011/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 1b44c7a9..15b3ed11 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -57,3 +57,6 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <img width="300" align="center" src="../../images/94.jpg" />
 </p>
 其中，fi代表了第i个神经元的传递函数，并定义W=Rij-1 （i,j＝1,2,…,n）为网络的权系数矩阵．为证明连续型网络的稳定性，Hopfield定义了如下的能量函数：
+<p align="center">
+<img width="300" align="center" src="../../images/95.jpg" />
+</p>

From df72e5a5668dddcc3107ebb7438a301258006b85 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:16:20 +0800
Subject: [PATCH 0012/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 15b3ed11..2ccafc27 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -60,3 +60,6 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <p align="center">
 <img width="300" align="center" src="../../images/95.jpg" />
 </p>
+
+
+

From d4ef8b6593c5daf65ebf69bef487f67b1df713be Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:16:44 +0800
Subject: [PATCH 0013/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 2ccafc27..0f931611 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -61,5 +61,9 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <img width="300" align="center" src="../../images/95.jpg" />
 </p>
 
+其中，f-1为神经元传递函数的反函数．经过推导后得出以下两点结论：一是对于具有单调递增传递函数且对称权系数矩阵的网络来说，其能量会随着时间的变化而趋于稳定；二是当且仅当网络中所有神经元的输出不再随时间变化时，则可以认为网络的能量保持不变。在将网络用于求解诸如旅行商的组合优化问题时，Hopfield将优化的目标函数转化为网络的能量函数，对应地将待求解问题的变量用网络中神经元的状态来表示。由这样的表示方式可知当网络的能量衰减到稳定值时，问题的最优解也随之求出。
+
+Hopfield网络按网络输入和输出的数字形式不同可分为离散型和连续型两种网络,即：离散型Hopfield神经网络----DHNN(Discrete Hopfield Neural Network)；连续型Hopfield神经网络----CHNN(ContinuesHopfield Neural Network)。
+
 
 

From 3f81e0edd921e7393198fa545878f033179cc091 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:17:49 +0800
Subject: [PATCH 0014/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 0f931611..adcbb4d9 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -65,5 +65,9 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 
 Hopfield网络按网络输入和输出的数字形式不同可分为离散型和连续型两种网络,即：离散型Hopfield神经网络----DHNN(Discrete Hopfield Neural Network)；连续型Hopfield神经网络----CHNN(ContinuesHopfield Neural Network)。
 
+DHNN结构：它是一种单层全反馈网络,共有n个神经元。每个神经元都通过连接权接收所有其它神经元输出反馈来的信息，其目的是为了让任一神经元的输出能接受所有神经元输出的控制,从而使各神经元能相互制约。
 
+DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）决定的，设计吸引子的核心就是如何设计一组合适的权值。为了使所设计的权值满足要求，权值矩阵应符合以下要求：(1)为保证异步方式工作时网络收敛，W应为对称阵；(2)为保证同步方式工作时网络收敛，W应为非负定对称阵；(3)保证给定的样本是网络的吸引子，并且要有一定的吸引域。
+
+具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
 

From 72d3e0bede40627f39b8f0808a4829170bf1ac50 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:23:57 +0800
Subject: [PATCH 0015/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index adcbb4d9..2bd8785a 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -71,3 +71,4 @@ DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）
 
 具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
 
+CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。

From f9408daf4ed5b97bbcee8cb9a32d02b016020219 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:24:28 +0800
Subject: [PATCH 0016/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 2bd8785a..68075c59 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -72,3 +72,6 @@ DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）
 具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
 
 CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
+
+
+#### 应用领域

From 8a9f2ca9bac89fec2eb21635d2b221562357868f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:25:02 +0800
Subject: [PATCH 0017/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 68075c59..bb842dbd 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -75,3 +75,4 @@ CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行
 
 
 #### 应用领域
+Hopfield是反馈归神经网络，主要应用于联想记忆、聚类以及优化计算等方面。

From e695be283b0b29a4e3d4b8cc55f893dfb46e8c89 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Jan 2018 09:25:29 +0800
Subject: [PATCH 0018/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index bb842dbd..3f4a1256 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -76,3 +76,12 @@ CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行
 
 #### 应用领域
 Hopfield是反馈归神经网络，主要应用于联想记忆、聚类以及优化计算等方面。
+
+
+#### 优缺点
+
+Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。
+
+Hopfield神经网络的提出就是与其实际应用密切相关。具有联系记忆的功能，具体为：
+
+联想记忆：输入--输出模式的各元素之间，并不存在一对一的映射关系，输入--输出模式的维数也不要求相同；联想记忆时，只给出输入模式部分信息，就能联想出完整的输出模式。即具有容错性。

From 1ee7073a23eeb265e3538d955b3e977b74c05719 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 09:09:11 +0800
Subject: [PATCH 0019/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 3f4a1256..ed0b9df2 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -3,7 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
-人工神经网络 （Artificial Neural Network，ANN）简称神经网络(NN)，是基于生物学中神经网络的基本原理，在理解和抽象了人脑结构和外界刺激响应机制后，以网络拓扑知识为理论基础，模拟人脑的神经系统对复杂信息的处理机制的一种数学模型，根植于神经科学、数学、思维科学、人工智能、统计学、物理学、计算机科学以及工程科学的一门技术，通常用于解决分类和回归问题。具有并行分布的处理能力、高容错性、智能化和自学习等能力的特征，本质上是一个有大量简单元件相互连接而成的复杂网络，具有高度的非线性，能够进行复杂的逻辑操作和非线性关系实现的系统。
+所谓的人工神经网络 （Artificial Neural Network，ANN）简称神经网络(NN)，是基于生物学中神经网络的基本原理，在理解和抽象了人脑结构和外界刺激响应机制后，以网络拓扑知识为理论基础，模拟人脑的神经系统对复杂信息的处理机制的一种数学模型，根植于神经科学、数学、思维科学、人工智能、统计学、物理学、计算机科学以及工程科学的一门技术，通常用于解决分类和回归问题。具有并行分布的处理能力、高容错性、智能化和自学习等能力的特征，本质上是一个有大量简单元件相互连接而成的复杂网络，具有高度的非线性，能够进行复杂的逻辑操作和非线性关系实现的系统。
 
 神经网络由大量的节点（或称神经元）之间相互联接构成，每个节点代表一种特定的输出函数，称为激活函数（activation function）；每两个节点间的连接都代表一个对于通过该连接信号的加权值，称之为权重（weight），神经网络就是通过这种方式来模拟人类的记忆。网络的输出则取决于网络的结构、网络的连接方式、权重和激活函数。而网络自身通常都是对自然界某种算法或者函数的逼近，也可能是对一种逻辑策略的表达，是对传统逻辑学演算的进一步延伸。
 

From 018d8fcf3ab8cde217822896c879ca52a949c200 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 7 Jan 2018 20:52:08 +0800
Subject: [PATCH 0020/1406] add DT

---
 assets/src/DT/DT.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)
 create mode 100644 assets/src/DT/DT.md

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
new file mode 100644
index 00000000..636ce113
--- /dev/null
+++ b/assets/src/DT/DT.md
@@ -0,0 +1,17 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+机器学习是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。主要研究计算机怎样模拟或实现人类的学习行为，以获取新的知识和技能，重新组织已有的知识结构，不断的改善自身的性能。
+
+机器学习理论主要是设计和分析一些让计算机可以自动“学习”的算法。这些算法是一类能从数据中自动分析获得规律，并利用规律对未知数据进行预测的算法。简而言之，机器学习主要以数据为基础，通过大数据本身，运用计算机自我学习来寻找数据本身的规律，而这是机器学习与统计分析的基本区别。
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+(1)监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+(2)监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+(3)半监督学习：介于监督学习和无监督学习之间,例如EM算法.
+
+如今的机器学习领域主要的研究工作在三个方面进行：1.面向任务的研究,研究和分析改进一组预定任务的执行性能的学习系统；2.认知模型，研究人类学习过程并进行计算模拟；3.理论的分析，从理论的层面探索可能的算法和独立的应用领域算法.
+
+#### 决策树
\ No newline at end of file

From 00f2cee4b1c53923d8ca80a54dd21f78f598b9cc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 20:54:54 +0800
Subject: [PATCH 0021/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 52626a6c..e10923f8 100644
--- a/README.md
+++ b/README.md
@@ -58,7 +58,7 @@
  * [CBA](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CBA/CBA.md)
  * [KNN](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KNN/KNN.md)
  * [Hopfield神经网络](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/HPD/HPD.md)
- * [决策树]()
+ * [决策树](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.md)
  * [聚类分析]()
  * [关联规则]()
  * [支持向量机（SVM）]()

From f4dfc23e70165c902b25c200ab03fc1841c6919d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 20:58:17 +0800
Subject: [PATCH 0022/1406] Update DT.md

---
 assets/src/DT/DT.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 636ce113..cb9cd9f2 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -14,4 +14,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 如今的机器学习领域主要的研究工作在三个方面进行：1.面向任务的研究,研究和分析改进一组预定任务的执行性能的学习系统；2.认知模型，研究人类学习过程并进行计算模拟；3.理论的分析，从理论的层面探索可能的算法和独立的应用领域算法.
 
-#### 决策树
\ No newline at end of file
+#### 决策树
+
+决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
+

From c4205f8ad1e5cc9c8b28e6ae49583e2fd2a2213e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 7 Jan 2018 21:00:31 +0800
Subject: [PATCH 0023/1406] change page of DT

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From 7648539122b84a6f5f111e9c3364f9d41e9c107e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:02:15 +0800
Subject: [PATCH 0024/1406] Update DT.md

---
 assets/src/DT/DT.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index cb9cd9f2..e4e38937 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -18,3 +18,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
 
+<p align="center">
+<img width="100" align="center" src="../../images/96.jpg" />
+</p>

From d7b432b9accfa07c7071a897c4b1b1d9ea0a143f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:02:27 +0800
Subject: [PATCH 0025/1406] Update DT.md

---
 assets/src/DT/DT.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index e4e38937..e5be74c3 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -21,3 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="100" align="center" src="../../images/96.jpg" />
 </p>
+决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。

From 1e2802d1d512e99a35410239bbaa76c94f31415a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:02:41 +0800
Subject: [PATCH 0026/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index e5be74c3..cb3c8649 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -19,6 +19,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
 
 <p align="center">
-<img width="100" align="center" src="../../images/96.jpg" />
+<img width="300" align="center" src="../../images/96.jpg" />
 </p>
 决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。

From cd4fb0025ce491ff0c1b5740debb09a4d9f37b74 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:03:01 +0800
Subject: [PATCH 0027/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index cb3c8649..da8835b3 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -19,6 +19,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
 
 <p align="center">
-<img width="300" align="center" src="../../images/96.jpg" />
+<img width="500" align="center" src="../../images/96.jpg" />
 </p>
 决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。

From bec1bd62980467404781a99d08846edc7a867c5b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:03:32 +0800
Subject: [PATCH 0028/1406] Update DT.md

---
 assets/src/DT/DT.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index da8835b3..9e556073 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -21,4 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/96.jpg" />
 </p>
+
 决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。
+
+构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。

From 53b7ee5be79e0208b423bbb5d8130375ac67a895 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Jan 2018 21:03:45 +0800
Subject: [PATCH 0029/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 9e556073..21bf47b9 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -24,4 +24,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。
 
-构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。
+构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。

From 137a3649652aa9741df451bfb33c9f304454a939 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:31:56 +0800
Subject: [PATCH 0030/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 21bf47b9..1d64ac4b 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -25,3 +25,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 决策树学习算法包含特征选择、决策树的生成和决策树的修剪过程，构造决策树的方法是采用自上而下的递归构造。
 
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
+
+信息增益算法：

From 45b98919fd0cd00ff289986d5eaf873273ea1379 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:37:14 +0800
Subject: [PATCH 0031/1406] Update DT.md

---
 assets/src/DT/DT.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 1d64ac4b..ff4e3e04 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,3 +27,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
+设D是s个样本的集合，具有n个不同的类别

From 498d04f5f8d4269b117d1905799ceb732994c946 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:38:32 +0800
Subject: [PATCH 0032/1406] change page of DT

---
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 assets/images/101.jpg | Bin 0 -> 239 bytes
 assets/images/102.jpg | Bin 0 -> 270 bytes
 assets/images/103.jpg | Bin 0 -> 573 bytes
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 assets/images/109.jpg | Bin 0 -> 329 bytes
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 assets/images/97.jpg  | Bin 0 -> 624 bytes
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 assets/images/99.jpg  | Bin 0 -> 238 bytes
 assets/src/DT/DT.md   |   2 +-
 15 files changed, 1 insertion(+), 1 deletion(-)
 create mode 100644 assets/images/100.jpg
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diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index ff4e3e04..fa5ccfe0 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,4 +27,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别
+设D是s个样本的集合，具有n个不同的类别<img width="300" align="center" src="../../images/97.jpg" />

From 9da5d829c68e2131dffe3f0528cfdfa49521df04 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:39:48 +0800
Subject: [PATCH 0033/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index fa5ccfe0..414e9734 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,4 +27,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="300" align="center" src="../../images/97.jpg" />
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />

From 655c0028421efe69763aaca4464243195f1c6408 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:40:35 +0800
Subject: [PATCH 0034/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 414e9734..0a17d482 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,4 +27,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="100" align="center" src="../../images/98.jpg" />是类<img width="100" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：

From 48336454073a9b3f6b2b21209068af8c0b1f1df4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:40:44 +0800
Subject: [PATCH 0035/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 0a17d482..b57d09cc 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -28,3 +28,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 信息增益算法：
 设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="100" align="center" src="../../images/98.jpg" />是类<img width="100" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
+
+

From 15a267c63b5bdba5b71236826af7d1e951c271c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:41:06 +0800
Subject: [PATCH 0036/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index b57d09cc..0f783249 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -28,5 +28,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 信息增益算法：
 设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="100" align="center" src="../../images/98.jpg" />是类<img width="100" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
-
+<p align="center">
+<img width="500" align="center" src="../../images/100.jpg" />
+</p>
 

From 8a14cfc95d951c4c0d8b8d613e5e9f14c7d2c6ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:41:33 +0800
Subject: [PATCH 0037/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 0f783249..b35545fc 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,8 +27,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="100" align="center" src="../../images/98.jpg" />是类<img width="100" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="40" align="center" src="../../images/98.jpg" />是类<img width="40" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
 <p align="center">
-<img width="500" align="center" src="../../images/100.jpg" />
+<img width="200" align="center" src="../../images/100.jpg" />
 </p>
 

From c1f2844dccc00061a8351eb5ac877e689129a0f3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Jan 2018 09:41:56 +0800
Subject: [PATCH 0038/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index b35545fc..aa6f5873 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,7 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="40" align="center" src="../../images/98.jpg" />是类<img width="40" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="20" align="center" src="../../images/98.jpg" />是类<img width="20" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
 <p align="center">
 <img width="200" align="center" src="../../images/100.jpg" />
 </p>

From d5a52e08160c15edfb356000e7da94442758b638 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:01:06 +0800
Subject: [PATCH 0039/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index aa6f5873..80e2b9aa 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -32,3 +32,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/100.jpg" />
 </p>
 
+
+其中为任意样本属于类的概率，并用估计。

From 0aa5e38dcfc6df3673713e14e1c2c1ffbedb9daf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:02:01 +0800
Subject: [PATCH 0040/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 80e2b9aa..b9191089 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -33,4 +33,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
-其中为任意样本属于类的概率，并用估计。
+其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类的概率，并用估计。

From c5a3820c73f1ef8306783efa78a6f20eb1fb366c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:02:57 +0800
Subject: [PATCH 0041/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index b9191089..6c5403e0 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -33,4 +33,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
-其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类的概率，并用估计。
+其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="20" align="center" src="../../images/102.jpg" />估计。

From 6a7d81a0c60444bb3811dea2f06e039f042ac0ab Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:03:10 +0800
Subject: [PATCH 0042/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 6c5403e0..7287cbfb 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -33,4 +33,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
-其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="20" align="center" src="../../images/102.jpg" />估计。
+其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。

From 10093fdc2d8a228cfef2a61abe460e331d5bb7ff Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:04:01 +0800
Subject: [PATCH 0043/1406] Update DT.md

---
 assets/src/DT/DT.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 7287cbfb..94132893 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -34,3 +34,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
+
+
+设属性A具有v个不同的值<img width="30" align="center" src="../../images/103.jpg" />

From 1e9324f62d1f940d1734ce85e1dfbf74a66ab099 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:05:08 +0800
Subject: [PATCH 0044/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 94132893..150a4f03 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="30" align="center" src="../../images/103.jpg" />
+设属性A具有v个不同的值<img width="100" align="center" src="../../images/103.jpg" />

From a77a58238c475d9ad45db7611abf42755a454030 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:05:24 +0800
Subject: [PATCH 0045/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 150a4f03..98408d0a 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="100" align="center" src="../../images/103.jpg" />
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />

From 031c63bf2f95f8902822aafe19d1e1556e84dc18 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:06:05 +0800
Subject: [PATCH 0046/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 98408d0a..a6eb1727 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集

From 6958a79d6c98af0d9cd22062e729abb2a4d7a019 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:06:25 +0800
Subject: [PATCH 0047/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index a6eb1727..2daa7341 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />

From 56ecf55b14ef3258112088db7642cea8984cf6f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:07:56 +0800
Subject: [PATCH 0048/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 2daa7341..f8fae8bc 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="30" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="30" align="center" src="../../images/106.jpg" />的一些样本。令是子集中类的样本数。根据划分成子集的经验熵为：

From d8df0b55885dfb9c9718c0440629a55de3a01eae Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:09:48 +0800
Subject: [PATCH 0049/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index f8fae8bc..aa62faa8 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="30" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="30" align="center" src="../../images/106.jpg" />的一些样本。令是子集中类的样本数。根据划分成子集的经验熵为：
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令是子集中类的样本数。根据划分成子集的经验熵为：

From 844a9fef87dfaa41fbf312e67467bd594f96a02a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:10:43 +0800
Subject: [PATCH 0050/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index aa62faa8..9ff1fad0 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令是子集中类的样本数。根据划分成子集的经验熵为：
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集中类的样本数。根据划分成子集的经验熵为：

From a355034daf27b85e130d4221aca4755f7413e3a2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:11:55 +0800
Subject: [PATCH 0051/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 9ff1fad0..c0ed2ad6 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集中类的样本数。根据划分成子集的经验熵为：
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/98.jpg" />中类的样本数。根据A划分成子集的经验熵为：

From 73afe398cbadd12e0d1f6a183587c24cb2252961 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:12:21 +0800
Subject: [PATCH 0052/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index c0ed2ad6..019e2f76 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,7 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="20" align="center" src="../../images/98.jpg" />是类<img width="20" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="20" align="center" src="../../images/98.jpg" />是类<img width="10" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
 <p align="center">
 <img width="200" align="center" src="../../images/100.jpg" />
 </p>
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/98.jpg" />中类的样本数。根据A划分成子集的经验熵为：
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="10" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：

From f674a3cc081bb8cca2b71efa1e706ad3e859a90c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:12:49 +0800
Subject: [PATCH 0053/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 019e2f76..5a91680c 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -27,7 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 构造的思路是，如果训练样本集合中的所有样本是同类的，则将之作为叶子节点，节点内容即是该类别标记。否则，根据某种策略（如信息熵或GINI系数）选择一个属性，按照属性的各个取值，把样本集合划分为若干子集合，使得每个子集上的所有样本在该属性上具有同样的属性值，然后再依次递归处理各个子集。这种思路实际上就是“分而治之”的道理。
 
 信息增益算法：
-设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="20" align="center" src="../../images/98.jpg" />是类<img width="10" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
+设D是s个样本的集合，具有n个不同的类别<img width="100" align="center" src="../../images/97.jpg" />，设<img width="20" align="center" src="../../images/98.jpg" />是类<img width="20" align="center" src="../../images/99.jpg" />的样本数，那么对给定的样本分类所需要的经验熵为：
 <p align="center">
 <img width="200" align="center" src="../../images/100.jpg" />
 </p>
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其中<img width="20" align="center" src="../../images/101.jpg" />为任意样本属于类<img width="20" align="center" src="../../images/99.jpg" />的概率，并用<img width="30" align="center" src="../../images/102.jpg" />估计。
 
 
-设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="10" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：
+设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：

From 388306dc1c53d424a5a8a6e97c057617a017b518 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:13:16 +0800
Subject: [PATCH 0054/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 5a91680c..db78cc31 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -37,3 +37,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：
+
+<p align="center">
+<img width="100" align="center" src="../../images/108.jpg" />
+</p>

From e7729d231dc838b3180fb7eb6d12228ef4588f0c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:14:22 +0800
Subject: [PATCH 0055/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index db78cc31..f22e2615 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -39,5 +39,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：
 
 <p align="center">
-<img width="100" align="center" src="../../images/108.jpg" />
+<img width="300" align="center" src="../../images/108.jpg" />
 </p>

From d1855184dc22cad101d735896ab577c1ce36506a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:14:35 +0800
Subject: [PATCH 0056/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index f22e2615..d1da4aab 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -39,5 +39,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 设属性A具有v个不同的值<img width="70" align="center" src="../../images/103.jpg" />,可以用A属性将集合D划分为v个子集<img width="70" align="center" src="../../images/104.jpg" />,其中<img width="20" align="center" src="../../images/105.jpg" />包含D中属性A上取值<img width="20" align="center" src="../../images/106.jpg" />的一些样本。令<img width="20" align="center" src="../../images/107.jpg" />是子集<img width="20" align="center" src="../../images/99.jpg" />中类的样本数。根据A划分成子集的经验熵为：
 
 <p align="center">
-<img width="300" align="center" src="../../images/108.jpg" />
+<img width="200" align="center" src="../../images/108.jpg" />
 </p>

From 4aff009cddf7c5e4fcc4a2ccb8a5702af81d028b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:15:15 +0800
Subject: [PATCH 0057/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index d1da4aab..3d348af9 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -41,3 +41,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="200" align="center" src="../../images/108.jpg" />
 </p>
+
+当<img width="20" align="center" src="../../images/109.jpg" />熵值越小，子集划分的纯度越高。

From c0efdc3f73d8d93bb5097d381bc7116062fe1187 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:15:27 +0800
Subject: [PATCH 0058/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 3d348af9..f35685cd 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -42,4 +42,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/108.jpg" />
 </p>
 
-当<img width="20" align="center" src="../../images/109.jpg" />熵值越小，子集划分的纯度越高。
+当<img width="40" align="center" src="../../images/109.jpg" />熵值越小，子集划分的纯度越高。

From 5ced6611922c7dacc6901ab187ec2fd21defb94e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:15:58 +0800
Subject: [PATCH 0059/1406] Update DT.md

---
 assets/src/DT/DT.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index f35685cd..377ba449 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -43,3 +43,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 当<img width="40" align="center" src="../../images/109.jpg" />熵值越小，子集划分的纯度越高。
+
+在属性A上分枝将获得的信息增益为：
+
+<p align="center">
+<img width="200" align="center" src="../../images/109.jpg" />
+</p>

From debcd0cdd44e3ebdf1eb0d94070a2cb03cd4e403 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:16:17 +0800
Subject: [PATCH 0060/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 377ba449..54e29875 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -47,5 +47,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在属性A上分枝将获得的信息增益为：
 
 <p align="center">
-<img width="200" align="center" src="../../images/109.jpg" />
+<img width="100" align="center" src="../../images/110.jpg" />
 </p>

From e9f4f8ee8fd1e0689ab5a60e10d28f4557754b0f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:16:29 +0800
Subject: [PATCH 0061/1406] Update DT.md

---
 assets/src/DT/DT.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 54e29875..1638a196 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -47,5 +47,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在属性A上分枝将获得的信息增益为：
 
 <p align="center">
-<img width="100" align="center" src="../../images/110.jpg" />
+<img width="200" align="center" src="../../images/110.jpg" />
 </p>

From feb23b50e6ff0a8f4e062b9b8445c781b0ac4200 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:16:56 +0800
Subject: [PATCH 0062/1406] Update DT.md

---
 assets/src/DT/DT.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 1638a196..72a17b77 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -49,3 +49,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="200" align="center" src="../../images/110.jpg" />
 </p>
+
+通过比较各特征的信息增益值，并比较它们的大小，选择信息增益最大的特征。
+
+决策树的剪枝
+
+剪枝是决策树停止分支的方法之一，剪枝有分预先剪枝和后剪枝两种。预先剪枝是在树的生长过程中设定一个指标，当达到该指标时就停止生长，这样做容易产生“视界局限”，就是一旦停止分支，使得节点N成为叶节点，就断绝了其后继节点进行“好”的分支操作的任何可能性。
+
+后剪枝中树首先要充分生长，直到叶节点都有最小的不纯度值为止，因而可以克服“视界局限”。然后对所有相邻的成对叶节点考虑是否消去它们，如果消去能引起令人满意的不纯度增长，那么执行消去，并令它们的公共父节点成为新的叶节点。这种“合并”叶节点的做法和节点分支的过程恰好相反，经过剪枝后叶节点常常会分布在很宽的层次上，树也变得非平衡。后剪枝技术的优点是克服了“视界局限”效应，而且无需保留部分样本用于交叉验证，所以可以充分利用全部训练集的信息。但后剪枝的计算量代价比预剪枝方法大得多，特别是在大样本集中，不过对于小样本的情况，后剪枝方法还是优于预先剪枝方法。

From eabc367e2034703c2ddc4193fb79213dea8add17 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:17:46 +0800
Subject: [PATCH 0063/1406] Update DT.md

---
 assets/src/DT/DT.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 72a17b77..165b7ea6 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -57,3 +57,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 剪枝是决策树停止分支的方法之一，剪枝有分预先剪枝和后剪枝两种。预先剪枝是在树的生长过程中设定一个指标，当达到该指标时就停止生长，这样做容易产生“视界局限”，就是一旦停止分支，使得节点N成为叶节点，就断绝了其后继节点进行“好”的分支操作的任何可能性。
 
 后剪枝中树首先要充分生长，直到叶节点都有最小的不纯度值为止，因而可以克服“视界局限”。然后对所有相邻的成对叶节点考虑是否消去它们，如果消去能引起令人满意的不纯度增长，那么执行消去，并令它们的公共父节点成为新的叶节点。这种“合并”叶节点的做法和节点分支的过程恰好相反，经过剪枝后叶节点常常会分布在很宽的层次上，树也变得非平衡。后剪枝技术的优点是克服了“视界局限”效应，而且无需保留部分样本用于交叉验证，所以可以充分利用全部训练集的信息。但后剪枝的计算量代价比预剪枝方法大得多，特别是在大样本集中，不过对于小样本的情况，后剪枝方法还是优于预先剪枝方法。
+
+
+#### 应用领域
+决策树经常在运筹学中使用，特别是在决策分析中，它帮助确定一个能最可能达到目标的策略。如果在实际中，决策不得不在没有完备知识的情况下被在线采用，一个决策树应该平行概率模型作为最佳的选择模型或在线选择模型算法。决策树的另一个使用是作为计算条件概率的描述性手段。

From 26f173a0b83b4067d52323e881806fdbb6fc4f1a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:18:14 +0800
Subject: [PATCH 0064/1406] Update DT.md

---
 assets/src/DT/DT.md | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/assets/src/DT/DT.md b/assets/src/DT/DT.md
index 165b7ea6..4aa52504 100644
--- a/assets/src/DT/DT.md
+++ b/assets/src/DT/DT.md
@@ -61,3 +61,27 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用领域
 决策树经常在运筹学中使用，特别是在决策分析中，它帮助确定一个能最可能达到目标的策略。如果在实际中，决策不得不在没有完备知识的情况下被在线采用，一个决策树应该平行概率模型作为最佳的选择模型或在线选择模型算法。决策树的另一个使用是作为计算条件概率的描述性手段。
+
+#### 优缺点
+
+优点：
+
+1. 决策树生成的模型很直观、简单、易懂；
+
+2. 决策树对数据的分布没有特别严格的要求；
+
+3. 对缺失值很宽容，几乎可以不做处理；
+
+4. 不容易受离群值影响；
+
+5. 决策树可以为其他模型算法挑选自变量。
+
+缺点：
+
+1. 决策树最大的缺点是其使用了贪心算法，贪心算法局限于其寻找的不是全局最优解。
+
+2. 决策树处理不了连续变量；
+
+3. 决策树缺乏丰富的监测指标和评价方法；
+
+4. 当某些自变量的类别数量比较多或者是区间变量时，决策树会产生过拟合的危险。

From 46ba52ed349b601e49dc95b0b97a21ab7b23f31e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:20:32 +0800
Subject: [PATCH 0065/1406] change page of CAS

---
 assets/src/CAS/CAS.md | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)
 create mode 100644 assets/src/CAS/CAS.md

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
new file mode 100644
index 00000000..4eef9b4d
--- /dev/null
+++ b/assets/src/CAS/CAS.md
@@ -0,0 +1,19 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+机器学习是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。主要研究计算机怎样模拟或实现人类的学习行为，以获取新的知识和技能，重新组织已有的知识结构，不断的改善自身的性能。
+
+机器学习理论主要是设计和分析一些让计算机可以自动“学习”的算法。这些算法是一类能从数据中自动分析获得规律，并利用规律对未知数据进行预测的算法。简而言之，机器学习主要以数据为基础，通过大数据本身，运用计算机自我学习来寻找数据本身的规律，而这是机器学习与统计分析的基本区别。
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+(1)监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+(2)无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+(3)半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 聚类分析

From 2d06e93da798ba2e7c44e5a930a9c0956aaa1fa7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 9 Jan 2018 09:21:41 +0800
Subject: [PATCH 0066/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index e10923f8..0154d86f 100644
--- a/README.md
+++ b/README.md
@@ -59,7 +59,7 @@
  * [KNN](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KNN/KNN.md)
  * [Hopfield神经网络](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/HPD/HPD.md)
  * [决策树](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.md)
- * [聚类分析]()
+ * [聚类分析](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CAS/CAS.md)
  * [关联规则]()
  * [支持向量机（SVM）]()
 

From 96e4248d982b91f663d21e6f818a86225e82b3d0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:15:08 +0800
Subject: [PATCH 0067/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 4eef9b4d..f412b783 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -17,3 +17,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 聚类分析
+
+聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。

From 17dee479472f03775ae0023f543d2ca58c3215e0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:15:25 +0800
Subject: [PATCH 0068/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index f412b783..e053c4af 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -19,3 +19,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 聚类分析
 
 聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
+
+一般把数据聚类归纳为一种非监督学习。

From 7b894452bad05692461910d408250ccaa810bfa7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:15:43 +0800
Subject: [PATCH 0069/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index e053c4af..adf82395 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -21,3 +21,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
 
 一般把数据聚类归纳为一种非监督学习。
+
+数据聚类算法可以分为结构性或者分散性。结构性算法利用以前成功使用过的聚类器进行分类，而分散型算法则是一次确定所有分类。结构性算法可以从上至下或者从下至上双向进行计算。从下至上算法从每个对象作为单独分类开始，不断融合其中相近的对象。而从上至下算法则是把所有对象作为一个整体分类，然后逐渐分小。
+
+分割式聚类算法，是一次性确定要产生的类别，这种算法也已应用于从下至上聚类算法。
+
+基于密度的聚类算法，是为了挖掘有任意形状特性的类别而发明的。此算法把一个类别视为数据集中大于某阈值的一个区域。DBSCAN和OPTICS是两个典型的算法。

From 365dd8c9e130b0a82317b7de14bdc000664eeae4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:16:00 +0800
Subject: [PATCH 0070/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index adf82395..ab7312fb 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -27,3 +27,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 分割式聚类算法，是一次性确定要产生的类别，这种算法也已应用于从下至上聚类算法。
 
 基于密度的聚类算法，是为了挖掘有任意形状特性的类别而发明的。此算法把一个类别视为数据集中大于某阈值的一个区域。DBSCAN和OPTICS是两个典型的算法。
+
+许多聚类算法在执行之前，需要指定从输入数据集中产生的分类个数。除非事先准备好一个合适的值，否则必须决定一个大概值，关于这个问题已经有一些现成的技术。
+
+在已经得到距离值之后，元素间可以被联系起来。通过分离和融合可以构建一个结构。传统上，表示的方法是树形数据结构， 然后对该结构进行修剪。树的根节点表示一个包含所有项目的类别，树叶表示与个别的项目相关的类别。
+
+层次聚类算法，要么是自下向上聚集型的，即从叶子节点开始，最终汇聚到根节点；要么是自顶向下分裂型的，即从根节点开始，递归的向下分裂。
+
+任意非负值的函数都可以用于衡量一对观测值之间的相似度。决定一个类别是否分裂或者合并的是一个连动的标准，它是两两观测值之间距离的函数。
+
+在一个指定高度上切割此树，可以得到一个相应精度的分类。

From d6313b4ad63922830534522dc256ad126f8ca4d3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:16:22 +0800
Subject: [PATCH 0071/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index ab7312fb..16063dac 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -37,3 +37,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 任意非负值的函数都可以用于衡量一对观测值之间的相似度。决定一个类别是否分裂或者合并的是一个连动的标准，它是两两观测值之间距离的函数。
 
 在一个指定高度上切割此树，可以得到一个相应精度的分类。
+
+
+主要可分为：划分方法（partitioning method），层次方法(hierarchical method)，基于密度的方法(density-basedmethod)，基于网格的方法(grid-based method)，和基于模型的方法(model-based method)。

From 56f71a2b8a5e17d6ae1ad44ebe19cd708da9021d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:16:41 +0800
Subject: [PATCH 0072/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 16063dac..ba550d79 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -40,3 +40,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 主要可分为：划分方法（partitioning method），层次方法(hierarchical method)，基于密度的方法(density-basedmethod)，基于网格的方法(grid-based method)，和基于模型的方法(model-based method)。
+
+分层聚类算法原理

From 81e9b6b6061da03b2b29e33b7fd9b86da787a246 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:19:17 +0800
Subject: [PATCH 0073/1406] change page of CAS

---
 assets/images/111.jpg | Bin 0 -> 13390 bytes
 assets/images/112.jpg | Bin 0 -> 554 bytes
 assets/images/113.jpg | Bin 0 -> 1287 bytes
 assets/images/114.jpg | Bin 0 -> 294 bytes
 assets/images/115.jpg | Bin 0 -> 697 bytes
 assets/images/116.jpg | Bin 0 -> 684 bytes
 6 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/111.jpg
 create mode 100644 assets/images/112.jpg
 create mode 100644 assets/images/113.jpg
 create mode 100644 assets/images/114.jpg
 create mode 100644 assets/images/115.jpg
 create mode 100644 assets/images/116.jpg

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From f68fab48c8a1a52dca7ed81e71ed180574579df2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:20:22 +0800
Subject: [PATCH 0074/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index ba550d79..7b9eff33 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -41,4 +41,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 主要可分为：划分方法（partitioning method），层次方法(hierarchical method)，基于密度的方法(density-basedmethod)，基于网格的方法(grid-based method)，和基于模型的方法(model-based method)。
 
-分层聚类算法原理
+* 分层聚类算法原理
+
+开始时将N个观测量（变量）视为N类；规定相似性统计量的测度，并计算相似系数矩阵；
+
+找出最大相似系数的观测量（变量）组：Sij为类Gi与类Gj的相似系数，S为相似系数矩阵或不相似系数矩阵，若S为相似系数矩阵，则依据Spq最小者挑选Gp与Gq (p>q)，若S为不相似系数（距离）矩阵，则依据Spq最大者挑选Gp与Gq进行聚类，即将Gp与Gq合并成一个新类Gt（t=q）；
+
+计算新类Gt与当前各类的相似性系数，更新相似系数矩阵S：将得到的新的系数代换与q相关的行与列，删除与p有关的行与列；
+
+重复过程：寻找最大相似系数观测变量组和计算相似系数矩阵，直至聚为一类；
+
+一共有六种分层聚类的方法，五种距离尺度标准。如：明考斯基距离、马氏距离、匹配距离等。

From 3d04be4ebe2eb1248703ff4d2848c635ee913a6d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:20:43 +0800
Subject: [PATCH 0075/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 7b9eff33..fab07bd9 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -52,3 +52,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 重复过程：寻找最大相似系数观测变量组和计算相似系数矩阵，直至聚为一类；
 
 一共有六种分层聚类的方法，五种距离尺度标准。如：明考斯基距离、马氏距离、匹配距离等。
+
+* 快速聚类算法原理
+

From d968000318a5ac7d4c999d53d6fb49af7360a5f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:21:30 +0800
Subject: [PATCH 0076/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index fab07bd9..ec7df25d 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -55,3 +55,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 * 快速聚类算法原理
 
+快速聚类以距离衡量样本间的亲疏程度，但其最终结果不是聚成一类，而是根据各聚类中心，将所有样本点聚成指定的类数。
+
+首先设置K个聚类的初始类中心点，计算所有样本点到K个类中心点的距离，按照距离最短的原则，将所有样本分派到各中心点所在的类中，形成一个新的K类，完成一次迭代过程。在下一次迭代过程中，重新计算K个类的类中心点，重复上述过程，直到达到指定的迭代次数或达到终止迭代的判断要求为止。
+
+其中K个聚类初始中心点的选取有以下方法：

From 758cf157bfc148bff2df14597404fe8290e4b7d4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:22:01 +0800
Subject: [PATCH 0077/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index ec7df25d..371c3ef2 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -60,3 +60,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 首先设置K个聚类的初始类中心点，计算所有样本点到K个类中心点的距离，按照距离最短的原则，将所有样本分派到各中心点所在的类中，形成一个新的K类，完成一次迭代过程。在下一次迭代过程中，重新计算K个类的类中心点，重复上述过程，直到达到指定的迭代次数或达到终止迭代的判断要求为止。
 
 其中K个聚类初始中心点的选取有以下方法：
+
+1.可以选取前K个观测变量值为初始中心点；
+
+2.最小最大原则：先选择所有样本数据中距离最远的两个值；并且选择第三个值，使得与前两个聚点的距离最小者等于所有其余数据的较小距离中最大的，依次按这个原则选取，直到最终确定K个中心点；用公式可以表示为：

From 272a24c6129d3d6871045640f18e7201fffd91fe Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:22:39 +0800
Subject: [PATCH 0078/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 371c3ef2..4f20c931 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -64,3 +64,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 1.可以选取前K个观测变量值为初始中心点；
 
 2.最小最大原则：先选择所有样本数据中距离最远的两个值；并且选择第三个值，使得与前两个聚点的距离最小者等于所有其余数据的较小距离中最大的，依次按这个原则选取，直到最终确定K个中心点；用公式可以表示为：
+<p align="center">
+<img width="200" align="center" src="../../images/111.jpg" />
+</p>

From 8281b87b0b7538872ec7e2a720a6f9633a63e561 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:22:52 +0800
Subject: [PATCH 0079/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 4f20c931..aeadf2fe 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -65,5 +65,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 2.最小最大原则：先选择所有样本数据中距离最远的两个值；并且选择第三个值，使得与前两个聚点的距离最小者等于所有其余数据的较小距离中最大的，依次按这个原则选取，直到最终确定K个中心点；用公式可以表示为：
 <p align="center">
-<img width="200" align="center" src="../../images/111.jpg" />
+<img width="500" align="center" src="../../images/111.jpg" />
 </p>

From 655ba2220dbc72eb97803c35a9e06ceabbb30fe7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:25:42 +0800
Subject: [PATCH 0080/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index aeadf2fe..75775cc2 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -67,3 +67,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/111.jpg" />
 </p>
+
+3.模糊聚类算法原理
+
+糊聚类算法根据研究对象本身的属性来构造模糊矩阵，在此基础上根据一定的隶属度来确定其分类系。系统的模糊聚类分析功能根据专家对研究对象的各指标进行打分得出原始数据。通过对原始数据进行变换、计算模糊相似矩阵、利用传递闭包法建立模糊等价矩阵，并根据给定不同的置信水平，求截阵等一系列过程对研究对象进行聚类得出模糊相似阵、分类关系阵和分类关系表。模糊聚类的具体算法过程如下：

From 50411cec84d9bf0f0d4072b14f133dbcd7febcd7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:26:30 +0800
Subject: [PATCH 0081/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 75775cc2..b2832d6f 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -71,3 +71,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 3.模糊聚类算法原理
 
 糊聚类算法根据研究对象本身的属性来构造模糊矩阵，在此基础上根据一定的隶属度来确定其分类系。系统的模糊聚类分析功能根据专家对研究对象的各指标进行打分得出原始数据。通过对原始数据进行变换、计算模糊相似矩阵、利用传递闭包法建立模糊等价矩阵，并根据给定不同的置信水平，求截阵等一系列过程对研究对象进行聚类得出模糊相似阵、分类关系阵和分类关系表。模糊聚类的具体算法过程如下：
+
+a.对原始数据进行变换。变换方法通常有标准化变换、极差变换、对数变换等。
+b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*=cosθ构成相似系数矩阵
+
+<p align="center">
+<img width="200" align="center" src="../../images/112.jpg" />
+</p>

From e3404235b654d77da1bbfe4dc6a9e43f82290f8c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:27:45 +0800
Subject: [PATCH 0082/1406] add photo

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/117.jpg

diff --git a/assets/images/117.jpg b/assets/images/117.jpg
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z7ZI_F^pr#}X@}-#J!ma)Q`ha`t7er<{$+)pF63C_X)^y_?xg1O=Mrp(zmRItl8|_P
z{sO`2MU3Xj<n9e#l|>sh7UhhmUQ|MBDm843uLK|Re!-aH)vvkmneXLUl+xb}Cy{nX
xWzK0E>L-P;SFqCJ&RdP@i)43tIrDvXKOv0hSA_^yzgp@aQ)E1ztOEfK{{oT_cg6q!

literal 0
HcmV?d00001


From 7f0dcbf0c1baf0d06403a18b0e07cbe333fda599 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:28:31 +0800
Subject: [PATCH 0083/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index b2832d6f..8667d986 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -76,5 +76,5 @@ a.对原始数据进行变换。变换方法通常有标准化变换、极差变
 b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*=cosθ构成相似系数矩阵
 
 <p align="center">
-<img width="200" align="center" src="../../images/112.jpg" />
+<img width="100" align="center" src="../../images/117.jpg" />
 </p>

From c7c42f0c4ce6bc3a6716c5c921bbce220db7f9f8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Jan 2018 09:28:44 +0800
Subject: [PATCH 0084/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 8667d986..6cdf03c5 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -76,5 +76,5 @@ a.对原始数据进行变换。变换方法通常有标准化变换、极差变
 b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*=cosθ构成相似系数矩阵
 
 <p align="center">
-<img width="100" align="center" src="../../images/117.jpg" />
+<img width="200" align="center" src="../../images/117.jpg" />
 </p>

From e4fda1de51af3000dbbc564274b6b2dde4b71127 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:05:01 +0800
Subject: [PATCH 0085/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 6cdf03c5..fe59713e 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -78,3 +78,6 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 <p align="center">
 <img width="200" align="center" src="../../images/117.jpg" />
 </p>
+
+在此基础上做如下变换：
+

From 8569393c7bbf8a2b4544345019aee72b04bc1dad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:06:38 +0800
Subject: [PATCH 0086/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index fe59713e..a2541dd8 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -80,4 +80,6 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 </p>
 
 在此基础上做如下变换：
-
+<p align="center">
+<img width="200" align="center" src="../../images/118.jpg" />
+</p>

From f016390226acce28f8bd85691b01bedfd04cdd90 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:07:27 +0800
Subject: [PATCH 0087/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index a2541dd8..23f9dd0f 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -83,3 +83,5 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 <p align="center">
 <img width="200" align="center" src="../../images/118.jpg" />
 </p>
+
+使得rij*被压缩到[0,1]区间内，R=rij构成了一个模糊矩阵。

From 13db4badbec80da3f1f4047e16fd541483df02d4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:07:56 +0800
Subject: [PATCH 0088/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 23f9dd0f..15abf9c7 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -85,3 +85,5 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 </p>
 
 使得rij*被压缩到[0,1]区间内，R=rij构成了一个模糊矩阵。
+
+c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→…→Rn,经过有限次褶积后使得Rn。R=Rn,由此得到模糊分类关系Rn。模糊褶积的运算法则：设A和B是n×p和p×m的模糊矩阵，则乘积C=A*B为n×m阵，其元素为：

From ab0017be75d66d8969a0b7e546c1a770e06800df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:08:19 +0800
Subject: [PATCH 0089/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 15abf9c7..84a44d89 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -87,3 +87,8 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 使得rij*被压缩到[0,1]区间内，R=rij构成了一个模糊矩阵。
 
 c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→…→Rn,经过有限次褶积后使得Rn。R=Rn,由此得到模糊分类关系Rn。模糊褶积的运算法则：设A和B是n×p和p×m的模糊矩阵，则乘积C=A*B为n×m阵，其元素为：
+
+<p align="center">
+<img width="200" align="center" src="../../images/119.jpg" />
+</p>
+

From de72fab9a6afc1ad8280f9ef8d6120b44f991281 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:09:12 +0800
Subject: [PATCH 0090/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 84a44d89..2e06133d 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -81,7 +81,7 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 
 在此基础上做如下变换：
 <p align="center">
-<img width="200" align="center" src="../../images/118.jpg" />
+<img width="200" align="center" src="../../images/112.jpg" />
 </p>
 
 使得rij*被压缩到[0,1]区间内，R=rij构成了一个模糊矩阵。
@@ -89,6 +89,6 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→…→Rn,经过有限次褶积后使得Rn。R=Rn,由此得到模糊分类关系Rn。模糊褶积的运算法则：设A和B是n×p和p×m的模糊矩阵，则乘积C=A*B为n×m阵，其元素为：
 
 <p align="center">
-<img width="200" align="center" src="../../images/119.jpg" />
+<img width="200" align="center" src="../../images/113.jpg" />
 </p>
 

From 3d57b6e25e678d01dd5286d0143332da9bfc1caa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:09:33 +0800
Subject: [PATCH 0091/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 2e06133d..8a717379 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -81,7 +81,7 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 
 在此基础上做如下变换：
 <p align="center">
-<img width="200" align="center" src="../../images/112.jpg" />
+<img width="50" align="center" src="../../images/112.jpg" />
 </p>
 
 使得rij*被压缩到[0,1]区间内，R=rij构成了一个模糊矩阵。
@@ -89,6 +89,6 @@ b.计算模糊相似矩阵。选取在[-1，1]区间中的普通相似系数rij*
 c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→…→Rn,经过有限次褶积后使得Rn。R=Rn,由此得到模糊分类关系Rn。模糊褶积的运算法则：设A和B是n×p和p×m的模糊矩阵，则乘积C=A*B为n×m阵，其元素为：
 
 <p align="center">
-<img width="200" align="center" src="../../images/113.jpg" />
+<img width="300" align="center" src="../../images/113.jpg" />
 </p>
 

From dbe447f83714f48603af3774ff07d4377bcce2f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:10:27 +0800
Subject: [PATCH 0092/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 8a717379..1c206164 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -92,3 +92,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="300" align="center" src="../../images/113.jpg" />
 </p>
 
+符号<img width="300" align="center" src="../../images/114.jpg" />

From 532e6a756bb5b134a9604325919bc13f84991c89 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:11:01 +0800
Subject: [PATCH 0093/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 1c206164..2f3762e6 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -92,4 +92,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="300" align="center" src="../../images/113.jpg" />
 </p>
 
-符号<img width="300" align="center" src="../../images/114.jpg" />
+符号<img width="100" align="center" src="../../images/114.jpg" />和<img width="100" align="center" src="../../images/115.jpg" />的含义是：

From a7d65a4a55d4c28ff1f70e5bdf1698283b8cc9de Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:11:22 +0800
Subject: [PATCH 0094/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 2f3762e6..421e303c 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -92,4 +92,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="300" align="center" src="../../images/113.jpg" />
 </p>
 
-符号<img width="100" align="center" src="../../images/114.jpg" />和<img width="100" align="center" src="../../images/115.jpg" />的含义是：
+符号<img width="50" align="center" src="../../images/114.jpg" />和<img width="50" align="center" src="../../images/115.jpg" />的含义是：

From 1aabe9b0dbfa560c5253aa4e802ed34257ee68dd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:12:49 +0800
Subject: [PATCH 0095/1406] change page CAS

---
 assets/images/119.jpg | Bin 0 -> 291 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/119.jpg

diff --git a/assets/images/119.jpg b/assets/images/119.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..3b0df401e46a21eafe1a50dfaa21b86bd12cb2db
GIT binary patch
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znzdzjf18(@)jMS5G*`4TH0if=_0)B?POzEeFh#X*a(nNz#yJxk;ucI@R8ux@@iOIE
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literal 0
HcmV?d00001


From 485ae4cfdba7112b9c937c9069bf7e2b09cedb1d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:13:46 +0800
Subject: [PATCH 0096/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 421e303c..95d07710 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -92,4 +92,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="300" align="center" src="../../images/113.jpg" />
 </p>
 
-符号<img width="50" align="center" src="../../images/114.jpg" />和<img width="50" align="center" src="../../images/115.jpg" />的含义是：
+符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="50" align="center" src="../../images/119.jpg" />的含义是：

From 0665ba004b8c38af2d4e823801229d579e0445ff Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:13:59 +0800
Subject: [PATCH 0097/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 95d07710..502fbf3a 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -92,4 +92,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="300" align="center" src="../../images/113.jpg" />
 </p>
 
-符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="50" align="center" src="../../images/119.jpg" />的含义是：
+符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="30" align="center" src="../../images/119.jpg" />的含义是：

From fec3e7c4abe0a40b02b353001b11aeea10994bdc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:14:29 +0800
Subject: [PATCH 0098/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 502fbf3a..ce42adc1 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -93,3 +93,10 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 </p>
 
 符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="30" align="center" src="../../images/119.jpg" />的含义是：
+
+<p align="center">
+<img width="500" align="center" src="../../images/115.jpg" />
+</p>
+<p align="center">
+<img width="500" align="center" src="../../images/116.jpg" />
+</p>

From 4088cc6f56f863be8d4279a4a66c63d471357ad7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:14:45 +0800
Subject: [PATCH 0099/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index ce42adc1..9876ec1e 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -95,8 +95,8 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="30" align="center" src="../../images/119.jpg" />的含义是：
 
 <p align="center">
-<img width="500" align="center" src="../../images/115.jpg" />
+<img width="200" align="center" src="../../images/115.jpg" />
 </p>
 <p align="center">
-<img width="500" align="center" src="../../images/116.jpg" />
+<img width="200" align="center" src="../../images/116.jpg" />
 </p>

From 3a74e386b05a55831b5a7326622392f09ddb57f3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:15:02 +0800
Subject: [PATCH 0100/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 9876ec1e..b5a4d9b9 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -95,8 +95,8 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 符号<img width="30" align="center" src="../../images/114.jpg" />和<img width="30" align="center" src="../../images/119.jpg" />的含义是：
 
 <p align="center">
-<img width="200" align="center" src="../../images/115.jpg" />
+<img width="150" align="center" src="../../images/115.jpg" />
 </p>
 <p align="center">
-<img width="200" align="center" src="../../images/116.jpg" />
+<img width="150" align="center" src="../../images/116.jpg" />
 </p>

From 07bbfb106adcd3d37a95048e371b734e78aae9bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:15:39 +0800
Subject: [PATCH 0101/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index b5a4d9b9..3192299c 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -100,3 +100,5 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <p align="center">
 <img width="150" align="center" src="../../images/116.jpg" />
 </p>
+
+4.进行聚类。给定不同的置信水平λ，求Rλ截阵，找出R的λ显示，得到普通的分类关系Rλ。当λ=1时，每个样品自成一类，随λ值的降低，由细到粗逐渐并类。

From 984b8bbdd52115cc226e9cbe5f563246e662b60e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:16:33 +0800
Subject: [PATCH 0102/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 3192299c..b8d63b26 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -101,4 +101,4 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 <img width="150" align="center" src="../../images/116.jpg" />
 </p>
 
-4.进行聚类。给定不同的置信水平λ，求Rλ截阵，找出R的λ显示，得到普通的分类关系Rλ。当λ=1时，每个样品自成一类，随λ值的降低，由细到粗逐渐并类。
+d.进行聚类。给定不同的置信水平λ，求Rλ截阵，找出R的λ显示，得到普通的分类关系Rλ。当λ=1时，每个样品自成一类，随λ值的降低，由细到粗逐渐并类。

From 527a2c3cfbca0b8bd68e862efeb6604326402b8f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:17:08 +0800
Subject: [PATCH 0103/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index b8d63b26..926495a3 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -102,3 +102,13 @@ c.建立模糊等价矩阵。对模糊矩阵进行褶积计算: R→R2→R3→
 </p>
 
 d.进行聚类。给定不同的置信水平λ，求Rλ截阵，找出R的λ显示，得到普通的分类关系Rλ。当λ=1时，每个样品自成一类，随λ值的降低，由细到粗逐渐并类。
+
+4..基于密度的聚类
+为了发现任意形状的聚类结果，提出了基于密度的聚类方法。这类方法将簇看作是数据空间中由低密度区域分割开的高密度对象区域。
+
+DBSCAN(Density-Based Spatial Clustering of Applications with Noise)是一个基于密度的聚类算法。该算法将具有足够高密度的区域划分为簇，并可以在带有“噪音”的空间数据库中发现任意形状的聚类。它定义簇为密度相连的点的最大集合。基于密度的聚类的基本想法涉及一些新的定义。
+
+
+
+
+

From e5dd6915ca223d10a6013ae5d205eaab827796d4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:17:26 +0800
Subject: [PATCH 0104/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 926495a3..6ae4ee6f 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -108,7 +108,17 @@ d.进行聚类。给定不同的置信水平λ，求Rλ截阵，找出R的λ显
 
 DBSCAN(Density-Based Spatial Clustering of Applications with Noise)是一个基于密度的聚类算法。该算法将具有足够高密度的区域划分为簇，并可以在带有“噪音”的空间数据库中发现任意形状的聚类。它定义簇为密度相连的点的最大集合。基于密度的聚类的基本想法涉及一些新的定义。
 
+n 一个给定对象周围半径ε内的区域称为该对象的ε-邻域。
 
+n 如果一个对象的ε-邻域至少包含最小数目MinPts 的对象，那么该对象称为核心对象。
+
+n 给定一个对象集合D，如果p是在q 的ε–邻域内，而q是一个核心对象，我们说对象p从对象q出发是直接密度可达的。
+
+n 如果存在一个对象链p1,p2,…,pn，p1=q，pn=p，对pi∈ D，1≤i≤n，pi+1 是从pi关于ε和 MinPts直接密度可达的，则对象p是从对象q关于ε和MinPts 密度可达的(density-reachable)。
+
+n 如果对象集合D中存在一个对象o，使得对象p和q是从o关于ε和MinPts 密度可达的，那么对象p和q是关于ε和MinPts 密度相连的（density-connected）。
+
+DBSCAN 通过检查数据库中每个点的ε-邻域来寻找聚类。如果一个点p的ε-邻域包含多于MinPts个点，则创建一个以p作为核心对象的新簇。DBSCAN 然后反复地寻找从这些核心对象直接密度可达的对象，这个过程可能涉及几个密度可达簇的合并。当没有新的点可以被添加到任何簇时，该过程结束。
 
 
 

From fca414ba277179a83f19551376686a5cf12b3504 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:18:06 +0800
Subject: [PATCH 0105/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index 6ae4ee6f..b7ec3322 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -120,5 +120,8 @@ n 如果对象集合D中存在一个对象o，使得对象p和q是从o关于ε
 
 DBSCAN 通过检查数据库中每个点的ε-邻域来寻找聚类。如果一个点p的ε-邻域包含多于MinPts个点，则创建一个以p作为核心对象的新簇。DBSCAN 然后反复地寻找从这些核心对象直接密度可达的对象，这个过程可能涉及几个密度可达簇的合并。当没有新的点可以被添加到任何簇时，该过程结束。
 
+#### 应用领域
+在商业上，聚类能帮助市场分析人员从客户基本库中发现不同的客户群，并且用购买模式来刻画不同的客户群的特征。在生物学上，聚类能用于推导植物和动物的分类，对基因进行分类，获得对种群中固有结构的认识。聚类在地球观测数据库中相似地区的确定，汽车保险持有者的分组，及根据房子的类型，价值，和地理位置对一个城市中房屋的分组上也可以发挥作用。聚类也能用于对Web 上的文档进行分类，以发现信息。作为一个数据挖掘的功能，聚类分析能作为一个独立的工具来获得数据分布的情况，观察每个簇的特点，集中对特定的某些簇作进一步的分析。此外，聚类分析可以作为其他算法（如分类等）的预处理步骤，这些算法再在生成的簇上进行处理。
+
 
 

From f0c1b9f5d719d07abe20665243aaeb2ceabc3d4c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:24:18 +0800
Subject: [PATCH 0106/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index b7ec3322..f6050795 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -124,4 +124,26 @@ DBSCAN 通过检查数据库中每个点的ε-邻域来寻找聚类。如果一
 在商业上，聚类能帮助市场分析人员从客户基本库中发现不同的客户群，并且用购买模式来刻画不同的客户群的特征。在生物学上，聚类能用于推导植物和动物的分类，对基因进行分类，获得对种群中固有结构的认识。聚类在地球观测数据库中相似地区的确定，汽车保险持有者的分组，及根据房子的类型，价值，和地理位置对一个城市中房屋的分组上也可以发挥作用。聚类也能用于对Web 上的文档进行分类，以发现信息。作为一个数据挖掘的功能，聚类分析能作为一个独立的工具来获得数据分布的情况，观察每个簇的特点，集中对特定的某些簇作进一步的分析。此外，聚类分析可以作为其他算法（如分类等）的预处理步骤，这些算法再在生成的簇上进行处理。
 
 
+#### 优缺点
 
+优点：
+
+聚类分析模型的优点就是直观，结论形式简明
+
+缺点
+
+1. 收敛太慢
+
+2. 算法复杂度高
+
+3. 不能发现非凸形状的簇，或大小差别很大的簇
+
+4. 需样本存在均值（限定数据种类）
+
+5. 需先确定聚类中心点的个数
+
+6. 对噪声和离群点敏感
+
+7. 最重要是结果不一定是全局最优，只能保证局部最优
+
+不同的聚类方法，也有一定的差异性，但总体表现为：K均值稳定，谱聚类效果好， 层次聚类快。

From 3de90dafc715177c28d0d69a06b7208d893e2308 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 11 Jan 2018 09:24:29 +0800
Subject: [PATCH 0107/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index f6050795..a8e97b2e 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -130,7 +130,7 @@ DBSCAN 通过检查数据库中每个点的ε-邻域来寻找聚类。如果一
 
 聚类分析模型的优点就是直观，结论形式简明
 
-缺点
+缺点：
 
 1. 收敛太慢
 

From a84fa736fa4c8e5fa238a90082147d3f93f31def Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:10:48 +0800
Subject: [PATCH 0108/1406] add ARS

---
 assets/src/ARS/ARS.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)
 create mode 100644 assets/src/ARS/ARS.md

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
new file mode 100644
index 00000000..426a08fe
--- /dev/null
+++ b/assets/src/ARS/ARS.md
@@ -0,0 +1,15 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+
+#### 关联规则

From a54d67e44c53114a8ce98fcaf9bcc89bae178a8b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:12:46 +0800
Subject: [PATCH 0109/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0154d86f..f57b4ed4 100644
--- a/README.md
+++ b/README.md
@@ -60,7 +60,7 @@
  * [Hopfield神经网络](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/HPD/HPD.md)
  * [决策树](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.md)
  * [聚类分析](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CAS/CAS.md)
- * [关联规则]()
+ * [关联规则](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
  * [支持向量机（SVM）]()
 
 后面的算法和我们的算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！

From 08611181abc9ccdf717fc45641252fde071a9dd8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:14:01 +0800
Subject: [PATCH 0110/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 426a08fe..f4d88ded 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -13,3 +13,4 @@
 
 
 #### 关联规则
+关联规则挖掘发现大量数据中项集之间有趣的关联或相关联系。随着大量数据不停地收集和存储，许多业界人士对于从他们的数据库中挖掘关联规则越来越感兴趣。从大量商务事务记录中发现有趣的关联关系，可以帮助许多商务决策的制定，如分类设计、交叉购物和贱卖分析。关联规则挖掘的一个典型例子是购物篮分析。该过程通过发现顾客放入其购物篮中不同商品之间联系，分析顾客的购买习惯。通过了解哪些商品频繁地被顾客同时购买，这种关联的发现可以帮助零售商制定营销策略。例如，在同一次去超级市场，如果顾客购买牛奶，他也购买面包（和什么类型的面包）的可能性有多大？通过帮助零售商有选择地经销和安排货架，这种信息可以引导销售。例如，将牛奶和面包尽可能放近一些，可以进一步刺激一次去商店同时购买这些商品。

From 2b8e6a7958fd221d6c0f4a5d9c87a9082cc1c3e9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:15:59 +0800
Subject: [PATCH 0111/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index f4d88ded..c325d36f 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -14,3 +14,6 @@
 
 #### 关联规则
 关联规则挖掘发现大量数据中项集之间有趣的关联或相关联系。随着大量数据不停地收集和存储，许多业界人士对于从他们的数据库中挖掘关联规则越来越感兴趣。从大量商务事务记录中发现有趣的关联关系，可以帮助许多商务决策的制定，如分类设计、交叉购物和贱卖分析。关联规则挖掘的一个典型例子是购物篮分析。该过程通过发现顾客放入其购物篮中不同商品之间联系，分析顾客的购买习惯。通过了解哪些商品频繁地被顾客同时购买，这种关联的发现可以帮助零售商制定营销策略。例如，在同一次去超级市场，如果顾客购买牛奶，他也购买面包（和什么类型的面包）的可能性有多大？通过帮助零售商有选择地经销和安排货架，这种信息可以引导销售。例如，将牛奶和面包尽可能放近一些，可以进一步刺激一次去商店同时购买这些商品。
+<p align="center">
+<img width="200" align="center" src="../../images/120.jpg" />
+</p>

From b9f44c4a8e78d66b42d899941be8e301964b5ff2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:17:14 +0800
Subject: [PATCH 0112/1406] change page

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From 0c4f8a040a480a1d9da30c4c674d4ab62c8f047d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:19:05 +0800
Subject: [PATCH 0113/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index f4d88ded..c325d36f 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -14,3 +14,6 @@
 
 #### 关联规则
 关联规则挖掘发现大量数据中项集之间有趣的关联或相关联系。随着大量数据不停地收集和存储，许多业界人士对于从他们的数据库中挖掘关联规则越来越感兴趣。从大量商务事务记录中发现有趣的关联关系，可以帮助许多商务决策的制定，如分类设计、交叉购物和贱卖分析。关联规则挖掘的一个典型例子是购物篮分析。该过程通过发现顾客放入其购物篮中不同商品之间联系，分析顾客的购买习惯。通过了解哪些商品频繁地被顾客同时购买，这种关联的发现可以帮助零售商制定营销策略。例如，在同一次去超级市场，如果顾客购买牛奶，他也购买面包（和什么类型的面包）的可能性有多大？通过帮助零售商有选择地经销和安排货架，这种信息可以引导销售。例如，将牛奶和面包尽可能放近一些，可以进一步刺激一次去商店同时购买这些商品。
+<p align="center">
+<img width="200" align="center" src="../../images/120.jpg" />
+</p>

From 9dac99eb7a208c0d2b94e454d4d121e487ce66b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:19:32 +0800
Subject: [PATCH 0114/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index c325d36f..6b88e078 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -17,3 +17,9 @@
 <p align="center">
 <img width="200" align="center" src="../../images/120.jpg" />
 </p>
+
+
+#### 应用领域
+关联分类算法是继贝叶斯( Bayes) 、支持向量机( SVM) 等机器学习方法之后的又一重要分类技术，广泛应用于文本分类、Web文档分类、医学图像分类。经典的关联分类算法有CBA、CMAR、CPAR；
+
+网络入侵检测技术作为防火墙技术强有力的助手，有效弥补了防火墙策略处理黑客攻击、信息窃取问题时出现的不足，成为网络安全监控系统可靠的保障。传统的入侵检测系统(IDS) 运用关联规则生成入侵检测标准规则库，通过判断网络数据与规则库的匹配度产生告警数据流。

From 2da4751f5dc9ec449ee23522902dcd32976583ef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:20:53 +0800
Subject: [PATCH 0115/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 6b88e078..8673c842 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -23,3 +23,10 @@
 关联分类算法是继贝叶斯( Bayes) 、支持向量机( SVM) 等机器学习方法之后的又一重要分类技术，广泛应用于文本分类、Web文档分类、医学图像分类。经典的关联分类算法有CBA、CMAR、CPAR；
 
 网络入侵检测技术作为防火墙技术强有力的助手，有效弥补了防火墙策略处理黑客攻击、信息窃取问题时出现的不足，成为网络安全监控系统可靠的保障。传统的入侵检测系统(IDS) 运用关联规则生成入侵检测标准规则库，通过判断网络数据与规则库的匹配度产生告警数据流。
+
+
+隐私保护数据挖掘是指在数据挖掘的过程中通过采用数据干扰和查询限制的基本策略对原始数据进行保护，避免商业敏感数据、个人隐私数据泄露。
+
+利用关联规则进行蛋白质结构预测，根据蛋白质序列的特点可以对这些序列数据进行量化和处理，再将关联规则算法用于序列数据集上寻找蛋白质序列中的关联关系。
+
+随着遥感导航定位、地球物理等卫星数量的增加，空间地球大数据为地球科学研究带来新机遇。传统数据分析方法以统计分析、非线性拟合为主，其在处理多维、海量数据时存在明显不足。基于关联规则的挖掘模式可以揭示海洋、陆地、大气等地球数据之间的关系，从而推动全球变化、灾害科学领域的发展。

From d4ffae4858b9de03d5c4fc162665d43ddb9dc061 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:21:16 +0800
Subject: [PATCH 0116/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 8673c842..2106bfc4 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -30,3 +30,22 @@
 利用关联规则进行蛋白质结构预测，根据蛋白质序列的特点可以对这些序列数据进行量化和处理，再将关联规则算法用于序列数据集上寻找蛋白质序列中的关联关系。
 
 随着遥感导航定位、地球物理等卫星数量的增加，空间地球大数据为地球科学研究带来新机遇。传统数据分析方法以统计分析、非线性拟合为主，其在处理多维、海量数据时存在明显不足。基于关联规则的挖掘模式可以揭示海洋、陆地、大气等地球数据之间的关系，从而推动全球变化、灾害科学领域的发展。
+
+#### 优缺点
+优点：
+
+1. 可以产生清晰有用的结果；
+
+2. 支持间接数据挖掘；
+
+3. 可以处理变长的数据；
+
+4. 它的计算的消耗量是可以预见的。
+
+缺点：
+
+1. 当问题变大时，计算量增长得厉害；
+
+2. 难以决定正确的数据；
+
+3. 容易忽略稀有的数据。

From 940363b5808c574dd9087ab4ce928ed441694645 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 12 Jan 2018 09:25:27 +0800
Subject: [PATCH 0117/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f57b4ed4..d5eba4ec 100644
--- a/README.md
+++ b/README.md
@@ -61,7 +61,7 @@
  * [决策树](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.md)
  * [聚类分析](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CAS/CAS.md)
  * [关联规则](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
- * [支持向量机（SVM）]()
+ * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
 
 后面的算法和我们的算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
 

From d46feb860ae2507355f5ce62fc13f6a78be9e2a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 13 Jan 2018 09:21:05 +0800
Subject: [PATCH 0118/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 38 +-------------------------------------
 1 file changed, 1 insertion(+), 37 deletions(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 2106bfc4..e05c9d92 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -12,40 +12,4 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 
-#### 关联规则
-关联规则挖掘发现大量数据中项集之间有趣的关联或相关联系。随着大量数据不停地收集和存储，许多业界人士对于从他们的数据库中挖掘关联规则越来越感兴趣。从大量商务事务记录中发现有趣的关联关系，可以帮助许多商务决策的制定，如分类设计、交叉购物和贱卖分析。关联规则挖掘的一个典型例子是购物篮分析。该过程通过发现顾客放入其购物篮中不同商品之间联系，分析顾客的购买习惯。通过了解哪些商品频繁地被顾客同时购买，这种关联的发现可以帮助零售商制定营销策略。例如，在同一次去超级市场，如果顾客购买牛奶，他也购买面包（和什么类型的面包）的可能性有多大？通过帮助零售商有选择地经销和安排货架，这种信息可以引导销售。例如，将牛奶和面包尽可能放近一些，可以进一步刺激一次去商店同时购买这些商品。
-<p align="center">
-<img width="200" align="center" src="../../images/120.jpg" />
-</p>
-
-
-#### 应用领域
-关联分类算法是继贝叶斯( Bayes) 、支持向量机( SVM) 等机器学习方法之后的又一重要分类技术，广泛应用于文本分类、Web文档分类、医学图像分类。经典的关联分类算法有CBA、CMAR、CPAR；
-
-网络入侵检测技术作为防火墙技术强有力的助手，有效弥补了防火墙策略处理黑客攻击、信息窃取问题时出现的不足，成为网络安全监控系统可靠的保障。传统的入侵检测系统(IDS) 运用关联规则生成入侵检测标准规则库，通过判断网络数据与规则库的匹配度产生告警数据流。
-
-
-隐私保护数据挖掘是指在数据挖掘的过程中通过采用数据干扰和查询限制的基本策略对原始数据进行保护，避免商业敏感数据、个人隐私数据泄露。
-
-利用关联规则进行蛋白质结构预测，根据蛋白质序列的特点可以对这些序列数据进行量化和处理，再将关联规则算法用于序列数据集上寻找蛋白质序列中的关联关系。
-
-随着遥感导航定位、地球物理等卫星数量的增加，空间地球大数据为地球科学研究带来新机遇。传统数据分析方法以统计分析、非线性拟合为主，其在处理多维、海量数据时存在明显不足。基于关联规则的挖掘模式可以揭示海洋、陆地、大气等地球数据之间的关系，从而推动全球变化、灾害科学领域的发展。
-
-#### 优缺点
-优点：
-
-1. 可以产生清晰有用的结果；
-
-2. 支持间接数据挖掘；
-
-3. 可以处理变长的数据；
-
-4. 它的计算的消耗量是可以预见的。
-
-缺点：
-
-1. 当问题变大时，计算量增长得厉害；
-
-2. 难以决定正确的数据；
-
-3. 容易忽略稀有的数据。
+#### 

From 842c4fa173b6a5171fb89f62c47e5481998c80a8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 13 Jan 2018 09:21:22 +0800
Subject: [PATCH 0119/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index e05c9d92..41161f67 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -12,4 +12,4 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 
-#### 
+#### 支持向量机（SVM）

From 996b04b4258f235f36c3bfeacffcfd83a64667df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 13 Jan 2018 09:21:34 +0800
Subject: [PATCH 0120/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 41161f67..4e50eff4 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -13,3 +13,4 @@
 
 
 #### 支持向量机（SVM）
+支持向量机建立在计算学习理论的结构风险最小化原则之上。其主要思想是针对两分类问题，在高维空间中寻找一个超平面作为两分类的分割，以保证最小的分类错误率，而且支持向量机一个重要的优点是可以处理线性不可分的情况。

From 01526ccde2db06488eadbb363d575e81d1c2939e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 13 Jan 2018 09:21:47 +0800
Subject: [PATCH 0121/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 4e50eff4..9fb10b31 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -14,3 +14,4 @@
 
 #### 支持向量机（SVM）
 支持向量机建立在计算学习理论的结构风险最小化原则之上。其主要思想是针对两分类问题，在高维空间中寻找一个超平面作为两分类的分割，以保证最小的分类错误率，而且支持向量机一个重要的优点是可以处理线性不可分的情况。
+支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。

From a94ae83bf77d33dfc8ed3f3b389223f37b14a620 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:39:01 +0800
Subject: [PATCH 0122/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 9fb10b31..23671c92 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -15,3 +15,6 @@
 #### 支持向量机（SVM）
 支持向量机建立在计算学习理论的结构风险最小化原则之上。其主要思想是针对两分类问题，在高维空间中寻找一个超平面作为两分类的分割，以保证最小的分类错误率，而且支持向量机一个重要的优点是可以处理线性不可分的情况。
 支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
+
+
+#### 应用背景

From e63fada61be607734dc8610fb4be38df0fffab45 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:39:13 +0800
Subject: [PATCH 0123/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 23671c92..3fe75fcb 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -18,3 +18,4 @@
 
 
 #### 应用背景
+支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。

From 28ec674489aea28b61de60b8e471c89c130d1362 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:39:27 +0800
Subject: [PATCH 0124/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 3fe75fcb..027b7cc5 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -19,3 +19,6 @@
 
 #### 应用背景
 支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
+
+
+#### 算法应用

From d83868d5da4c68a6b2bf8f9ed7ee30fba4604e32 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:39:37 +0800
Subject: [PATCH 0125/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 027b7cc5..6b75ab24 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -22,3 +22,4 @@
 
 
 #### 算法应用
+用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。

From 77b719d7ac68e1595f7bc2c96d13d95d4eb462da Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:39:59 +0800
Subject: [PATCH 0126/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 6b75ab24..6a25c9bb 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -22,4 +22,7 @@
 
 
 #### 算法应用
-用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+
+1.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+
+2.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。

From 4ae6304d1d4766e1e595160012ea453cace0c381 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:40:30 +0800
Subject: [PATCH 0127/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 6a25c9bb..97ef57b5 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -26,3 +26,5 @@
 1.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
 
 2.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+
+3.用于医学中分类蛋白质，超过90%的化合物能够被正确分类。用于手写字体识别。

From 7d14e907d6611959be5e7b56ce0da61d9726eb23 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:41:08 +0800
Subject: [PATCH 0128/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 97ef57b5..fa88f286 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -28,3 +28,6 @@
 2.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
 
 3.用于医学中分类蛋白质，超过90%的化合物能够被正确分类。用于手写字体识别。
+
+
+

From 6de5c61d59c7819d405787fdf66703399dc62d34 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:41:29 +0800
Subject: [PATCH 0129/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index fa88f286..4fe79f05 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -17,7 +17,7 @@
 支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
 
 
-#### 应用背景
+#### 算法背景
 支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
 
 

From a174af4c60ca5fc6006c2c04a9dc8c6b4e388989 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:41:51 +0800
Subject: [PATCH 0130/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 4fe79f05..73c90a09 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -17,7 +17,7 @@
 支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
 
 
-#### 算法背景
+#### 背景
 支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
 
 

From 93536ab8d2e1fcb9a5c7fd410568eb9ee146c954 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Jan 2018 10:42:01 +0800
Subject: [PATCH 0131/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 73c90a09..4fe79f05 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -17,7 +17,7 @@
 支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
 
 
-#### 背景
+#### 算法背景
 支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
 
 

From 401cdedf72fe131180bf2ca632b797433c86b6f2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:13:06 +0800
Subject: [PATCH 0132/1406] change page

---
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 assets/images/122.jpg | Bin 0 -> 1925 bytes
 assets/images/123.jpg | Bin 0 -> 8666 bytes
 assets/images/124.jpg | Bin 0 -> 9712 bytes
 4 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/121.jpg
 create mode 100644 assets/images/122.jpg
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From 466a4491df08708185ede2e955306f8a2d93bb80 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:15:24 +0800
Subject: [PATCH 0133/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d5eba4ec..85c5fed0 100644
--- a/README.md
+++ b/README.md
@@ -61,7 +61,7 @@
  * [决策树](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.md)
  * [聚类分析](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CAS/CAS.md)
  * [关联规则](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
- * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
+ * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/SVM/SVM.md)
 
 后面的算法和我们的算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
 

From 0d6f317bc9e48dd1b90e7d1a4159d16233b044f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:17:39 +0800
Subject: [PATCH 0134/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 22 ++++++++++++----------
 1 file changed, 12 insertions(+), 10 deletions(-)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 4fe79f05..769d8080 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -12,22 +12,24 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 
-#### 支持向量机（SVM）
-支持向量机建立在计算学习理论的结构风险最小化原则之上。其主要思想是针对两分类问题，在高维空间中寻找一个超平面作为两分类的分割，以保证最小的分类错误率，而且支持向量机一个重要的优点是可以处理线性不可分的情况。
-支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
+#### 关联规则
+“关联规则”（Association Rules）是数据挖掘的主要技术之一，用于从庞大的数据库中寻找有用或有趣的模式和规则。关联规则最初产生于购物篮分析，它通过发现顾客放入其购物篮中不同商品之间的联系，分析顾客购买行为中隐含的有趣模式，从而指导销售商制订营销策略。单维关联规则特指只涉及单个属性项的关联规则。
 
+设 I = { i1 , i2 ,..., im }是项的集合。设任务相关的数据D 是数据库事务的集合，其中每个事务T是项的集合，使得T ⊆ I。每一个事务有一个标识符，称作TID。设A 是一个项集，事务T 包含A当且仅当A ⊆ T。关联规则是形如A ⇒ B 的蕴涵式，其中A ⊂ I，B ⊂ I，并且A ∩ B =∅。规则A ⇒B 在事务集D 中成立，具有支持度s，其中s 是D 中事务包含A ∪ B（即A 和B 二者）的百分比。它是概率P(A ∪ B)。规则A ⇒ B 在事务集D 中具有置信度c，如果D 中包含A 的事务同时也包含B的百分比是c。这是条件概率P(B |A)。即 support (A ⇒ B ) = P(A ∪ B) confidence (A ⇒ B ) = P(B |A)
 
-#### 算法背景
-支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
-
+同时满足最小支持度阈值(min_sup)和最小置信度阈值(min_conf)的规则称作强规则。为方便计，我们用0%和100%之间的值，而不是用0 到1 之间的值表示支持度和置信度。项的集合称为项集。包含k 个项的项集称为k-项集。集合{computer, financial_management_software}是一个2-项集。项集的出现频率是包含项集的事务数，简称为项集的频率、支持计数或计数。项集满足最小支持度min_sup，如果项集的出现频率大于或等于min_sup 与D 中事务总数的乘积。如果项集满足最小支持度，则称它为频繁项集。频繁k -项集的集合通常记作Lk。关联规则的挖掘是一个两步的过程：
 
-#### 算法应用
+1. 找出所有频繁项集：根据定义，这些项集出现的频繁性至少和预定义的最小支持计数一样。
 
-1.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+2. 由频繁项集产生强关联规则：根据定义，这些规则必须满足最小支持度和最小置信度。
 
-2.用于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+如果愿意，也可以使用附加的兴趣度度量。这两步中，第二步最容易。挖掘关联规则的总体性能由第一步决定。
 
-3.用于医学中分类蛋白质，超过90%的化合物能够被正确分类。用于手写字体识别。
 
+#### 算法背景
+关联规则挖掘发现大量数据中项集之间有趣的关联或相关联系。随着大量数据不停地收集和存储，许多业界人士对于从他们的数据库中挖掘关联规则越来越感兴趣。从大量商务事务记录中发现有趣的关联关系，可以帮助许多商务决策的制定，如分类设计、交叉购物和贱卖分析。关联规则挖掘的一个典型例子是购物篮分析。该过程通过发现顾客放入其购物篮中不同商品之间联系，分析顾客的购买习惯。通过了解哪些商品频繁地被顾客同时购买，这种关联的发现可以帮助零售商制定营销策略。例如，在同一次去超级市场，如果顾客购买牛奶，他也购买面包（和什么类型的面包）的可能性有多大？通过帮助零售商有选择地经销和安排货架，这种信息可以引导销售。例如，将牛奶和面包尽可能放近一些，可以进一步刺激一次去商店同时购买这些商品。
+<p align="center">
+<img width="300" align="center" src="../../images/120.jpg" />
+</p>
 
 

From 7ac90525c335b8fd5465406d23b846d1a6073880 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:18:11 +0800
Subject: [PATCH 0135/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 769d8080..9a319353 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -32,4 +32,15 @@
 <img width="300" align="center" src="../../images/120.jpg" />
 </p>
 
+#### 应用领域
+关联分类算法是继贝叶斯( Bayes) 、支持向量机( SVM) 等机器学习方法之后的又一重要分类技术，广泛应用于文本分类、Web文档分类、医学图像分类。经典的关联分类算法有CBA、CMAR、CPAR；
+
+网络入侵检测技术作为防火墙技术强有力的助手，有效弥补了防火墙策略处理黑客攻击、信息窃取问题时出现的不足，成为网络安全监控系统可靠的保障。传统的入侵检测系统(IDS) 运用关联规则生成入侵检测标准规则库，通过判断网络数据与规则库的匹配度产生告警数据流。
+
+隐私保护数据挖掘是指在数据挖掘的过程中通过采用数据干扰和查询限制的基本策略对原始数据进行保护，避免商业敏感数据、个人隐私数据泄露。
+
+利用关联规则进行蛋白质结构预测，根据蛋白质序列的特点可以对这些序列数据进行量化和处理，再将关联规则算法用于序列数据集上寻找蛋白质序列中的关联关系。
+
+随着遥感导航定位、地球物理等卫星数量的增加，空间地球大数据为地球科学研究带来新机遇。传统数据分析方法以统计分析、非线性拟合为主，其在处理多维、海量数据时存在明显不足。基于关联规则的挖掘模式可以揭示海洋、陆地、大气等地球数据之间的关系，从而推动全球变化、灾害科学领域的发展。
+
 

From e63683697a7b7124acd1fe9a44942e780366dbca Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:18:52 +0800
Subject: [PATCH 0136/1406] Update ARS.md

---
 assets/src/ARS/ARS.md | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/assets/src/ARS/ARS.md b/assets/src/ARS/ARS.md
index 9a319353..7e2bce45 100644
--- a/assets/src/ARS/ARS.md
+++ b/assets/src/ARS/ARS.md
@@ -43,4 +43,22 @@
 
 随着遥感导航定位、地球物理等卫星数量的增加，空间地球大数据为地球科学研究带来新机遇。传统数据分析方法以统计分析、非线性拟合为主，其在处理多维、海量数据时存在明显不足。基于关联规则的挖掘模式可以揭示海洋、陆地、大气等地球数据之间的关系，从而推动全球变化、灾害科学领域的发展。
 
+#### 优缺点
 
+优点：
+
+1. 可以产生清晰有用的结果；
+
+2. 支持间接数据挖掘；
+
+3. 可以处理变长的数据；
+
+4. 它的计算的消耗量是可以预见的。
+
+缺点：
+
+1. 当问题变大时，计算量增长得厉害；
+
+2. 难以决定正确的数据；
+
+3. 容易忽略稀有的数据。

From e70620c334354f7dcfe074b2100d93179ddd8a11 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:20:17 +0800
Subject: [PATCH 0137/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 103bc278..c4bd6dd4 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -17,3 +17,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 支持向量机
+支持向量机建立在计算学习理论的结构风险最小化原则之上。其主要思想是针对两分类问题，在高维空间中寻找一个超平面作为两分类的分割，以保证最小的分类错误率，而且支持向量机一个重要的优点是可以处理线性不可分的情况。
+
+支持向量机学习的基本思想是求解能够正确划分训练数据集并且使得几何间隔最大的分离超平面，满足几何间隔最大的超平面是唯一的。
+<p align="center">
+<img width="300" align="center" src="../../images/121.jpg" />
+</p>

From dfeecac2c9c8b836271a9ed222689b78ebb3f30f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:20:37 +0800
Subject: [PATCH 0138/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index c4bd6dd4..e88f7e29 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -23,3 +23,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/121.jpg" />
 </p>
+
+支持向量
+<p align="center">
+<img width="300" align="center" src="../../images/122.jpg" />
+</p>

From f0dbff9448ad448a971fa24dab61237da1d12a8a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:21:04 +0800
Subject: [PATCH 0139/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index e88f7e29..8d87f770 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -28,3 +28,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/122.jpg" />
 </p>
+
+求出⍵和b的最优解。
+
+从而得到分离的超平面：
+<p align="center">
+<img width="300" align="center" src="../../images/123.jpg" />
+</p>

From 25bfbac9f38fa9223108ce791d690effd69258a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:21:20 +0800
Subject: [PATCH 0140/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 8d87f770..683fc39a 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -26,12 +26,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 支持向量
 <p align="center">
-<img width="300" align="center" src="../../images/122.jpg" />
+<img width="200" align="center" src="../../images/122.jpg" />
 </p>
 
 求出⍵和b的最优解。
 
 从而得到分离的超平面：
 <p align="center">
-<img width="300" align="center" src="../../images/123.jpg" />
+<img width="100" align="center" src="../../images/123.jpg" />
 </p>

From 35b1e95c7c2d88cab105acdcaae4a8a4950d6521 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:22:26 +0800
Subject: [PATCH 0141/1406] change page SVM

---
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 create mode 100644 assets/images/125.jpg

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From 6df7ce033f406d33da0a5c7942ebe2c8e06433bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:22:54 +0800
Subject: [PATCH 0142/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 683fc39a..67d2f8a3 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -28,6 +28,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="200" align="center" src="../../images/122.jpg" />
 </p>
+<p align="center">
+<img width="200" align="center" src="../../images/125.jpg" />
+</p>
 
 求出⍵和b的最优解。
 

From bfa108c29a98cfe9f07efb29d4ba9f6c93058972 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:23:29 +0800
Subject: [PATCH 0143/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 67d2f8a3..1ec488e1 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -38,3 +38,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="100" align="center" src="../../images/123.jpg" />
 </p>
+分类决策函数
+<p align="center">
+<img width="100" align="center" src="../../images/124.jpg" />
+</p>
+
+其中，C＞0为惩罚参数。

From c372621d24fb88b929ceed598dc43e89fcb1914d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:23:41 +0800
Subject: [PATCH 0144/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 1ec488e1..98184494 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -40,7 +40,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 分类决策函数
 <p align="center">
-<img width="100" align="center" src="../../images/124.jpg" />
+<img width="200" align="center" src="../../images/124.jpg" />
 </p>
 
 其中，C＞0为惩罚参数。

From 632529938879adb612c2e38c444b33a6d9b26c40 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:24:07 +0800
Subject: [PATCH 0145/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 98184494..c61d9525 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -44,3 +44,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 其中，C＞0为惩罚参数。
+
+
+#### 算法背景
+支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。

From 22633d30aeb9ca6a1b1c20cf1929fef4e2a2d882 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:24:37 +0800
Subject: [PATCH 0146/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index c61d9525..04fdaac6 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -48,3 +48,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 算法背景
 支持向量机的第一篇论文由Vladimir Vapnik 和他的同事Bernhard Boser 及Isabelle Guyon 于1992年发表，前期基础工作早在20世纪60年代就已经出现，虽然SVM的训练非常缓慢，但由于其对复杂的非线性边界的建模能力，他们是非常准确的，并且和其他模型相比，他们不太容易发生过拟合，因此在手写数字识别、对象识别以及基准时间序列预测检验等方面成功应用。
+
+#### 应用领域
+1.于文本和超文本的分类，在归纳和直推方法中都可以显著减少所需要的有类标的样本数。
+
+2.图像分类。实验结果显示：在经过三到四轮相关反馈之后，比起传统的查询优化方案，支持向量机能够取得更好的搜索准确度。
+
+3.用于医学中分类蛋白质，超过90%的化合物能够被正确分类。用于手写字体识别。

From 5f79772f80ff9dcc79acff7b858d9e8649817d27 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 15 Jan 2018 09:25:00 +0800
Subject: [PATCH 0147/1406] Update SVM.md

---
 assets/src/SVM/SVM.md | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/assets/src/SVM/SVM.md b/assets/src/SVM/SVM.md
index 04fdaac6..67d73d24 100644
--- a/assets/src/SVM/SVM.md
+++ b/assets/src/SVM/SVM.md
@@ -55,3 +55,24 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 2.图像分类。实验结果显示：在经过三到四轮相关反馈之后，比起传统的查询优化方案，支持向量机能够取得更好的搜索准确度。
 
 3.用于医学中分类蛋白质，超过90%的化合物能够被正确分类。用于手写字体识别。
+
+#### 优缺点
+
+SVM的优点
+
+1. 可以解决小样本情况下的机器学习问题。
+
+2. 可以提高泛化性能。
+
+3. 可以解决高维问题。
+
+4. 可以解决非线性问题。
+
+5. 可以避免神经网络结构选择和局部极小点问题。
+
+SVM的缺点：
+
+1. 对缺失数据敏感。
+
+2. 对非线性问题没有通用解决方案，必须谨慎选择Kernelfunction来处理。
+

From 93f172e05cc2f718ee44dcbff9a6154ebc2237da Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 08:46:13 +0800
Subject: [PATCH 0148/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index a9e87a2e..0ced4a66 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -17,3 +17,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 线性回归是利用数理统计中回归分析，来确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法，运用十分广泛。其表达形式为y = w'x+e，e为误差服从均值为0的正态分布。
 回归分析中，只包括一个自变量和一个因变量，且二者的关系可用一条直线近似表示，这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量，且因变量和自变量之间是线性关系，则称为多元线性回归分析。
 
+#### 单变量模型
+

From 815b34a0952d395d8cf2f70f2efb9e16ec1f0aa4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 08:55:57 +0800
Subject: [PATCH 0149/1406] chang RAM

---
 assets/images/126.jpg     | Bin 0 -> 3116 bytes
 assets/src/RAM/RAM.0.2.md |  25 +++++++++++++++++++++++++
 2 files changed, 25 insertions(+)
 create mode 100644 assets/images/126.jpg

diff --git a/assets/images/126.jpg b/assets/images/126.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..e2259e52edbd2327427e1c6ea0778a89f190e914
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diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 0ced4a66..9ea01347 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -18,4 +18,29 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 回归分析中，只包括一个自变量和一个因变量，且二者的关系可用一条直线近似表示，这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量，且因变量和自变量之间是线性关系，则称为多元线性回归分析。
 
 #### 单变量模型
+模型
+
+<mtable>
+  <mlabeledtr>
+    <mtd id="mjx-eqn-1_1">
+      <mtext>(1)</mtext>
+    </mtd>
+    <mtd>
+      <mi>f</mi>
+      <mo stretchy="false">(</mo>
+      <mi mathvariant="bold-italic">x</mi>
+      <mo stretchy="false">)</mo>
+      <mo>=</mo>
+      <msup>
+        <mi mathvariant="bold-italic">w</mi>
+        <mi>T</mi>
+      </msup>
+      <mi mathvariant="bold-italic">x</mi>
+      <mo>+</mo>
+      <mi>b</mi>
+    </mtd>
+  </mlabeledtr>
+</mtable>
+
+目标函数（最小二乘参数估计）
 

From 11e0e0c31f46de36d9f0c89b7b94ed5421e39ebb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 08:57:15 +0800
Subject: [PATCH 0150/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 9ea01347..99bfa8c0 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,6 +20,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 <mtable>
   <mlabeledtr>
     <mtd id="mjx-eqn-1_1">
@@ -41,6 +42,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
     </mtd>
   </mlabeledtr>
 </mtable>
-
+</math>
 目标函数（最小二乘参数估计）
 

From ed5718ee9ab1cba39c81074d616bff4ac8b14a90 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 08:58:39 +0800
Subject: [PATCH 0151/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 99bfa8c0..45d28d72 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -43,5 +43,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
   </mlabeledtr>
 </mtable>
 </math>
+线性模型(linear model)简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 目标函数（最小二乘参数估计）
 

From 53fcbc68494aebe8e794a142c60dcc812fd7b495 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 08:59:57 +0800
Subject: [PATCH 0152/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 29 +++++------------------------
 1 file changed, 5 insertions(+), 24 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 45d28d72..601593c5 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -19,30 +19,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 单变量模型
 模型
+<p>
+  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>w</mi><mi>T</mi></msup><mi>x</mi><mo>+</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">f(x)=w^Tx+b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8413309999999999em;"></span><span class="strut bottom" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathit">b</span></span></span></span>
+</p>
 
-<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
-<mtable>
-  <mlabeledtr>
-    <mtd id="mjx-eqn-1_1">
-      <mtext>(1)</mtext>
-    </mtd>
-    <mtd>
-      <mi>f</mi>
-      <mo stretchy="false">(</mo>
-      <mi mathvariant="bold-italic">x</mi>
-      <mo stretchy="false">)</mo>
-      <mo>=</mo>
-      <msup>
-        <mi mathvariant="bold-italic">w</mi>
-        <mi>T</mi>
-      </msup>
-      <mi mathvariant="bold-italic">x</mi>
-      <mo>+</mo>
-      <mi>b</mi>
-    </mtd>
-  </mlabeledtr>
-</mtable>
-</math>
-线性模型(linear model)简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
+线性模型(linear model)
+简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 目标函数（最小二乘参数估计）
 

From c149606b3278d4d702ed3a85f926ee005d37c3ea Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:03:10 +0800
Subject: [PATCH 0153/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 601593c5..6ba24041 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -27,3 +27,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 目标函数（最小二乘参数估计）
 
+#### 代码例子

From 159dd39678e5f37f6ac8a9c6104718a20e30e69c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:07:55 +0800
Subject: [PATCH 0154/1406] chaneg page

---
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 assets/images/128.jpg     | Bin 0 -> 13493 bytes
 assets/images/129.jpg     | Bin 0 -> 12080 bytes
 assets/src/RAM/RAM.0.2.md |  39 +++++++++++++++++++++++++++++++++++++-
 4 files changed, 38 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/127.jpg
 create mode 100644 assets/images/128.jpg
 create mode 100644 assets/images/129.jpg

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HcmV?d00001

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 6ba24041..2f1077d0 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,7 +20,25 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 <p>
-  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>w</mi><mi>T</mi></msup><mi>x</mi><mo>+</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">f(x)=w^Tx+b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8413309999999999em;"></span><span class="strut bottom" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathit">b</span></span></span></span>
+  <span class="katex">
+  <span class="katex-mathml">
+  <math><semantics>
+  <mrow>
+      <mi>f</mi>
+      <mo>(</mo><mi>x</mi><mo>)</mo>
+      <mo>=</mo>
+      <msup><mi>w</mi><mi>T</mi></msup>
+      <mi>x</mi>
+      <mo>+</mo>
+      <mi>b</mi>
+  </mrow>
+  <annotation encoding="application/x-tex">f(x)=w^Tx+b</annotation>
+  </semantics></math></span>
+  <span class="katex-html" aria-hidden="true">
+  <span class="strut" style="height:0.8413309999999999em;"></span>
+  <span class="strut bottom" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mrel">=</span>
+  <span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix">
+  <span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathit">b</span></span></span></span>
 </p>
 
 线性模型(linear model)
@@ -28,3 +46,22 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 目标函数（最小二乘参数估计）
 
 #### 代码例子
+
+```markdown
+    #Indicate the matplotlib to show the graphics inline
+    %matplotlib inline 
+    import matplotlib.pyplot as plt # import matplotlib
+    import numpy as np # import numpy
+    import tensorflow as tf
+    import numpy as np
+    
+    trX = np.linspace(-1, 1, 101) #Create a linear space of 101 points between 1 and 1
+    trY = 2 * trX + np.random.randn(*trX.shape) * 0.4 + 0.2 #Create The y function based on the x axis
+    plt.figure() # Create a new figure
+    plt.scatter(trX,trY) #Plot a scatter draw of the random datapoints
+    plt.plot (trX, .2 + 2 * trX) # Draw one line with the line function
+```
+
+<p align="center">
+<img width="200" align="center" src="../../images/127.jpg" />
+</p>

From 6ac14a4bb9b8935499141296d69c8900f2ff7eb4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:08:28 +0800
Subject: [PATCH 0155/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 2f1077d0..b9177ca0 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -63,5 +63,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 ```
 
 <p align="center">
-<img width="200" align="center" src="../../images/127.jpg" />
+<img width="300" align="center" src="../../images/127.jpg" />
 </p>

From 3cffba799f862c1b36fdf5c2f274f07e4717af16 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:08:53 +0800
Subject: [PATCH 0156/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index b9177ca0..31917c7e 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -65,3 +65,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/127.jpg" />
 </p>
+
+单变量示例
+<p align="center">
+<img width="300" align="center" src="../../images/128.jpg" />
+</p>

From e81e2192990cf28672b87ba66d26c569005e3a7b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:09:29 +0800
Subject: [PATCH 0157/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 47 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 31917c7e..486a2600 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -70,3 +70,50 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/128.jpg" />
 </p>
+
+```markdown
+   #!/usr/bin/env python
+# h(X)= b + wX
+%matplotlib inline
+import tensorflow as tf
+import numpy as np
+import matplotlib.pyplot as plt
+
+def model(X, w, b):
+    return tf.mul(X, w) + b
+
+trX = np.linspace(-1, 1, 101).astype(np.float32)
+# create a y value which is approximately linear but with some random noise
+trY = 2 * trX + np.random.randn(*trX.shape) * 0.33 + 10
+
+# create a shared variable (like theano.shared) for the weight matrix
+w = tf.Variable(tf.random_uniform([1], -1.0, 1.0))
+b = tf.Variable(tf.zeros([1]))
+cost = tf.reduce_mean(tf.square(trY-model(trX, w, b)))
+
+# construct an optimizer to minimize cost and fit line to my data
+train_op = tf.train.GradientDescentOptimizer(0.01).minimize(cost)
+
+# Launch the graph in a session
+with tf.Session() as sess:
+    # you need to initialize variables (in this case just variable W)
+    tf.initialize_all_variables().run()
+
+    for i in range(1000):
+        sess.run(train_op)
+
+    print "w should be something around [2]: ", sess.run(w)
+    print "b should be something around [10]:", sess.run(b)
+
+    plt.plot(trX, trY, "ro", label="Orinal data")
+    plt.plot(trX, w.eval()*trX + b.eval(), label="Fitted line")
+    plt.legend()
+    plt.show()
+
+    # Plot with pandas
+    #import pandas as pd
+    #fig, axes = plt.subplots(nrows=1, ncols=1)
+    #pd.DataFrame({'x':trX,'y':trY}).plot.scatter(x='x', y='y', ax=axes, color='red')
+    #pd.DataFrame({'x':trX,'y':w.eval()*trX + b.eval()}).plot.scatter(x='x', y='y', ax=axes, color='blue')
+```
+

From 81a8fd36dc4e31213d924ee1394e9fe690738f1e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:09:57 +0800
Subject: [PATCH 0158/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 486a2600..f7c9e1e9 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -117,3 +117,8 @@ with tf.Session() as sess:
     #pd.DataFrame({'x':trX,'y':w.eval()*trX + b.eval()}).plot.scatter(x='x', y='y', ax=axes, color='blue')
 ```
 
+```markdown
+   w should be something around [2]:  [ 2.00981951]
+   b should be something around [10]: [ 9.98865509]
+```
+

From 72e52db0bce7c10510b30d358ab0d4a968831489 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:10:33 +0800
Subject: [PATCH 0159/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index f7c9e1e9..0e2a582f 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -72,7 +72,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 ```markdown
-   #!/usr/bin/env python
+#!/usr/bin/env python
 # h(X)= b + wX
 %matplotlib inline
 import tensorflow as tf
@@ -122,3 +122,7 @@ with tf.Session() as sess:
    b should be something around [10]: [ 9.98865509]
 ```
 
+<p align="center">
+<img width="300" align="center" src="../../images/128.jpg" />
+</p>
+

From 49a0553d32cc4e0098ce4f0cfc2307f0bbc668bf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Jan 2018 09:11:59 +0800
Subject: [PATCH 0160/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 120 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 118 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 0e2a582f..42fd8021 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -66,7 +66,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/127.jpg" />
 </p>
 
-单变量示例
+#### 单变量示例
 <p align="center">
 <img width="300" align="center" src="../../images/128.jpg" />
 </p>
@@ -123,6 +123,122 @@ with tf.Session() as sess:
 ```
 
 <p align="center">
-<img width="300" align="center" src="../../images/128.jpg" />
+<img width="300" align="center" src="../../images/129.jpg" />
 </p>
 
+#### 多变量示例
+多变量其实就是输入变成了矩阵：
+
+```markdown
+#!/usr/bin/env python
+# h(X)= B + WX
+%matplotlib inline
+import tensorflow as tf
+import numpy as np
+import matplotlib.pyplot as plt
+
+def model(X, w, b):
+    return tf.mul(w, X) + b
+
+trX = np.mgrid[-1:1:0.01, -10:10:0.1].reshape(2, -1).T
+trW = np.array([3, 5])
+trY = trW*trX + np.random.randn(*trX.shape) + [20, 100]
+
+w = tf.Variable(np.array([1., 1.]).astype(np.float32))
+b = tf.Variable(np.array([[1., 1.]]).astype(np.float32))
+cost = tf.reduce_mean(tf.square(trY-model(trX, w, b))) 
+
+# construct an optimizer to minimize cost and fit line to my data
+train_op = tf.train.GradientDescentOptimizer(0.05).minimize(cost)
+
+# Launch the graph in a session
+with tf.Session() as sess:
+    # you need to initialize variables (in this case just variable W)
+    tf.initialize_all_variables().run()
+
+    for i in range(1000):
+        if i % 99 == 0:
+            print "Cost at step", i, "is:", cost.eval()
+        sess.run(train_op)
+
+    print "w should be something around [3, 5]: ", sess.run(w)
+    print "b should be something around [20,100]:", sess.run(b)
+Cost at step 0 is: 5329.87
+Cost at step 99 is: 1.22204
+Cost at step 198 is: 0.998043
+Cost at step 297 is: 0.997083
+Cost at step 396 is: 0.997049
+Cost at step 495 is: 0.997049
+Cost at step 594 is: 0.997049
+Cost at step 693 is: 0.997049
+Cost at step 792 is: 0.997049
+Cost at step 891 is: 0.997049
+Cost at step 990 is: 0.997049
+w should be something around [3, 5]:  [ 3.00108743  5.00054932]
+b should be something around [20,100]: [[  20.00317383  100.00382233]]
+tensorflow示例
+import tensorflow as tf
+
+# initialize variables/model parameters
+W = tf.Variable(tf.zeros([2, 1]), name="weights")
+b = tf.Variable(0., name="bias")
+
+def inference(X):
+    # compute inference model over data X and return the result
+    return tf.matmul(X, W) + b
+
+def loss(X, Y):
+    # compute loss over training data X and expected outputs Y
+    Y_predicted = inference(X)
+    return tf.reduce_sum(tf.squared_difference(Y, Y_predicted))
+
+def inputs():
+    # read/generate input training data X and expected outputs Y
+    weight_age = [[84, 46], [73, 20], [65, 52], [70, 30], [76, 57], [69, 25], [63, 28], [72, 36], [79, 57], [75, 44], [27, 24], [89, 31], [65, 52], [57, 23], [59, 60], [69, 48], [60, 34], [79, 51], [75, 50], [82, 34], [59, 46], [67, 23], [85, 37], [55, 40], [63, 30]]
+    blood_fat_content = [354, 190, 405, 263, 451, 302, 288, 385, 402, 365, 209, 290, 346, 254, 395, 434, 220, 374, 308, 220, 311, 181, 274, 303, 244]
+
+    return tf.to_float(weight_age), tf.to_float(blood_fat_content)
+
+def train(total_loss):
+    # train / adjust model parameters according to computed total loss
+    learning_rate = 0.000001
+    return tf.train.GradientDescentOptimizer(learning_rate).minimize(total_loss)
+
+
+def evaluate(sess, X, Y):
+    # evaluate the resulting trained model
+    print sess.run(inference([[80., 25.]])) # ~ 303
+    print sess.run(inference([[65., 25.]])) # ~ 256
+
+# Create a saver.
+# saver = tf.train.Saver()
+
+# Launch the graph in a session, setup boilerplate
+with tf.Session() as sess:
+    tf.initialize_all_variables().run()
+
+    X, Y = inputs()
+
+    total_loss = loss(X, Y)
+    train_op = train(total_loss)
+
+    coord = tf.train.Coordinator()
+    threads = tf.train.start_queue_runners(sess=sess, coord=coord)
+
+    # actual training loop
+    training_steps = 1000
+    for step in range(training_steps):
+        sess.run([train_op])
+        # for debugging and learning purposes, see how the loss gets decremented
+        # through training steps
+        if step % 10 == 0:
+            print "loss at step ", step, ":", sess.run([total_loss])
+        # save training checkpoints in case loosing them
+        # if step % 1000 == 0:
+        #     saver.save(sess, 'my-model', global_step=step)
+
+    evaluate(sess, X, Y)
+    coord.request_stop()
+    coord.join(threads)
+    # saver.save(sess, 'my-model', global_step=training_steps)
+```

From 63d3d4e885446773dc869f11c7a16e44f3292280 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:18:54 +0800
Subject: [PATCH 0161/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 42fd8021..f5d7d334 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -43,8 +43,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
+
 目标函数（最小二乘参数估计）
 
+<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>J</mi><mo>=</mo><msub><mrow><mi>arg</mi><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mo>(</mo><mi>w</mi><mo separator="true">,</mo><mi>b</mi><mo>)</mo></mrow></msub><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mo>(</mo><msub><mi>y</mi><mi>i</mi></msub><mo>−</mo><mi>w</mi><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">J={\arg min}_{(w,b)}\sum_{i=1}^{m}(y_i-wx_i-b)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:1.2335479999999999em;vertical-align:-0.41944em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.09618em;">J</span><span class="mrel">=</span><span class="mord"><span class="mord textstyle uncramped"><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mord mathit">m</span><span class="mord mathit">i</span><span class="mord mathit">n</span></span><span class="msupsub"><span class="vlist"><span style="top:0.24444em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mopen mtight">(</span><span class="mord mathit mtight" style="margin-right:0.02691em;">w</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">b</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathit mtight">m</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mbin">−</span><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mbin">−</span><span class="mord mathit">b</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span></p>
+
+
+
 #### 代码例子
 
 ```markdown

From 7d6ad634cab1aec47fc2be8189ed7b35d02cab9a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:21:13 +0800
Subject: [PATCH 0162/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 119 ++++++++++++++++++++++++++++++++++++--
 1 file changed, 113 insertions(+), 6 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index f5d7d334..b0dc19a3 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -46,10 +46,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 目标函数（最小二乘参数估计）
 
-<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>J</mi><mo>=</mo><msub><mrow><mi>arg</mi><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mo>(</mo><mi>w</mi><mo separator="true">,</mo><mi>b</mi><mo>)</mo></mrow></msub><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mo>(</mo><msub><mi>y</mi><mi>i</mi></msub><mo>−</mo><mi>w</mi><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">J={\arg min}_{(w,b)}\sum_{i=1}^{m}(y_i-wx_i-b)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:1.2335479999999999em;vertical-align:-0.41944em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.09618em;">J</span><span class="mrel">=</span><span class="mord"><span class="mord textstyle uncramped"><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mord mathit">m</span><span class="mord mathit">i</span><span class="mord mathit">n</span></span><span class="msupsub"><span class="vlist"><span style="top:0.24444em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mopen mtight">(</span><span class="mord mathit mtight" style="margin-right:0.02691em;">w</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">b</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathit mtight">m</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mbin">−</span><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mbin">−</span><span class="mord mathit">b</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span></p>
-
-
-
 #### 代码例子
 
 ```markdown
@@ -166,8 +162,8 @@ with tf.Session() as sess:
             print "Cost at step", i, "is:", cost.eval()
         sess.run(train_op)
 
-    print "w should be something around [3, 5]: ", sess.run(w)
-    print "b should be something around [20,100]:", sess.run(b)
+print "w should be something around [3, 5]: ", sess.run(w)
+print "b should be something around [20,100]:", sess.run(b)
 Cost at step 0 is: 5329.87
 Cost at step 99 is: 1.22204
 Cost at step 198 is: 0.998043
@@ -247,3 +243,114 @@ with tf.Session() as sess:
     coord.join(threads)
     # saver.save(sess, 'my-model', global_step=training_steps)
 ```
+#### 输出：
+
+
+```markdown
+  loss at step  0 : [54929292.0]
+loss at step  10 :  [14629748.0]
+loss at step  20 :  [7090800.0]
+loss at step  30 :  [5680201.0]
+loss at step  40 :  [5416011.0]
+loss at step  50 :  [5366280.5]
+loss at step  60 :  [5356678.0]
+loss at step  70 :  [5354588.0]
+loss at step  80 :  [5353913.0]
+loss at step  90 :  [5353510.0]
+loss at step  100 : [5353166.0]
+loss at step  110 : [5352839.5]
+loss at step  120 : [5352525.0]
+loss at step  130 : [5352218.5]
+loss at step  140 : [5351921.0]
+loss at step  150 : [5351631.5]
+loss at step  160 : [5351349.0]
+loss at step  170 : [5351075.0]
+loss at step  180 : [5350808.0]
+loss at step  190 : [5350549.5]
+loss at step  200 : [5350297.0]
+loss at step  210 : [5350050.5]
+loss at step  220 : [5349814.0]
+loss at step  230 : [5349580.5]
+loss at step  240 : [5349356.0]
+loss at step  250 : [5349134.0]
+loss at step  260 : [5348922.0]
+loss at step  270 : [5348712.5]
+loss at step  280 : [5348511.5]
+loss at step  290 : [5348313.5]
+loss at step  300 : [5348123.5]
+loss at step  310 : [5347935.0]
+loss at step  320 : [5347753.5]
+loss at step  330 : [5347577.5]
+loss at step  340 : [5347405.0]
+loss at step  350 : [5347237.0]
+loss at step  360 : [5347073.0]
+loss at step  370 : [5346915.0]
+loss at step  380 : [5346761.0]
+loss at step  390 : [5346611.0]
+loss at step  400 : [5346464.5]
+loss at step  410 : [5346320.5]
+loss at step  420 : [5346182.5]
+loss at step  430 : [5346047.5]
+loss at step  440 : [5345914.0]
+loss at step  450 : [5345786.0]
+loss at step  460 : [5345662.0]
+loss at step  470 : [5345539.5]
+loss at step  480 : [5345420.5]
+loss at step  490 : [5345305.5]
+loss at step  500 : [5345193.0]
+loss at step  510 : [5345082.5]
+loss at step  520 : [5344976.5]
+loss at step  530 : [5344871.0]
+loss at step  540 : [5344771.0]
+loss at step  550 : [5344670.5]
+loss at step  560 : [5344574.5]
+loss at step  570 : [5344480.5]
+loss at step  580 : [5344388.0]
+loss at step  590 : [5344298.0]
+loss at step  600 : [5344212.0]
+loss at step  610 : [5344127.0]
+loss at step  620 : [5344042.5]
+loss at step  630 : [5343962.0]
+loss at step  640 : [5343882.0]
+loss at step  650 : [5343805.5]
+loss at step  660 : [5343729.5]
+loss at step  670 : [5343657.0]
+loss at step  680 : [5343584.0]
+loss at step  690 : [5343514.5]
+loss at step  700 : [5343446.5]
+loss at step  710 : [5343380.0]
+loss at step  720 : [5343314.5]
+loss at step  730 : [5343250.0]
+loss at step  740 : [5343187.5]
+loss at step  750 : [5343128.0]
+loss at step  760 : [5343067.5]
+loss at step  770 : [5343010.5]
+loss at step  780 : [5342952.5]
+loss at step  790 : [5342897.5]
+loss at step  800 : [5342843.0]
+loss at step  810 : [5342791.5]
+loss at step  820 : [5342738.5]
+loss at step  830 : [5342688.5]
+loss at step  840 : [5342638.5]
+loss at step  850 : [5342589.5]
+loss at step  860 : [5342543.0]
+loss at step  870 : [5342496.5]
+loss at step  880 : [5342449.5]
+loss at step  890 : [5342406.0]
+loss at step  900 : [5342363.0]
+loss at step  910 : [5342319.5]
+loss at step  920 : [5342277.5]
+loss at step  930 : [5342236.0]
+loss at step  940 : [5342197.5]
+loss at step  950 : [5342157.0]
+loss at step  960 : [5342118.5]
+loss at step  970 : [5342080.5]
+loss at step  980 : [5342043.0]
+loss at step  990 : [5342007.5]
+[[ 318.77984619]]
+[[ 266.52853394]]
+```
+
+
+
+

From 8dc11ed87f93df5744ae0f52b52022be00754a95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:22:39 +0800
Subject: [PATCH 0163/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index b0dc19a3..95a73fc9 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -247,7 +247,7 @@ with tf.Session() as sess:
 
 
 ```markdown
-  loss at step  0 : [54929292.0]
+loss at step  0 : [54929292.0]
 loss at step  10 :  [14629748.0]
 loss at step  20 :  [7090800.0]
 loss at step  30 :  [5680201.0]

From 24e96e24066911b3f971f35cdcc47f14deec6120 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:22:55 +0800
Subject: [PATCH 0164/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 95a73fc9..72df920d 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -352,5 +352,7 @@ loss at step  990 : [5342007.5]
 ```
 
 
+#### sklearn示例
+
 
 

From cc27a2e4413acece431d52d32aea13af320ff891 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:23:38 +0800
Subject: [PATCH 0165/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 72df920d..5c7f2020 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -354,5 +354,8 @@ loss at step  990 : [5342007.5]
 
 #### sklearn示例
 
+```markdown
+
+```
 
 

From 4e670f0c55a83f9300295d94f8c343f1b5cc4d7b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:23:43 +0800
Subject: [PATCH 0166/1406] Update RAM.0.2.md


From b315af3b80ca51ea801266ec15590e982ea07a36 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:23:56 +0800
Subject: [PATCH 0167/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 5c7f2020..43c551c0 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -355,7 +355,17 @@ loss at step  990 : [5342007.5]
 #### sklearn示例
 
 ```markdown
-
+import tensorflow.contrib.learn.python.learn as learn
+from sklearn import datasets, metrics, preprocessing
+
+boston = datasets.load_boston()
+x = preprocessing.StandardScaler().fit_transform(boston.data)
+feature_columns = learn.infer_real_valued_columns_from_input(x)
+regressor = learn.LinearRegressor(feature_columns=feature_columns)
+regressor.fit(x, boston.target, steps=200, batch_size=32)
+boston_predictions = list(regressor.predict(x, as_iterable=True))
+score = metrics.mean_squared_error(boston_predictions, boston.target)
+print ("MSE: %f" % score)
 ```
 
 

From 0d70052cd321a1477e3420f781d4134f46dd3478 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:31:04 +0800
Subject: [PATCH 0168/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 85c5fed0..d82967f2 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,7 @@
 深度学习：深度学习是基于机器学习延伸出来的一个新的领域，由以人大脑结构为启发的神经网络算法为起源加之模型结构深度的增加发展，并伴随大数据和计算能力的提高而产生的一系列新的算法。
 深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
 
- * [深度神经网络](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.md)
+ * [深度神经网络](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.01.md)
  * [深度学习的入门]()
  * [深度学习的应用案例]()
  * [深度学习所需要的数据]()

From be93dacdd6ea15c0b96d42d1359670546b638cf4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 09:36:57 +0800
Subject: [PATCH 0169/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d82967f2..df94316f 100644
--- a/README.md
+++ b/README.md
@@ -24,7 +24,7 @@
 深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
 
  * [深度神经网络](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.01.md)
- * [深度学习的入门]()
+ * [深度学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.02.md)
  * [深度学习的应用案例]()
  * [深度学习所需要的数据]()
 

From 56a835f75d815f15111411802814c22f59ace616 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 17:35:30 +0800
Subject: [PATCH 0170/1406] change page of Readme

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index df94316f..caa73ded 100644
--- a/README.md
+++ b/README.md
@@ -164,6 +164,7 @@
 * [无监督神经元](https://blog.openai.com/unsupervised-sentiment-neuron/)
 * [Tensorflow实践](https://tensorflow.feisky.xyz/install/cpu.html)
 * [Artificial Intelligence](https://github.com/owainlewis/awesome-artificial-intelligence)
+* [Tensorflow新手入门](http://www.tensorfly.cn/tfdoc/tutorials/mnist_beginners.html)
 
 ### 机器学习
 觉得此文章不错可以给我star！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！

From 338324f360ed3a61aae211d04ca122dbf6468c3f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 21:31:46 +0800
Subject: [PATCH 0171/1406] chaneg page of RAM

---
 assets/images/130.jpg     | Bin 0 -> 3014 bytes
 assets/images/131.jpg     | Bin 0 -> 1433 bytes
 assets/images/132.jpg     | Bin 0 -> 2731 bytes
 assets/images/133.jpg     | Bin 0 -> 2503 bytes
 assets/images/134.jpg     | Bin 0 -> 1645 bytes
 assets/images/135.jpg     | Bin 0 -> 10549 bytes
 assets/src/RAM/RAM.0.2.md |  29 ++++++++---------------------
 7 files changed, 8 insertions(+), 21 deletions(-)
 create mode 100644 assets/images/130.jpg
 create mode 100644 assets/images/131.jpg
 create mode 100644 assets/images/132.jpg
 create mode 100644 assets/images/133.jpg
 create mode 100644 assets/images/134.jpg
 create mode 100644 assets/images/135.jpg

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diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 43c551c0..a6e65c83 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -19,32 +19,19 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 单变量模型
 模型
-<p>
-  <span class="katex">
-  <span class="katex-mathml">
-  <math><semantics>
-  <mrow>
-      <mi>f</mi>
-      <mo>(</mo><mi>x</mi><mo>)</mo>
-      <mo>=</mo>
-      <msup><mi>w</mi><mi>T</mi></msup>
-      <mi>x</mi>
-      <mo>+</mo>
-      <mi>b</mi>
-  </mrow>
-  <annotation encoding="application/x-tex">f(x)=w^Tx+b</annotation>
-  </semantics></math></span>
-  <span class="katex-html" aria-hidden="true">
-  <span class="strut" style="height:0.8413309999999999em;"></span>
-  <span class="strut bottom" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mrel">=</span>
-  <span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix">
-  <span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathit">b</span></span></span></span>
+<p align="center">
+<img width="100" align="center" src="../../images/131.jpg" />
 </p>
-
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 
 目标函数（最小二乘参数估计）
+<p align="center">
+<img width="100" align="center" src="../../images/130.jpg" />
+</p>
+
+#### 多变量模型
+
 
 #### 代码例子
 

From fad37fa65d52aab8ad2a5a9363dd9d9b09bd6a55 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:33:20 +0800
Subject: [PATCH 0172/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index a6e65c83..e3043512 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,14 +20,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 <p align="center">
-<img width="100" align="center" src="../../images/131.jpg" />
+<img width="300" align="center" src="../../images/131.jpg" />
 </p>
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 
 目标函数（最小二乘参数估计）
 <p align="center">
-<img width="100" align="center" src="../../images/130.jpg" />
+<img width="300" align="center" src="../../images/130.jpg" />
 </p>
 
 #### 多变量模型

From a58de3baab5817dd7cdc10e8c5543a0120503c8f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:33:44 +0800
Subject: [PATCH 0173/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index e3043512..a7e9ccad 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,14 +20,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 <p align="center">
-<img width="300" align="center" src="../../images/131.jpg" />
+<img width="230" align="center" src="../../images/131.jpg" />
 </p>
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 
 目标函数（最小二乘参数估计）
 <p align="center">
-<img width="300" align="center" src="../../images/130.jpg" />
+<img width="230" align="center" src="../../images/130.jpg" />
 </p>
 
 #### 多变量模型

From 8779037b3b5d43bdf566ad82b7b278ae1007353f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:34:34 +0800
Subject: [PATCH 0174/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index a7e9ccad..1ddddad5 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -30,6 +30,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="230" align="center" src="../../images/130.jpg" />
 </p>
 
+多变量时可以表示为矩阵
+<p align="center">
+<img width="230" align="center" src="../../images/132.jpg" />
+</p>
+
+
+
 #### 多变量模型
 
 

From 63197f794ecd18880f7e9b2875be2b41552acde1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:35:48 +0800
Subject: [PATCH 0175/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 1ddddad5..69f1ddd3 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,19 +20,19 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 <p align="center">
-<img width="230" align="center" src="../../images/131.jpg" />
+<img width="260" align="center" src="../../images/131.jpg" />
 </p>
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
 
 目标函数（最小二乘参数估计）
 <p align="center">
-<img width="230" align="center" src="../../images/130.jpg" />
+<img width="260" align="center" src="../../images/130.jpg" />
 </p>
 
 多变量时可以表示为矩阵
 <p align="center">
-<img width="230" align="center" src="../../images/132.jpg" />
+<img width="260" align="center" src="../../images/132.jpg" />
 </p>
 
 

From dd2238820ea52a4fdba3f70d31dec661210532c2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:36:18 +0800
Subject: [PATCH 0176/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 69f1ddd3..3a0d297d 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -20,7 +20,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 单变量模型
 模型
 <p align="center">
-<img width="260" align="center" src="../../images/131.jpg" />
+<img width="230" align="center" src="../../images/131.jpg" />
 </p>
 线性模型(linear model)
 简单, 易于建模, 但却蕴含着机器学习的重要思想.由于w直观地表达了各属性在预测中的重要性, 所以线性模型有着很好的可解释性(comprehensibility).
@@ -32,7 +32,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 多变量时可以表示为矩阵
 <p align="center">
-<img width="260" align="center" src="../../images/132.jpg" />
+<img width="270" align="center" src="../../images/132.jpg" />
 </p>
 
 

From 5d4f8cb52c6bf134e6d75f4f76e987c0f713f172 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:37:18 +0800
Subject: [PATCH 0177/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 3a0d297d..2f6a519e 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -35,6 +35,19 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="270" align="center" src="../../images/132.jpg" />
 </p>
 
+目标函数为
+<p align="center">
+<img width="270" align="center" src="../../images/133.jpg" />
+</p>
+
+当$X^TX$为满秩矩阵时，可以得到最优解
+<p align="center">
+<img width="270" align="center" src="../../images/134.jpg" />
+</p>
+
+<p align="center">
+<img width="270" align="center" src="../../images/135.jpg" />
+</p>
 
 
 #### 多变量模型

From ca3de75c47ff93383c2138bd237ff9d33da26841 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:38:17 +0800
Subject: [PATCH 0178/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 2f6a519e..91285c12 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -42,11 +42,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 当$X^TX$为满秩矩阵时，可以得到最优解
 <p align="center">
-<img width="270" align="center" src="../../images/134.jpg" />
+<img width="240" align="center" src="../../images/134.jpg" />
 </p>
 
-<p align="center">
-<img width="270" align="center" src="../../images/135.jpg" />
+<p>
+<img width="350" align="center" src="../../images/135.jpg" />
 </p>
 
 

From 5161d762bc17b79e18bee5f77a8749a76dd240a5 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 21:40:58 +0800
Subject: [PATCH 0179/1406] chaneg page of RAM

---
 assets/images/135.jpg     | Bin 10549 -> 2184 bytes
 assets/src/RAM/RAM.0.2.md |   8 +++++---
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/assets/images/135.jpg b/assets/images/135.jpg
index 90f716e48772c55d2dd61a964ade3e5387a99f57..70c06d1f45b6154bb54dd086978a4f058a4fe830 100644
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diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 91285c12..153bd513 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -45,9 +45,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="240" align="center" src="../../images/134.jpg" />
 </p>
 
-<p>
-<img width="350" align="center" src="../../images/135.jpg" />
-</p>
+注意：
+    1.多变量时需要对输入数据作归一化，如<img width="240" align="center" src="../../images/135.jpg" />
+    
+ 
+    
 
 
 #### 多变量模型

From b69aa126978e8abb8ce81a73c1c58c75a7c4c02f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 21:42:35 +0800
Subject: [PATCH 0180/1406] chaneg page

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 assets/images/135.jpg

diff --git a/assets/images/135.jpg b/assets/images/135.jpg
deleted file mode 100644
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From dc995897c72cd86d0ab83c97bdc9d4ecb21f6301 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:45:07 +0800
Subject: [PATCH 0181/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 153bd513..e7d894fe 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -30,6 +30,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="260" align="center" src="../../images/130.jpg" />
 </p>
 
+#### 多变量模型
+
 多变量时可以表示为矩阵
 <p align="center">
 <img width="270" align="center" src="../../images/132.jpg" />
@@ -46,15 +48,17 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 注意：
-    1.多变量时需要对输入数据作归一化，如<img width="240" align="center" src="../../images/135.jpg" />
+   
+   1.多变量时需要对输入数据作归一化，如<img width="240" align="center" src="../../images/135.jpg" />
     
+   2.实际计算过程中（如使用梯度下降算法）学习率的选择方法
+   
+   * 收敛慢时，增大学习率
+   * 不收敛时，减小学习率
+   * 学习率的选择范围一般为..., 0.001, 0.01, 0.1, 1, 10, ...
  
     
 
-
-#### 多变量模型
-
-
 #### 代码例子
 
 ```markdown

From d2e0f210abe4aba7878b8135b5c63a238094b8c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 21:47:49 +0800
Subject: [PATCH 0182/1406] change page of RAM

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
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From 4873c81b2337b4f6b849c5ffcfd1c3788dbbc1d5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:49:49 +0800
Subject: [PATCH 0183/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index e7d894fe..2ac8fc06 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -49,10 +49,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 注意：
    
-   1.多变量时需要对输入数据作归一化，如<img width="240" align="center" src="../../images/135.jpg" />
-    
+   1.多变量时需要对输入数据作归一化，如<img width="140" align="center" src="../../images/135.jpg" />
    2.实际计算过程中（如使用梯度下降算法）学习率的选择方法
-   
    * 收敛慢时，增大学习率
    * 不收敛时，减小学习率
    * 学习率的选择范围一般为..., 0.001, 0.01, 0.1, 1, 10, ...

From cebf2c5ffed73ae6e8d88e6867e3f1a4acff4076 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 21:50:29 +0800
Subject: [PATCH 0184/1406] Update RAM.0.2.md

---
 assets/src/RAM/RAM.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 2ac8fc06..9d5d6796 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -50,6 +50,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 注意：
    
    1.多变量时需要对输入数据作归一化，如<img width="140" align="center" src="../../images/135.jpg" />
+  
    2.实际计算过程中（如使用梯度下降算法）学习率的选择方法
    * 收敛慢时，增大学习率
    * 不收敛时，减小学习率

From 9974167633db3133ae857c074f181fdb70ee75cd Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 22:09:43 +0800
Subject: [PATCH 0185/1406] chaneg page of RAM

---
 assets/src/RAM/RAM.0.3.md | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)
 create mode 100644 assets/src/RAM/RAM.0.3.md

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
new file mode 100644
index 00000000..e1ab52c5
--- /dev/null
+++ b/assets/src/RAM/RAM.0.3.md
@@ -0,0 +1,18 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+回归方法是对数值型连续随机变量进行预测和建模的监督学习算法。其特点是标注的数据集具有数值型的目标变量。回归的目的是预测数值型的目标值。
+
+
+常用的回归方法包括:
+* 线性回归：使用超平面拟合数据集 
+* 最近邻算法：通过搜寻最相似的训练样本来预测新样本的值
+* 决策树和回归树：将数据集分割为不同分支而实现分层学习
+* 集成方法：组合多个弱学习算法构造一种强学习算法，如随机森林（RF）和梯度提升树（GBM）等
+* 深度学习：使用多层神经网络学习复杂模型
+
+#### 逻辑回归
+
+逻辑回归对应线性回归，但旨在解决分类问题，即将模型的输出转换为0/1值。逻辑回归直接对分类的可能性进行建模，无需事先假设数据的分布。
+
+最理想的转换函数为单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
\ No newline at end of file

From 3bdd37a025ca59ceaca3cb40e8e7c8dc3ad77923 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 17 Jan 2018 22:18:33 +0800
Subject: [PATCH 0186/1406] change page of RAM'

---
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 assets/images/137.jpg | Bin 0 -> 2528 bytes
 assets/images/138.jpg | Bin 0 -> 1069 bytes
 assets/images/139.jpg | Bin 0 -> 1882 bytes
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 assets/images/142.jpg | Bin 0 -> 5175 bytes
 assets/images/143.jpg | Bin 0 -> 5184 bytes
 assets/images/144.jpg | Bin 0 -> 851 bytes
 assets/images/145.jpg | Bin 0 -> 2109 bytes
 assets/images/146.jpg | Bin 0 -> 1445 bytes
 11 files changed, 0 insertions(+), 0 deletions(-)
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 create mode 100644 assets/images/137.jpg
 create mode 100644 assets/images/138.jpg
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From 32d0c6a2cf1db6f2423f12f64249671156ab1784 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:19:34 +0800
Subject: [PATCH 0187/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index caa73ded..05a9592d 100644
--- a/README.md
+++ b/README.md
@@ -68,7 +68,7 @@
 #### 算法模型
  * [回归算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.1.md)
      * [线性回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.2.md)  
-     * [逻辑回归]()  
+     * [逻辑回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.3.md)  
      * [多元自适应回归(MARS)]()  
      * [本地散点平滑估计(LOESS)]()  
  * [基于实例的学习算法]() 

From 19808ae6ec9c9603c0c9345cc42a7dd3d4a64bd8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:20:24 +0800
Subject: [PATCH 0188/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index e1ab52c5..4448d15e 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -15,4 +15,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 逻辑回归对应线性回归，但旨在解决分类问题，即将模型的输出转换为0/1值。逻辑回归直接对分类的可能性进行建模，无需事先假设数据的分布。
 
-最理想的转换函数为单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
\ No newline at end of file
+最理想的转换函数为单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
+
+<p align="center">
+<img width="260" align="center" src="../../images/136.jpg" />
+</p>

From 78aa98b120534e6955bb7b17a58d956af728f3b9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:26:33 +0800
Subject: [PATCH 0189/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 4448d15e..335f2d9a 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -18,5 +18,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 最理想的转换函数为单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
 
 <p align="center">
-<img width="260" align="center" src="../../images/136.jpg" />
+<img width="230" align="center" src="../../images/136.jpg" />
+</p>
+
+这样，模型就变成了
+<p align="center">
+<img width="230" align="center" src="../../images/137.jpg" />
 </p>

From 93c2a430c7664baea2a3029d3fb879beb1413b84 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:27:17 +0800
Subject: [PATCH 0190/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 335f2d9a..7046def3 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -25,3 +25,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="230" align="center" src="../../images/137.jpg" />
 </p>
+
+如果将$y$看作是样本$x$作为正例的可能性，那么可以得到反应$x$作为正例的相对可能性对数几率（logit）
+<p align="center">
+<img width="230" align="center" src="../../images/138.jpg" />
+</p>

From b7fd98812462c1355ee7013fcf876e889f01a248 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:27:36 +0800
Subject: [PATCH 0191/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 7046def3..279d1983 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -23,10 +23,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 这样，模型就变成了
 <p align="center">
-<img width="230" align="center" src="../../images/137.jpg" />
+<img width="240" align="center" src="../../images/137.jpg" />
 </p>
 
 如果将$y$看作是样本$x$作为正例的可能性，那么可以得到反应$x$作为正例的相对可能性对数几率（logit）
 <p align="center">
-<img width="230" align="center" src="../../images/138.jpg" />
+<img width="200" align="center" src="../../images/138.jpg" />
 </p>

From 210e42be287ef2bffc2d32657c59af2af6c4ee8d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:28:14 +0800
Subject: [PATCH 0192/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 279d1983..1871fb00 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -30,3 +30,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="200" align="center" src="../../images/138.jpg" />
 </p>
+
+#### 逻辑回归算法

From 6a75c7036cca3a4b1e010e4cec500d74bbd5c3e5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 17 Jan 2018 22:28:40 +0800
Subject: [PATCH 0193/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 1871fb00..ea2ab28e 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -32,3 +32,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 #### 逻辑回归算法
+
+可以使用极大似然估计法来估计参数$w$和$b$
+

From 19db62a4a193904e9fdd89032cbc54e42cd66b4b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:14:44 +0800
Subject: [PATCH 0194/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index ea2ab28e..d36b89da 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,3 +35,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
+假设<img width="100" align="center" src="../../images/139.jpg" />，似然函数为<img width="100" align="center" src="../../images/140.jpg" />

From 69b14c87a2b611bdd728dc45f3a2c02f9ef9ea80 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:15:00 +0800
Subject: [PATCH 0195/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index d36b89da..f8932c6f 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,4 +35,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
-假设<img width="100" align="center" src="../../images/139.jpg" />，似然函数为<img width="100" align="center" src="../../images/140.jpg" />
+假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="190" align="center" src="../../images/140.jpg" />

From eff96fc40c6e8542689f81b622c7693348a5a4ac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:15:48 +0800
Subject: [PATCH 0196/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index f8932c6f..2d9397ba 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,4 +35,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
-假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="190" align="center" src="../../images/140.jpg" />
+假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="200" align="center" src="../../images/141.jpg" />

From e639fc29bc9b414f84a093a014c44d7a9a765907 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:16:01 +0800
Subject: [PATCH 0197/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 2d9397ba..9b607ef3 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,4 +35,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
-假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="200" align="center" src="../../images/141.jpg" />
+假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="300" align="center" src="../../images/141.jpg" />

From 31131f88909caef38f189a6597ba2667f5419aa1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:16:14 +0800
Subject: [PATCH 0198/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 9b607ef3..28e554f8 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,4 +35,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
-假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="300" align="center" src="../../images/141.jpg" />
+假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="400" align="center" src="../../images/141.jpg" />

From 0e4061ccdd39e9fa6c737f21417526bc4c90b607 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:16:47 +0800
Subject: [PATCH 0199/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 28e554f8..20424a12 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -35,4 +35,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 可以使用极大似然估计法来估计参数$w$和$b$
 
-假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="400" align="center" src="../../images/141.jpg" />
+假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="460" align="center" src="../../images/141.jpg" />，
+<img width="190" align="center" src="../../images/142.jpg" />

From 6f3e52ffb12c3d1d6da17593892843995927a91f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:17:00 +0800
Subject: [PATCH 0200/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 20424a12..6a6089bd 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -36,4 +36,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 可以使用极大似然估计法来估计参数$w$和$b$
 
 假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="460" align="center" src="../../images/141.jpg" />，
-<img width="190" align="center" src="../../images/142.jpg" />
+<img width="460" align="center" src="../../images/142.jpg" />

From bf0f953221e1e75641b40e3b16f5811620f150b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:17:21 +0800
Subject: [PATCH 0201/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 6a6089bd..df227bbb 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -37,3 +37,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="460" align="center" src="../../images/141.jpg" />，
 <img width="460" align="center" src="../../images/142.jpg" />
+然后就可以使用梯度下降算法、牛顿法或者BFGS等拟牛顿法来求解了。

From d15e6bfa380f3b6b4cb9eaff7e29eab03cea7e6d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:18:14 +0800
Subject: [PATCH 0202/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index df227bbb..08e245e0 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -38,3 +38,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 假设<img width="190" align="center" src="../../images/139.jpg" />，似然函数为<img width="200" align="center" src="../../images/140.jpg" />，那么对数似然函数为<img width="460" align="center" src="../../images/141.jpg" />，
 <img width="460" align="center" src="../../images/142.jpg" />
 然后就可以使用梯度下降算法、牛顿法或者BFGS等拟牛顿法来求解了。
+
+
+#### 正则化
+
+在模型过于复杂的情况下，模型会学习到很多特征，从而导致可能把所有训练样本都拟合到，这样就导致了过拟合。解决过拟合可以从两个方面入手，一是减少模型复杂度，一是增加训练集个数。而正则化就是减少模型复杂度的一个方法。
+
+一般是在目标函数(经验风险)中加上一个正则化项<img width="200" align="center" src="../../images/143.jpg" />

From e172b7bbbffea0e794aaa0c3694b0a7bfb311c18 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:18:51 +0800
Subject: [PATCH 0203/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 08e245e0..608900f0 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -44,4 +44,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在模型过于复杂的情况下，模型会学习到很多特征，从而导致可能把所有训练样本都拟合到，这样就导致了过拟合。解决过拟合可以从两个方面入手，一是减少模型复杂度，一是增加训练集个数。而正则化就是减少模型复杂度的一个方法。
 
-一般是在目标函数(经验风险)中加上一个正则化项<img width="200" align="center" src="../../images/143.jpg" />
+一般是在目标函数(经验风险)中加上一个正则化项<img width="400" align="center" src="../../images/144.jpg" />

From a6ca71fdabd71d905d13bb6a100f5d206a34712e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:19:03 +0800
Subject: [PATCH 0204/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 608900f0..90d631da 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -44,4 +44,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在模型过于复杂的情况下，模型会学习到很多特征，从而导致可能把所有训练样本都拟合到，这样就导致了过拟合。解决过拟合可以从两个方面入手，一是减少模型复杂度，一是增加训练集个数。而正则化就是减少模型复杂度的一个方法。
 
-一般是在目标函数(经验风险)中加上一个正则化项<img width="400" align="center" src="../../images/144.jpg" />
+一般是在目标函数(经验风险)中加上一个正则化项<img width="100" align="center" src="../../images/144.jpg" />

From fca19c3f8cf9bbc23071a5a25712cbeb035a1a3c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:19:18 +0800
Subject: [PATCH 0205/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 90d631da..5e00be8f 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -44,4 +44,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在模型过于复杂的情况下，模型会学习到很多特征，从而导致可能把所有训练样本都拟合到，这样就导致了过拟合。解决过拟合可以从两个方面入手，一是减少模型复杂度，一是增加训练集个数。而正则化就是减少模型复杂度的一个方法。
 
-一般是在目标函数(经验风险)中加上一个正则化项<img width="100" align="center" src="../../images/144.jpg" />
+一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />

From 34dc2c1d1736a2fef09bcef41077c8c888cc7f46 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:20:06 +0800
Subject: [PATCH 0206/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 5e00be8f..ea02e34b 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -44,4 +44,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在模型过于复杂的情况下，模型会学习到很多特征，从而导致可能把所有训练样本都拟合到，这样就导致了过拟合。解决过拟合可以从两个方面入手，一是减少模型复杂度，一是增加训练集个数。而正则化就是减少模型复杂度的一个方法。
 
-一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />
+一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />，即
+
+<img width="40" align="center" src="../../images/143.jpg" />

From f3004bcd26e5c66fbaa62c432514b8eb9ece10ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:20:22 +0800
Subject: [PATCH 0207/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index ea02e34b..dac5f9a1 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -46,4 +46,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />，即
 
-<img width="40" align="center" src="../../images/143.jpg" />
+<img width="400" align="center" src="../../images/143.jpg" />

From 6ac9dec00a015adfddf55ee16b89b8cd5d37142e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:20:58 +0800
Subject: [PATCH 0208/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index dac5f9a1..a41037ce 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -46,4 +46,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />，即
 
-<img width="400" align="center" src="../../images/143.jpg" />
+<img width="460" align="center" src="../../images/143.jpg" />
+而这个正则化项一般会采用L1范数或者L2范数。其形式分别为<img width="400" align="center" src="../../images/145.jpg" />

From bc0b768bf1fa16fb6410cb5b9dea646f24d286b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:21:13 +0800
Subject: [PATCH 0209/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index a41037ce..66fafedc 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -47,4 +47,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />，即
 
 <img width="460" align="center" src="../../images/143.jpg" />
-而这个正则化项一般会采用L1范数或者L2范数。其形式分别为<img width="400" align="center" src="../../images/145.jpg" />
+而这个正则化项一般会采用L1范数或者L2范数。其形式分别为<img width="300" align="center" src="../../images/145.jpg" />

From 6813b2ccc94e036745ce3fd9252e3f982c8b1834 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 18 Jan 2018 09:21:39 +0800
Subject: [PATCH 0210/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 66fafedc..baffe4e7 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -47,4 +47,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 一般是在目标函数(经验风险)中加上一个正则化项<img width="40" align="center" src="../../images/144.jpg" />，即
 
 <img width="460" align="center" src="../../images/143.jpg" />
-而这个正则化项一般会采用L1范数或者L2范数。其形式分别为<img width="300" align="center" src="../../images/145.jpg" />
+而这个正则化项一般会采用L1范数或者L2范数。其形式分别为：<img width="300" align="center" src="../../images/145.jpg" />

From fc0008940b7e64270d04b69e861bfacfd6f0e7b7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 08:57:53 +0800
Subject: [PATCH 0211/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index baffe4e7..b08e285d 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -48,3 +48,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 <img width="460" align="center" src="../../images/143.jpg" />
 而这个正则化项一般会采用L1范数或者L2范数。其形式分别为：<img width="300" align="center" src="../../images/145.jpg" />
+
+
+#### 类别不均衡问题

From 3a41c32246c4d95e344f3a9fb646cdeccc044b28 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 08:58:25 +0800
Subject: [PATCH 0212/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index b08e285d..962a7e14 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -51,3 +51,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 类别不均衡问题
+
+类别不均衡是指分类任务中不同类别的训练样例数目差别很大的情况。解决这类问题的基本思路是“再缩放（rescaling）”，即令
+
+<img width="300" align="center" src="../../images/146.jpg" />

From 49d0d44b2d7bbd1bd7e239dda3fff626407a0f9c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 08:58:50 +0800
Subject: [PATCH 0213/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 962a7e14..62521c9d 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -54,4 +54,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 类别不均衡是指分类任务中不同类别的训练样例数目差别很大的情况。解决这类问题的基本思路是“再缩放（rescaling）”，即令
 
-<img width="300" align="center" src="../../images/146.jpg" />
+<img width="200" align="center" src="../../images/146.jpg" /> 其中，$m^-$为反例数目，$m^+$为正例数目）

From 4be3de86fb812adfd0fa4bbb3ac367c3a49263e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 08:59:13 +0800
Subject: [PATCH 0214/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 62521c9d..ace88028 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -55,3 +55,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 类别不均衡是指分类任务中不同类别的训练样例数目差别很大的情况。解决这类问题的基本思路是“再缩放（rescaling）”，即令
 
 <img width="200" align="center" src="../../images/146.jpg" /> 其中，$m^-$为反例数目，$m^+$为正例数目）
+
+然而，这个方法的实际操作却很难。实际使用上通常使用下列的方法
+

From 8d4ccf1e999199402030ed67bfb358ffdcd66db0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:00:11 +0800
Subject: [PATCH 0215/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index ace88028..e79e63a2 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -56,5 +56,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 <img width="200" align="center" src="../../images/146.jpg" /> 其中，$m^-$为反例数目，$m^+$为正例数目）
 
-然而，这个方法的实际操作却很难。实际使用上通常使用下列的方法
+然而，这个方法的实际操作却很难。实际使用上通常使用的方法：
 
+* 欠采样：去除一些样例使得不同类别的训练样例数目平衡。注意随机丢弃样例可能会导致丢失一些重要信息。
+* 过采样：增加一些样例使得不同类别的训练样例数目平衡。注意不能简单对原样本重复采样，否则会导致严重的过拟合
+* 直接基于原始训练集进行学习，但在使用最终模型预测时使用再缩放（也称为阈值移动）

From 6a551752e19958b60cfc78f3f3a37487f5a876a5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:01:07 +0800
Subject: [PATCH 0216/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index e79e63a2..48062512 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -61,3 +61,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 欠采样：去除一些样例使得不同类别的训练样例数目平衡。注意随机丢弃样例可能会导致丢失一些重要信息。
 * 过采样：增加一些样例使得不同类别的训练样例数目平衡。注意不能简单对原样本重复采样，否则会导致严重的过拟合
 * 直接基于原始训练集进行学习，但在使用最终模型预测时使用再缩放（也称为阈值移动）
+
+
+#### 示例代码
+
+
+

From 61481ff0a815a9cb86217c9f03c317a09d728e50 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:14:26 +0800
Subject: [PATCH 0217/1406] change page of RAM

---
 assets/src/RAM/RAM.0.3.md | 131 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 129 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 48062512..ebe371a1 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -65,5 +65,132 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 示例代码
 
-
-
+```markdown
+
+import os
+import tensorflow as tf
+
+# initialize variables/model parameters
+W = tf.Variable(tf.zeros([5, 1]), name="weights")
+b = tf.Variable(0., name="bias")
+
+def read_csv(batch_size, file_name, record_defaults):
+    filename_queue = tf.train.string_input_producer(
+        [os.path.dirname(__file__) + "/" + file_name])
+
+    reader = tf.TextLineReader(skip_header_lines=1)
+    key, value = reader.read(filename_queue)
+
+    # decode_csv will convert a Tensor from type string (the text line) in
+    # a tuple of tensor columns with the specified defaults, which also
+    # sets the data type for each column
+    decoded = tf.decode_csv(value, record_defaults=record_defaults)
+
+    # batch actually reads the file and loads "batch_size" rows in a single
+    # tensor
+    return tf.train.shuffle_batch(decoded,
+                                  batch_size=batch_size,
+                                  capacity=batch_size * 50,
+                                  min_after_dequeue=batch_size)
+
+def inference(X):
+    # compute inference model over data X and return the result
+    return tf.sigmoid(tf.matmul(X, W) + b)
+
+def loss(X, Y):
+    # compute loss over training data X and expected outputs Y
+    return tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(
+        tf.matmul(X, W) + b, Y))
+
+def inputs():
+    # data is downloaded from https://www.kaggle.com/c/titanic/data.
+    passenger_id, survived, pclass, name, sex, age, sibsp, parch, ticket, fare,\
+        cabin, embarked = read_csv(100,
+                                   "train.csv",
+                                   [[0.0], [0.0], [0], [""],
+                                    [""], [0.0], [0.0], [0.0],
+                                    [""], [0.0], [""], [""]])
+
+    # convert categorical data
+    is_first_class = tf.to_float(tf.equal(pclass, [1]))
+    is_second_class = tf.to_float(tf.equal(pclass, [2]))
+    is_third_class = tf.to_float(tf.equal(pclass, [3]))
+    gender = tf.to_float(tf.equal(sex, ["female"]))
+
+    # Finally we pack all the features in a single matrix;
+    # We then transpose to have a matrix with one example per row and one
+    # feature per column.
+    features = tf.transpose(
+        tf.pack([is_first_class,
+                 is_second_class,
+                 is_third_class,
+                 gender,
+                 age]))
+    survived = tf.reshape(survived, [100, 1])
+
+    return features, survived
+
+
+def train(total_loss):
+    # train / adjust model parameters according to computed total loss
+    learning_rate = 0.01
+    return tf.train.GradientDescentOptimizer(learning_rate).minimize(
+        total_loss)
+
+
+def evaluate(sess, X, Y):
+    # evaluate the resulting trained model
+    predicted = tf.cast(inference(X) > 0.5, tf.float32)
+
+    print sess.run(tf.reduce_mean(tf.cast(tf.equal(predicted, Y), tf.float32)))
+
+# Create a saver.
+# saver = tf.train.Saver()
+
+# Launch the graph in a session, setup boilerplate
+with tf.Session() as sess:
+    tf.initialize_all_variables().run()
+
+    X, Y = inputs()
+
+    total_loss = loss(X, Y)
+    train_op = train(total_loss)
+
+    coord = tf.train.Coordinator()
+    threads = tf.train.start_queue_runners(sess=sess, coord=coord)
+
+    # actual training loop
+    training_steps = 1000
+    for step in range(training_steps):
+        sess.run([train_op])
+        # for debugging and learning purposes, see how the loss gets decremented
+        # through training steps
+        if step % 100 == 0:
+            print "loss at step ", step, ":", sess.run([total_loss])
+        # save training checkpoints in case loosing them
+        # if step % 1000 == 0:
+        #     saver.save(sess, 'my-model', global_step=step)
+
+    evaluate(sess, X, Y)
+    coord.request_stop()
+    coord.join(threads)
+    # saver.save(sess, 'my-model', global_step=training_steps)
+
+```
+
+
+
+```markdown
+
+loss at step  0 : [1.0275139]
+loss at step  100 : [1.389969]
+loss at step  200 : [1.4667224]
+loss at step  300 : [0.67178178]
+loss at step  400 : [0.568793]
+loss at step  500 : [0.48835525]
+loss at step  600 : [1.0899736]
+loss at step  700 : [0.84278578]
+loss at step  800 : [1.0500686]
+loss at step  900 : [0.89417559]
+0.72
+```

From 2425a7f93e3c84997b11940a01fe9fdb4188bc9f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:16:43 +0800
Subject: [PATCH 0218/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 71 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index ebe371a1..12f71f1c 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -194,3 +194,74 @@ loss at step  800 : [1.0500686]
 loss at step  900 : [0.89417559]
 0.72
 ```
+
+#### minst回归示例
+
+
+```markdown
+import tensorflow as tf
+import numpy as np
+import input_data
+
+# Import MINST data
+mnist = input_data.read_data_sets("../MNIST_data/", one_hot=True)
+Extracting ../MNIST_data/train-images-idx3-ubyte.gz
+Extracting ../MNIST_data/train-labels-idx1-ubyte.gz
+Extracting ../MNIST_data/t10k-images-idx3-ubyte.gz
+Extracting ../MNIST_data/t10k-labels-idx1-ubyte.gz
+# Parameters
+learning_rate = 0.01
+training_epochs = 25
+batch_size = 100
+display_step = 1
+
+# tf Graph Input
+x = tf.placeholder("float", [None, 784]) # mnist data image of shape 28*28=784
+y = tf.placeholder("float", [None, 10]) # 0-9 digits recognition => 10 classes
+
+# Create model
+def init_weights(shape):
+    return tf.Variable(tf.random_normal(shape, stddev=0.01))
+
+def model(X, w):
+    return tf.matmul(X, w)
+
+# like in linear regression, we need a shared variable weight matrix
+# for logistic regression
+w = init_weights([784, 10]) 
+
+# Construct model
+# compute mean cross entropy (softmax is applied internally)
+cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(model(x, w), y)) 
+train_op = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost) # construct optimizer
+predict_op = tf.argmax(model(x, w), 1) # at predict time, evaluate the argmax of the logistic regression
+
+# Launch the graph
+with tf.Session() as sess:
+    tf.initialize_all_variables().run()
+
+    # Training cycle
+    for epoch in range(training_epochs):
+        avg_cost = 0.
+        total_batch = int(mnist.train.num_examples/batch_size)
+        # Loop over all batches
+        for i in range(total_batch):
+            batch_xs, batch_ys = mnist.train.next_batch(batch_size)
+            # Fit training using batch data
+            sess.run(train_op, feed_dict={x: batch_xs, y: batch_ys})
+            # Compute average loss
+            avg_cost += sess.run(cost, feed_dict={x: batch_xs, y: batch_ys})/total_batch
+        # Display logs per epoch step
+        if epoch % display_step == 0:
+            print "Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost)
+
+    print "Optimization Finished!"
+
+    # Test model
+    correct_prediction = tf.equal(predict_op, tf.argmax(y, 1))
+    # Calculate accuracy
+    accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
+    print "Accuracy:", accuracy.eval({x: mnist.test.images, y: mnist.test.labels})
+
+```
+

From c8e12d02c61ae9ebf9fe3ad14089ca7b0724e9b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:18:47 +0800
Subject: [PATCH 0219/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 12f71f1c..3333a341 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -209,6 +209,8 @@ Extracting ../MNIST_data/train-images-idx3-ubyte.gz
 Extracting ../MNIST_data/train-labels-idx1-ubyte.gz
 Extracting ../MNIST_data/t10k-images-idx3-ubyte.gz
 Extracting ../MNIST_data/t10k-labels-idx1-ubyte.gz
+
+
 # Parameters
 learning_rate = 0.01
 training_epochs = 25
@@ -265,3 +267,35 @@ with tf.Session() as sess:
 
 ```
 
+```markdown
+Epoch: 0001 cost= 1.181141054
+Epoch: 0002 cost= 0.664358092
+Epoch: 0003 cost= 0.553026987
+Epoch: 0004 cost= 0.499294951
+Epoch: 0005 cost= 0.466518660
+Epoch: 0006 cost= 0.443856266
+Epoch: 0007 cost= 0.427351894
+Epoch: 0008 cost= 0.414347254
+Epoch: 0009 cost= 0.403219846
+Epoch: 0010 cost= 0.394844531
+Epoch: 0011 cost= 0.387121435
+Epoch: 0012 cost= 0.380693078
+Epoch: 0013 cost= 0.375634897
+Epoch: 0014 cost= 0.369904718
+Epoch: 0015 cost= 0.365776612
+Epoch: 0016 cost= 0.361626607
+Epoch: 0017 cost= 0.358361928
+Epoch: 0018 cost= 0.354674878
+Epoch: 0019 cost= 0.351685582
+Epoch: 0020 cost= 0.349124772
+Epoch: 0021 cost= 0.346287186
+Epoch: 0022 cost= 0.344134942
+Epoch: 0023 cost= 0.341778976
+Epoch: 0024 cost= 0.340130984
+Epoch: 0025 cost= 0.337454195
+Optimization Finished!
+Accuracy: 0.9122
+
+```
+
+#### sklearn示例

From 64ca278e0a0b17fabc0711fd425389cf17d0937a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:19:39 +0800
Subject: [PATCH 0220/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 41 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 3333a341..497ce7d1 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -299,3 +299,44 @@ Accuracy: 0.9122
 ```
 
 #### sklearn示例
+
+```markdown
+from sklearn import datasets
+from sklearn import metrics
+import tensorflow as tf
+import tensorflow.contrib.layers.python.layers as layers
+import tensorflow.contrib.learn.python.learn as learn
+
+iris = datasets.load_iris()
+
+def my_model(features, labels):
+  """DNN with three hidden layers."""
+  # Convert the labels to a one-hot tensor of shape (length of features, 3) and
+  # with a on-value of 1 for each one-hot vector of length 3.
+  labels = tf.one_hot(labels, 3, 1, 0)
+
+  # Create three fully connected layers respectively of size 10, 20, and 10.
+  features = layers.stack(features, layers.fully_connected, [10, 20, 10])
+
+  # Create two tensors respectively for prediction and loss.
+  prediction, loss = (
+      tf.contrib.learn.models.logistic_regression(features, labels)
+  )
+
+  # Create a tensor for training op.
+  train_op = tf.contrib.layers.optimize_loss(
+      loss, tf.contrib.framework.get_global_step(), optimizer='Adagrad',
+      learning_rate=0.1)
+
+  return {'class': tf.argmax(prediction, 1), 'prob': prediction}, loss, train_op
+
+classifier = learn.Estimator(model_fn=my_model)
+classifier.fit(iris.data, iris.target, steps=1000)
+
+y_predicted = [
+  p['class'] for p in classifier.predict(iris.data, as_iterable=True)]
+score = metrics.accuracy_score(iris.target, y_predicted)
+print('Accuracy: {0:f}'.format(score))
+```
+
+

From 5328ffe4699889045f14592551118fc0130c89dd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:20:57 +0800
Subject: [PATCH 0221/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 497ce7d1..46e03833 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -300,7 +300,7 @@ Accuracy: 0.9122
 
 #### sklearn示例
 
-```markdown
+```python
 from sklearn import datasets
 from sklearn import metrics
 import tensorflow as tf

From 9aa6c2ebaedb0003c5e4ed8ffe0ad0e269449c1b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:26:04 +0800
Subject: [PATCH 0222/1406] change page of Ram0.4

---
 assets/src/RAM/RAM.0.2.md | 12 ++++++------
 assets/src/RAM/RAM.0.3.md |  8 ++++----
 assets/src/RAM/RAM.0.4.md | 21 +++++++++++++++++++++
 3 files changed, 31 insertions(+), 10 deletions(-)
 create mode 100644 assets/src/RAM/RAM.0.4.md

diff --git a/assets/src/RAM/RAM.0.2.md b/assets/src/RAM/RAM.0.2.md
index 9d5d6796..66416a4a 100644
--- a/assets/src/RAM/RAM.0.2.md
+++ b/assets/src/RAM/RAM.0.2.md
@@ -60,7 +60,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 代码例子
 
-```markdown
+```python
     #Indicate the matplotlib to show the graphics inline
     %matplotlib inline 
     import matplotlib.pyplot as plt # import matplotlib
@@ -84,7 +84,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/128.jpg" />
 </p>
 
-```markdown
+```python
 #!/usr/bin/env python
 # h(X)= b + wX
 %matplotlib inline
@@ -130,7 +130,7 @@ with tf.Session() as sess:
     #pd.DataFrame({'x':trX,'y':w.eval()*trX + b.eval()}).plot.scatter(x='x', y='y', ax=axes, color='blue')
 ```
 
-```markdown
+```python
    w should be something around [2]:  [ 2.00981951]
    b should be something around [10]: [ 9.98865509]
 ```
@@ -142,7 +142,7 @@ with tf.Session() as sess:
 #### 多变量示例
 多变量其实就是输入变成了矩阵：
 
-```markdown
+```python
 #!/usr/bin/env python
 # h(X)= B + WX
 %matplotlib inline
@@ -258,7 +258,7 @@ with tf.Session() as sess:
 #### 输出：
 
 
-```markdown
+```python
 loss at step  0 : [54929292.0]
 loss at step  10 :  [14629748.0]
 loss at step  20 :  [7090800.0]
@@ -366,7 +366,7 @@ loss at step  990 : [5342007.5]
 
 #### sklearn示例
 
-```markdown
+```python
 import tensorflow.contrib.learn.python.learn as learn
 from sklearn import datasets, metrics, preprocessing
 
diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 46e03833..a25d8d6c 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -65,7 +65,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 示例代码
 
-```markdown
+```python
 
 import os
 import tensorflow as tf
@@ -180,7 +180,7 @@ with tf.Session() as sess:
 
 
 
-```markdown
+```python
 
 loss at step  0 : [1.0275139]
 loss at step  100 : [1.389969]
@@ -198,7 +198,7 @@ loss at step  900 : [0.89417559]
 #### minst回归示例
 
 
-```markdown
+```python
 import tensorflow as tf
 import numpy as np
 import input_data
@@ -267,7 +267,7 @@ with tf.Session() as sess:
 
 ```
 
-```markdown
+```python
 Epoch: 0001 cost= 1.181141054
 Epoch: 0002 cost= 0.664358092
 Epoch: 0003 cost= 0.553026987
diff --git a/assets/src/RAM/RAM.0.4.md b/assets/src/RAM/RAM.0.4.md
new file mode 100644
index 00000000..72bf48fd
--- /dev/null
+++ b/assets/src/RAM/RAM.0.4.md
@@ -0,0 +1,21 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+回归方法是对数值型连续随机变量进行预测和建模的监督学习算法。其特点是标注的数据集具有数值型的目标变量。回归的目的是预测数值型的目标值。
+
+
+常用的回归方法包括:
+* 线性回归：使用超平面拟合数据集 
+* 最近邻算法：通过搜寻最相似的训练样本来预测新样本的值
+* 决策树和回归树：将数据集分割为不同分支而实现分层学习
+* 集成方法：组合多个弱学习算法构造一种强学习算法，如随机森林（RF）和梯度提升树（GBM）等
+* 深度学习：使用多层神经网络学习复杂模型
+
+#### 多元自适应回归样条
+多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。
+该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优势在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。
+文章在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
+在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。
+研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符;
+神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。
+论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
\ No newline at end of file

From 5a066b4d54d82580703ba70337bb97b9a31f9b8a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 19 Jan 2018 09:33:17 +0800
Subject: [PATCH 0223/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 05a9592d..ab353ed3 100644
--- a/README.md
+++ b/README.md
@@ -69,7 +69,7 @@
  * [回归算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.1.md)
      * [线性回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.2.md)  
      * [逻辑回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.3.md)  
-     * [多元自适应回归(MARS)]()  
+     * [多元自适应回归(MARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.4.md)  
      * [本地散点平滑估计(LOESS)]()  
  * [基于实例的学习算法]() 
      * [K-邻近算法（KNN）]()

From 38de360581209b272c060ae7832baf9174ea510e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 20 Jan 2018 10:06:13 +0800
Subject: [PATCH 0224/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index a25d8d6c..84c24d55 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -15,7 +15,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 逻辑回归对应线性回归，但旨在解决分类问题，即将模型的输出转换为0/1值。逻辑回归直接对分类的可能性进行建模，无需事先假设数据的分布。
 
-最理想的转换函数为单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
+最理想的转换函数是单位阶跃函数（也称Heaviside函数），但单位阶跃函数是不连续的，没法在实际计算中使用。故而，在分类过程中更常使用对数几率函数（即sigmoid函数）：
 
 <p align="center">
 <img width="230" align="center" src="../../images/136.jpg" />

From 9c5a4634595b1e3bef5092509998151fb4a2e8bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 20 Jan 2018 10:07:39 +0800
Subject: [PATCH 0225/1406] Update RAM.0.4.md

---
 assets/src/RAM/RAM.0.4.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.4.md b/assets/src/RAM/RAM.0.4.md
index 72bf48fd..001c7fa9 100644
--- a/assets/src/RAM/RAM.0.4.md
+++ b/assets/src/RAM/RAM.0.4.md
@@ -12,10 +12,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 深度学习：使用多层神经网络学习复杂模型
 
 #### 多元自适应回归样条
+
 多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。
 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优势在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。
 文章在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
+
 在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。
 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符;
 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。
-论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
\ No newline at end of file
+论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。

From 9f06a431c1a2fef54f9e37d04c2a3f6c4de93d44 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 21 Jan 2018 18:20:39 +0800
Subject: [PATCH 0226/1406] chaneg apge

---
 assets/src/RAM/RAM.0.5.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)
 create mode 100644 assets/src/RAM/RAM.0.5.md

diff --git a/assets/src/RAM/RAM.0.5.md b/assets/src/RAM/RAM.0.5.md
new file mode 100644
index 00000000..ae47f6a6
--- /dev/null
+++ b/assets/src/RAM/RAM.0.5.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+回归方法是对数值型连续随机变量进行预测和建模的监督学习算法。其特点是标注的数据集具有数值型的目标变量。回归的目的是预测数值型的目标值。
+
+
+常用的回归方法包括:
+* 线性回归：使用超平面拟合数据集 
+* 最近邻算法：通过搜寻最相似的训练样本来预测新样本的值
+* 决策树和回归树：将数据集分割为不同分支而实现分层学习
+* 集成方法：组合多个弱学习算法构造一种强学习算法，如随机森林（RF）和梯度提升树（GBM）等
+* 深度学习：使用多层神经网络学习复杂模型
+
+#### 本地散点平滑估计

From 4bb689e02f20f2ae192c231b3c8d1532089e88e8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 21 Jan 2018 18:26:32 +0800
Subject: [PATCH 0227/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ab353ed3..a517a540 100644
--- a/README.md
+++ b/README.md
@@ -70,7 +70,7 @@
      * [线性回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.2.md)  
      * [逻辑回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.3.md)  
      * [多元自适应回归(MARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.4.md)  
-     * [本地散点平滑估计(LOESS)]()  
+     * [本地散点平滑估计(LOESS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.5.md)  
  * [基于实例的学习算法]() 
      * [K-邻近算法（KNN）]()
      * [学习矢量化（LVQ）]()

From 4e28c30c2a41457a7509db77d35c0ac3be8ea46e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:07:00 +0800
Subject: [PATCH 0228/1406] Update RAM.0.4.md

---
 assets/src/RAM/RAM.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RAM/RAM.0.4.md b/assets/src/RAM/RAM.0.4.md
index 001c7fa9..2ab6f60d 100644
--- a/assets/src/RAM/RAM.0.4.md
+++ b/assets/src/RAM/RAM.0.4.md
@@ -21,3 +21,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符;
 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。
 论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
+
+MARS是回归的自适应过程，非常适合高维问题（比如，存在大量的输入）。可以从两个角度来理解它，首先，它可以看成是逐步线性回归的推广，其次，也可以看成是为了提高CART在回归中的效果而进行的改进。我们从第一种观点引入MARS，接着与CART联系起来。

From 8939adaf15ba8410519cc03e34e06ba89ca0583a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:24:05 +0800
Subject: [PATCH 0229/1406] Update RAM.0.5.md

---
 assets/src/RAM/RAM.0.5.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/RAM/RAM.0.5.md b/assets/src/RAM/RAM.0.5.md
index ae47f6a6..614365a3 100644
--- a/assets/src/RAM/RAM.0.5.md
+++ b/assets/src/RAM/RAM.0.5.md
@@ -12,3 +12,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 深度学习：使用多层神经网络学习复杂模型
 
 #### 本地散点平滑估计
+
+本地散点平滑估计（Locally Estimated Scatterplot Smoothing，LOESS），事先不用确定参数数量
+
+优点：.直接、快速 知名度高
+
+缺点：要求严格的假设,需要处理异常值.

From 1bfff2250a869f5769ca386bf6b48b0c4a3ece62 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:24:31 +0800
Subject: [PATCH 0230/1406] Update RAM.0.5.md

---
 assets/src/RAM/RAM.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.5.md b/assets/src/RAM/RAM.0.5.md
index 614365a3..fb3196aa 100644
--- a/assets/src/RAM/RAM.0.5.md
+++ b/assets/src/RAM/RAM.0.5.md
@@ -13,7 +13,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 本地散点平滑估计
 
-本地散点平滑估计（Locally Estimated Scatterplot Smoothing，LOESS），事先不用确定参数数量
+本地散点平滑估计（Locally Estimated Scatterplot Smoothing，LOESS），事先不用确定参数数量，每次预测的时候，用指定的样本点周围的样本点进行临时训练，确定参数。
 
 优点：.直接、快速 知名度高
 

From dd38426b5b4ac6ecb4c71bf77e9f2b26dc06fe22 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:25:00 +0800
Subject: [PATCH 0231/1406] Update RAM.0.5.md

---
 assets/src/RAM/RAM.0.5.md | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/assets/src/RAM/RAM.0.5.md b/assets/src/RAM/RAM.0.5.md
index fb3196aa..8b69f08b 100644
--- a/assets/src/RAM/RAM.0.5.md
+++ b/assets/src/RAM/RAM.0.5.md
@@ -15,6 +15,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 本地散点平滑估计（Locally Estimated Scatterplot Smoothing，LOESS），事先不用确定参数数量，每次预测的时候，用指定的样本点周围的样本点进行临时训练，确定参数。
 
-优点：.直接、快速 知名度高
 
-缺点：要求严格的假设,需要处理异常值.
+
+
+
+
+
+
+
+#### 优缺点
+
+优点：直接、快速 知名度高。
+
+缺点：要求严格的假设,需要处理异常值。

From 8a6cc0a145256210334fbda03d93647a79012fed Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:35:32 +0800
Subject: [PATCH 0232/1406] change page

---
 assets/src/BA/BA.0.1.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 assets/src/BA/BA.0.1.md

diff --git a/assets/src/BA/BA.0.1.md b/assets/src/BA/BA.0.1.md
new file mode 100644
index 00000000..2f102421
--- /dev/null
+++ b/assets/src/BA/BA.0.1.md
@@ -0,0 +1,12 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 基于实例的学习算法
+
+常用的回归方法包括:
+* K-邻近算法（KNN)
+* 最近邻算法：通过搜寻最相似的训练样本来预测新样本的值
+* 决策树和回归树：将数据集分割为不同分支而实现分层学习
+* 集成方法：组合多个弱学习算法构造一种强学习算法，如随机森林（RF）和梯度提升树（GBM）等
+* 深度学习：使用多层神经网络学习复杂模型

From 53c289d74e15b058d50c9662a1303745c34bd974 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:38:06 +0800
Subject: [PATCH 0233/1406] Update BA.0.1.md

---
 assets/src/BA/BA.0.1.md | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/assets/src/BA/BA.0.1.md b/assets/src/BA/BA.0.1.md
index 6af911e1..237cbb6f 100644
--- a/assets/src/BA/BA.0.1.md
+++ b/assets/src/BA/BA.0.1.md
@@ -3,9 +3,3 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 基于实例的学习算法
-
-常用的回归方法包括:
-* K-邻近算法（KNN)
-* 学习矢量化（LVQ）
-* 自组织映射算法（SOM）
-* 局部加权学习算法（LWL）

From 36f56d7a882c796527a5d806d5ca297aa41b1248 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 22 Jan 2018 09:38:47 +0800
Subject: [PATCH 0234/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index a517a540..891ed617 100644
--- a/README.md
+++ b/README.md
@@ -71,7 +71,7 @@
      * [逻辑回归](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.3.md)  
      * [多元自适应回归(MARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.4.md)  
      * [本地散点平滑估计(LOESS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.5.md)  
- * [基于实例的学习算法]() 
+ * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
      * [K-邻近算法（KNN）]()
      * [学习矢量化（LVQ）]()
      * [自组织映射算法（SOM）]()

From 94a7b24fcc6a4ae829c104650ecff47e11e99141 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:25:53 +0800
Subject: [PATCH 0235/1406] change page of BA

---
 assets/src/BA/BA.0.1.md | 6 ++++++
 assets/src/BA/BA.0.2.md | 5 +++++
 2 files changed, 11 insertions(+)
 create mode 100644 assets/src/BA/BA.0.2.md

diff --git a/assets/src/BA/BA.0.1.md b/assets/src/BA/BA.0.1.md
index 237cbb6f..d3ce0c98 100644
--- a/assets/src/BA/BA.0.1.md
+++ b/assets/src/BA/BA.0.1.md
@@ -3,3 +3,9 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 基于实例的学习算法
+
+常用的基于实例的学习算法包括:
+* K-邻近算法(KNN)
+* 学习矢量化(LVQ)
+* 自组织映射算法(SOM)
+* 局部加权学习算法(LWL)
diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
new file mode 100644
index 00000000..df8f9dca
--- /dev/null
+++ b/assets/src/BA/BA.0.2.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### K-邻近算法（KNN）

From 34c7bf2ab8ffa8d1409f27ca327fbaa78eaa4b2c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:32:38 +0800
Subject: [PATCH 0236/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 891ed617..a472afbd 100644
--- a/README.md
+++ b/README.md
@@ -72,7 +72,7 @@
      * [多元自适应回归(MARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.4.md)  
      * [本地散点平滑估计(LOESS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.5.md)  
  * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
-     * [K-邻近算法（KNN）]()
+     * [K-邻近算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）]()
      * [自组织映射算法（SOM）]()
      * [局部加权学习算法（LWL）]()

From d3e376c8728d19d36a528bbbc9f0a534665cf28e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:33:04 +0800
Subject: [PATCH 0237/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index df8f9dca..2cee0cd7 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -3,3 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### K-邻近算法（KNN）
+
+K最近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
+
+其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：

From 4fdc7ed7aad1cc7aad44c678e26408cd8ce7531c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:36:25 +0800
Subject: [PATCH 0238/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 2cee0cd7..6e26d42d 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -7,3 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 K最近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
 
 其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：
+<p align="center">
+<img width="200" align="center" src="../../images/87.jpg" />
+</p>

From cd40362176dcfecfe42281a907bdffe5f72582f4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:37:30 +0800
Subject: [PATCH 0239/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 6e26d42d..587d5f2b 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -2,7 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### K-邻近算法（KNN）
+#### K-近邻算法（KNN）
 
 K最近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
 

From 81391a0806ed9fa86699158e4ea345f5d26f31b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:38:04 +0800
Subject: [PATCH 0240/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index a472afbd..614e973f 100644
--- a/README.md
+++ b/README.md
@@ -72,7 +72,7 @@
      * [多元自适应回归(MARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.4.md)  
      * [本地散点平滑估计(LOESS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.5.md)  
  * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
-     * [K-邻近算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
+     * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）]()
      * [自组织映射算法（SOM）]()
      * [局部加权学习算法（LWL）]()

From 463cb771478328d60f3aeb09e799166b8fb8b73e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:41:35 +0800
Subject: [PATCH 0241/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 587d5f2b..f26678e8 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -4,9 +4,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### K-近邻算法（KNN）
 
-K最近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
+K近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
+
+k近邻（k-Nearest Neighbors）采用向量空间模型来分类，是一种常用的监督学习方法。它的工作原理为：给定测试样本，基于某种距离度量找出训练集中与其最靠近的k个训练样本，然后基于这k个“邻居”的信息来进行预测。通常，在分类任务中可使用“投票法”，即选择这k个样本中出现最多的类别标记作为预测结果；在回归任务中可使用“平均法”，即将这k个样本的实值输出标记的平均值作为预测结果；还可基于距离远近进行加权平均或加权投票，距离越近的样本权重越大。
+
 
 其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：
 <p align="center">
 <img width="200" align="center" src="../../images/87.jpg" />
 </p>
+

From 291443dd23b7a4a10343c6a0e3b35876a0019c55 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:41:51 +0800
Subject: [PATCH 0242/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index f26678e8..ff44c8dc 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -8,6 +8,10 @@ K近邻算法是一种基于类比的分类方法，主要通过给定的检验
 
 k近邻（k-Nearest Neighbors）采用向量空间模型来分类，是一种常用的监督学习方法。它的工作原理为：给定测试样本，基于某种距离度量找出训练集中与其最靠近的k个训练样本，然后基于这k个“邻居”的信息来进行预测。通常，在分类任务中可使用“投票法”，即选择这k个样本中出现最多的类别标记作为预测结果；在回归任务中可使用“平均法”，即将这k个样本的实值输出标记的平均值作为预测结果；还可基于距离远近进行加权平均或加权投票，距离越近的样本权重越大。
 
+k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学习技术在训练阶段仅仅是把样本保存起来，训练时间开销为零，待收到测试样本后再进行处理。
+
+最近邻分类器虽然简单，但它的泛化错误率不超过贝叶斯最优分类器的错误率的两倍。
+
 
 其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：
 <p align="center">

From 82f47c32cf99721a1ee1e7a352e1400dba845062 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:50:55 +0800
Subject: [PATCH 0243/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index ff44c8dc..fc06c881 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -18,3 +18,20 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 <img width="200" align="center" src="../../images/87.jpg" />
 </p>
 
+注意：为了防止具有较大初始值域的属性比较小初始值域的属性的权重过大，在计算距离之前，需对每个属性值进行规范化。一般的规划方法有最小-最大规范化，零均值规范化，小数定标规范化等。
+
+最小-最大规范化：将原始数据值映射到[0,1]空间中，假定minA和maxA分别是属性A的最小值和最大值，则规范化的公式为：
+<p align="center">
+<img width="150" align="center" src="../../images/88.jpg" />
+</p>
+零均值规范化：基于属性A的均值和标准差上的规范化方法，具体计算如下：
+<p align="center">
+<img width="80" align="center" src="../../images/89.jpg" />
+</p>
+
+小数定标规范化：通过移动属性A的小数点位置进行规范化，小数点的移动位数依赖于A的最大绝对值。具体计算如下：(其中j是使得MAX（ v’ ）<1的最小整数)
+<p align="center">
+<img width="50" align="center" src="../../images/90.jpg" />
+</p>
+
+最近邻数K的确定，主要原理是选取产生最小误差率的k值。每次从k=1开始，使用检验集估计分类器的误差率；每次都允许增加一个近邻，重复该过程，选择误差率最小的k值。

From 82405bbe9b3840e67fe4ff50dc9bf40d20daa538 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Jan 2018 09:51:31 +0800
Subject: [PATCH 0244/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index fc06c881..55b7e00b 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -35,3 +35,9 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 </p>
 
 最近邻数K的确定，主要原理是选取产生最小误差率的k值。每次从k=1开始，使用检验集估计分类器的误差率；每次都允许增加一个近邻，重复该过程，选择误差率最小的k值。
+
+
+
+#### 案例
+
+

From de2d5a147d1e225bc497eff6d8be1388bb1eab00 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 08:44:18 +0800
Subject: [PATCH 0245/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 55b7e00b..78a36d72 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -38,6 +38,6 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 
 
 
-#### 案例
+#### 应用案例
 
 

From 88505bcbaef09a29021d495862034e2d04084c4c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 08:45:09 +0800
Subject: [PATCH 0246/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 78a36d72..ed0c051b 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -41,3 +41,19 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 #### 应用案例
 
 
+```python
+    #Indicate the matplotlib to show the graphics inline
+    %matplotlib inline 
+    import matplotlib.pyplot as plt # import matplotlib
+    import numpy as np # import numpy
+    import tensorflow as tf
+    import numpy as np
+    
+    trX = np.linspace(-1, 1, 101) #Create a linear space of 101 points between 1 and 1
+    trY = 2 * trX + np.random.randn(*trX.shape) * 0.4 + 0.2 #Create The y function based on the x axis
+    plt.figure() # Create a new figure
+    plt.scatter(trX,trY) #Plot a scatter draw of the random datapoints
+    plt.plot (trX, .2 + 2 * trX) # Draw one line with the line function
+```
+
+

From 7d29be03b44f0ee625eaa56ead31ffea46b45a3a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 08:45:19 +0800
Subject: [PATCH 0247/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 11 -----------
 1 file changed, 11 deletions(-)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index ed0c051b..3a6f2a00 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -42,18 +42,7 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 
 
 ```python
-    #Indicate the matplotlib to show the graphics inline
-    %matplotlib inline 
-    import matplotlib.pyplot as plt # import matplotlib
-    import numpy as np # import numpy
-    import tensorflow as tf
-    import numpy as np
     
-    trX = np.linspace(-1, 1, 101) #Create a linear space of 101 points between 1 and 1
-    trY = 2 * trX + np.random.randn(*trX.shape) * 0.4 + 0.2 #Create The y function based on the x axis
-    plt.figure() # Create a new figure
-    plt.scatter(trX,trY) #Plot a scatter draw of the random datapoints
-    plt.plot (trX, .2 + 2 * trX) # Draw one line with the line function
 ```
 
 

From f5a91fb9b72fc91df96db5977401c9bd37d7172b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 12:42:02 +0800
Subject: [PATCH 0248/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 49 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 3a6f2a00..1b263888 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -43,6 +43,55 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 
 ```python
     
+    %matplotlib inline
+    import time
+    import numpy as np
+    import tensorflow as tf
+    import matplotlib.pyplot as plt
+    from sklearn.datasets.samples_generator import make_circles
+
+    N=210
+    K=2
+    MAX_ITERS = 1000
+    cut=int(N*0.7)
+
+    # 生成训练和测试数据集
+    data, features = make_circles(n_samples=N, shuffle=True, noise= 0.12, factor=0.4)
+    tr_data, tr_features= data[:cut], features[:cut]
+    te_data,te_features=data[cut:], features[cut:]
+
+    fig, ax = plt.subplots()
+    ax.scatter(tr_data.transpose()[0], tr_data.transpose()[1], marker = 'o', s = 100, c = tr_features, cmap=plt.cm.coolwarm )
+    ax.set_title('Train data')
+    plt.show()
+
+    start = time.time()
+
+    points=tf.Variable(data)
+    cluster_assignments = tf.Variable(tf.zeros([N], dtype=tf.int64))
+
+    sess = tf.Session()
+    sess.run(tf.initialize_all_variables())
+
+    te_learned_features=[]
+    for i, j in zip(te_data, te_features):
+        distances = tf.reduce_sum(tf.square(tf.sub(i , tr_data)),reduction_indices=1)
+        neighbor = tf.arg_min(distances,0)
+
+        #print tr_features[sess.run(neighbor)]
+        te_learned_features.append(tr_features[sess.run(neighbor)])
+
+    accuracy = tf.reduce_mean(tf.cast(tf.equal(te_learned_features, te_features), "float"))
+
+    fig, ax = plt.subplots()
+    ax.scatter(te_data.transpose()[0], te_data.transpose()[1], marker = 'o', s = 100, c = te_learned_features,       cmap=plt.cm.coolwarm )
+    ax.set_title('Test result')
+    plt.show()
+
+    end = time.time()
+    print ("Found in %.2f seconds" % (end-start))
+    print "Cluster assignments:", test
+    print "Accuracy:", sess.run(accuracy)
 ```
 
 

From 63aaf110367ebd104a025a502dc8b4e85d3059ee Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 24 Jan 2018 22:17:24 +0800
Subject: [PATCH 0249/1406] change page of BA

---
 assets/images/147.jpg     | Bin 0 -> 64663 bytes
 assets/images/148.jpg     | Bin 0 -> 38329 bytes
 assets/src/BA/BA.0.2.md   |   4 ++++
 assets/src/RAM/RAM.0.5.md |   2 --
 4 files changed, 4 insertions(+), 2 deletions(-)
 create mode 100644 assets/images/147.jpg
 create mode 100644 assets/images/148.jpg

diff --git a/assets/images/147.jpg b/assets/images/147.jpg
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literal 0
HcmV?d00001

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 1b263888..de22d5ac 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -94,4 +94,8 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
     print "Accuracy:", sess.run(accuracy)
 ```
 
+<p align="center">
+<img width="400" align="center" src="../../images/147.jpg" />
+</p>
+
 
diff --git a/assets/src/RAM/RAM.0.5.md b/assets/src/RAM/RAM.0.5.md
index 8b69f08b..74285dc5 100644
--- a/assets/src/RAM/RAM.0.5.md
+++ b/assets/src/RAM/RAM.0.5.md
@@ -21,8 +21,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 
-
-
 #### 优缺点
 
 优点：直接、快速 知名度高。

From 24bd9881b73d49eb6f9c96309bd10c77a5f247a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 22:18:16 +0800
Subject: [PATCH 0250/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index de22d5ac..9011a842 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -98,4 +98,8 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 <img width="400" align="center" src="../../images/147.jpg" />
 </p>
 
+<p align="center">
+<img width="400" align="center" src="../../images/148.jpg" />
+</p>
+
 

From a2ecf7b155dd0914c239dfe6513f6a1d2d2a7f2c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 22:18:47 +0800
Subject: [PATCH 0251/1406] Update BA.0.2.md

---
 assets/src/BA/BA.0.2.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.2.md b/assets/src/BA/BA.0.2.md
index 9011a842..8ca25db8 100644
--- a/assets/src/BA/BA.0.2.md
+++ b/assets/src/BA/BA.0.2.md
@@ -102,4 +102,8 @@ k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学
 <img width="400" align="center" src="../../images/148.jpg" />
 </p>
 
-
+```python
+Found in 6.73 seconds
+Cluster assignments: [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]
+Accuracy: 1.0
+```

From 280e2405deb5b5e7341641094854ba2583030be1 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 24 Jan 2018 22:19:37 +0800
Subject: [PATCH 0252/1406] change page

---
 assets/src/BA/BA.0.3.md | 109 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)
 create mode 100644 assets/src/BA/BA.0.3.md

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
new file mode 100644
index 00000000..8ca25db8
--- /dev/null
+++ b/assets/src/BA/BA.0.3.md
@@ -0,0 +1,109 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### K-近邻算法（KNN）
+
+K近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
+
+k近邻（k-Nearest Neighbors）采用向量空间模型来分类，是一种常用的监督学习方法。它的工作原理为：给定测试样本，基于某种距离度量找出训练集中与其最靠近的k个训练样本，然后基于这k个“邻居”的信息来进行预测。通常，在分类任务中可使用“投票法”，即选择这k个样本中出现最多的类别标记作为预测结果；在回归任务中可使用“平均法”，即将这k个样本的实值输出标记的平均值作为预测结果；还可基于距离远近进行加权平均或加权投票，距离越近的样本权重越大。
+
+k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学习技术在训练阶段仅仅是把样本保存起来，训练时间开销为零，待收到测试样本后再进行处理。
+
+最近邻分类器虽然简单，但它的泛化错误率不超过贝叶斯最优分类器的错误率的两倍。
+
+
+其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：
+<p align="center">
+<img width="200" align="center" src="../../images/87.jpg" />
+</p>
+
+注意：为了防止具有较大初始值域的属性比较小初始值域的属性的权重过大，在计算距离之前，需对每个属性值进行规范化。一般的规划方法有最小-最大规范化，零均值规范化，小数定标规范化等。
+
+最小-最大规范化：将原始数据值映射到[0,1]空间中，假定minA和maxA分别是属性A的最小值和最大值，则规范化的公式为：
+<p align="center">
+<img width="150" align="center" src="../../images/88.jpg" />
+</p>
+零均值规范化：基于属性A的均值和标准差上的规范化方法，具体计算如下：
+<p align="center">
+<img width="80" align="center" src="../../images/89.jpg" />
+</p>
+
+小数定标规范化：通过移动属性A的小数点位置进行规范化，小数点的移动位数依赖于A的最大绝对值。具体计算如下：(其中j是使得MAX（ v’ ）<1的最小整数)
+<p align="center">
+<img width="50" align="center" src="../../images/90.jpg" />
+</p>
+
+最近邻数K的确定，主要原理是选取产生最小误差率的k值。每次从k=1开始，使用检验集估计分类器的误差率；每次都允许增加一个近邻，重复该过程，选择误差率最小的k值。
+
+
+
+#### 应用案例
+
+
+```python
+    
+    %matplotlib inline
+    import time
+    import numpy as np
+    import tensorflow as tf
+    import matplotlib.pyplot as plt
+    from sklearn.datasets.samples_generator import make_circles
+
+    N=210
+    K=2
+    MAX_ITERS = 1000
+    cut=int(N*0.7)
+
+    # 生成训练和测试数据集
+    data, features = make_circles(n_samples=N, shuffle=True, noise= 0.12, factor=0.4)
+    tr_data, tr_features= data[:cut], features[:cut]
+    te_data,te_features=data[cut:], features[cut:]
+
+    fig, ax = plt.subplots()
+    ax.scatter(tr_data.transpose()[0], tr_data.transpose()[1], marker = 'o', s = 100, c = tr_features, cmap=plt.cm.coolwarm )
+    ax.set_title('Train data')
+    plt.show()
+
+    start = time.time()
+
+    points=tf.Variable(data)
+    cluster_assignments = tf.Variable(tf.zeros([N], dtype=tf.int64))
+
+    sess = tf.Session()
+    sess.run(tf.initialize_all_variables())
+
+    te_learned_features=[]
+    for i, j in zip(te_data, te_features):
+        distances = tf.reduce_sum(tf.square(tf.sub(i , tr_data)),reduction_indices=1)
+        neighbor = tf.arg_min(distances,0)
+
+        #print tr_features[sess.run(neighbor)]
+        te_learned_features.append(tr_features[sess.run(neighbor)])
+
+    accuracy = tf.reduce_mean(tf.cast(tf.equal(te_learned_features, te_features), "float"))
+
+    fig, ax = plt.subplots()
+    ax.scatter(te_data.transpose()[0], te_data.transpose()[1], marker = 'o', s = 100, c = te_learned_features,       cmap=plt.cm.coolwarm )
+    ax.set_title('Test result')
+    plt.show()
+
+    end = time.time()
+    print ("Found in %.2f seconds" % (end-start))
+    print "Cluster assignments:", test
+    print "Accuracy:", sess.run(accuracy)
+```
+
+<p align="center">
+<img width="400" align="center" src="../../images/147.jpg" />
+</p>
+
+<p align="center">
+<img width="400" align="center" src="../../images/148.jpg" />
+</p>
+
+```python
+Found in 6.73 seconds
+Cluster assignments: [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]
+Accuracy: 1.0
+```

From af028fdcf9ee48fe52d33ec11a2dacbb8e33be35 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 22:20:40 +0800
Subject: [PATCH 0253/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 614e973f..f80f8b4c 100644
--- a/README.md
+++ b/README.md
@@ -73,7 +73,7 @@
      * [本地散点平滑估计(LOESS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.5.md)  
  * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
      * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
-     * [学习矢量化（LVQ）]()
+     * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
      * [自组织映射算法（SOM）]()
      * [局部加权学习算法（LWL）]()
  * [正则化算法]()    

From c8c9a834a0bc92ccd52ee7d14287e5be993895e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 22:21:11 +0800
Subject: [PATCH 0254/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 101 ----------------------------------------
 1 file changed, 101 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 8ca25db8..dc84ae55 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -4,106 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### K-近邻算法（KNN）
 
-K近邻算法是一种基于类比的分类方法，主要通过给定的检验组与和它相似的训练组进行比较来学习。训练组用n个属性来描述，每个元组代表n维空间上的点。当给定一个未知元组时，K最近邻分类法搜索该模式空间，找出最接近未知元组的k个训练组，并将未知元组指派到模式空间中它的k个最近邻中的多数类中。
 
-k近邻（k-Nearest Neighbors）采用向量空间模型来分类，是一种常用的监督学习方法。它的工作原理为：给定测试样本，基于某种距离度量找出训练集中与其最靠近的k个训练样本，然后基于这k个“邻居”的信息来进行预测。通常，在分类任务中可使用“投票法”，即选择这k个样本中出现最多的类别标记作为预测结果；在回归任务中可使用“平均法”，即将这k个样本的实值输出标记的平均值作为预测结果；还可基于距离远近进行加权平均或加权投票，距离越近的样本权重越大。
 
-k近邻没有显式的训练过程，是“懒惰学习”的代表。此类学习技术在训练阶段仅仅是把样本保存起来，训练时间开销为零，待收到测试样本后再进行处理。
-
-最近邻分类器虽然简单，但它的泛化错误率不超过贝叶斯最优分类器的错误率的两倍。
-
-
-其中“最近邻”主要是以距离来度量的，一般使用欧几里得距离度量两个点或元组的距离，也可以使用曼哈顿距离或其他距离；欧几里得距离的主要计算公式如下：
-<p align="center">
-<img width="200" align="center" src="../../images/87.jpg" />
-</p>
-
-注意：为了防止具有较大初始值域的属性比较小初始值域的属性的权重过大，在计算距离之前，需对每个属性值进行规范化。一般的规划方法有最小-最大规范化，零均值规范化，小数定标规范化等。
-
-最小-最大规范化：将原始数据值映射到[0,1]空间中，假定minA和maxA分别是属性A的最小值和最大值，则规范化的公式为：
-<p align="center">
-<img width="150" align="center" src="../../images/88.jpg" />
-</p>
-零均值规范化：基于属性A的均值和标准差上的规范化方法，具体计算如下：
-<p align="center">
-<img width="80" align="center" src="../../images/89.jpg" />
-</p>
-
-小数定标规范化：通过移动属性A的小数点位置进行规范化，小数点的移动位数依赖于A的最大绝对值。具体计算如下：(其中j是使得MAX（ v’ ）<1的最小整数)
-<p align="center">
-<img width="50" align="center" src="../../images/90.jpg" />
-</p>
-
-最近邻数K的确定，主要原理是选取产生最小误差率的k值。每次从k=1开始，使用检验集估计分类器的误差率；每次都允许增加一个近邻，重复该过程，选择误差率最小的k值。
-
-
-
-#### 应用案例
-
-
-```python
-    
-    %matplotlib inline
-    import time
-    import numpy as np
-    import tensorflow as tf
-    import matplotlib.pyplot as plt
-    from sklearn.datasets.samples_generator import make_circles
-
-    N=210
-    K=2
-    MAX_ITERS = 1000
-    cut=int(N*0.7)
-
-    # 生成训练和测试数据集
-    data, features = make_circles(n_samples=N, shuffle=True, noise= 0.12, factor=0.4)
-    tr_data, tr_features= data[:cut], features[:cut]
-    te_data,te_features=data[cut:], features[cut:]
-
-    fig, ax = plt.subplots()
-    ax.scatter(tr_data.transpose()[0], tr_data.transpose()[1], marker = 'o', s = 100, c = tr_features, cmap=plt.cm.coolwarm )
-    ax.set_title('Train data')
-    plt.show()
-
-    start = time.time()
-
-    points=tf.Variable(data)
-    cluster_assignments = tf.Variable(tf.zeros([N], dtype=tf.int64))
-
-    sess = tf.Session()
-    sess.run(tf.initialize_all_variables())
-
-    te_learned_features=[]
-    for i, j in zip(te_data, te_features):
-        distances = tf.reduce_sum(tf.square(tf.sub(i , tr_data)),reduction_indices=1)
-        neighbor = tf.arg_min(distances,0)
-
-        #print tr_features[sess.run(neighbor)]
-        te_learned_features.append(tr_features[sess.run(neighbor)])
-
-    accuracy = tf.reduce_mean(tf.cast(tf.equal(te_learned_features, te_features), "float"))
-
-    fig, ax = plt.subplots()
-    ax.scatter(te_data.transpose()[0], te_data.transpose()[1], marker = 'o', s = 100, c = te_learned_features,       cmap=plt.cm.coolwarm )
-    ax.set_title('Test result')
-    plt.show()
-
-    end = time.time()
-    print ("Found in %.2f seconds" % (end-start))
-    print "Cluster assignments:", test
-    print "Accuracy:", sess.run(accuracy)
-```
-
-<p align="center">
-<img width="400" align="center" src="../../images/147.jpg" />
-</p>
-
-<p align="center">
-<img width="400" align="center" src="../../images/148.jpg" />
-</p>
-
-```python
-Found in 6.73 seconds
-Cluster assignments: [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]
-Accuracy: 1.0
-```

From 585dd6c69d12a529b0cdd8ee40fb9eb27c16e461 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 24 Jan 2018 22:21:39 +0800
Subject: [PATCH 0255/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index dc84ae55..75aab738 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -2,7 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### K-近邻算法（KNN）
+#### 学习矢量化
 
 
 

From 64c105bd1f8430fa70020e68eab0e3872b1813a4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:20:39 +0800
Subject: [PATCH 0256/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 75aab738..725e9bea 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -4,5 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 学习矢量化
 
+1. 网络结构 
+单层的神经元网络在输入节点与输出节点之间全互联，主要竟争是神经元之间的竞争；当神经元响应时候，该神经元输出为1，否则为0。
 
 

From 5a040fb8a91bc4f607411b6b012a11d84972c2b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:20:56 +0800
Subject: [PATCH 0257/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 725e9bea..cccbf052 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -4,7 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 学习矢量化
 
-1. 网络结构 
-单层的神经元网络在输入节点与输出节点之间全互联，主要竟争是神经元之间的竞争；当神经元响应时候，该神经元输出为1，否则为0。
+学习矢量量化（Learning Vector Quantization，简称LVQ），与1988年提出的一种用于模式分类的有监督学习算法，是一种结构简单、功能强大的有监督式神经网络分类算法。典型的学习矢量量化算法有：LVQ1、LVQ2、LVQ3，其中，前两种算法应用较为广泛，尤其以LVQ2应用最为广泛和有效。 
 
 

From ccd7854825729f73dbd755ea95ff2b108eedc190 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:21:56 +0800
Subject: [PATCH 0258/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index cccbf052..95de5ddb 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -4,6 +4,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 学习矢量化
 
-学习矢量量化（Learning Vector Quantization，简称LVQ），与1988年提出的一种用于模式分类的有监督学习算法，是一种结构简单、功能强大的有监督式神经网络分类算法。典型的学习矢量量化算法有：LVQ1、LVQ2、LVQ3，其中，前两种算法应用较为广泛，尤其以LVQ2应用最为广泛和有效。 
+学习矢量量化（Learning Vector Quantization，简称LVQ），与1988年提出的一种用于模式分类的有监督学习算法，是一种结构简单、功能强大的有监督式神经网络分类算法。典型的学习矢量量化算法有：LVQ1、LVQ2、LVQ3，其中，前两种算法应用较为广泛，尤其以LVQ2应用最为广泛和有效。  
+
+学习矢量量化是一种结构简单、功能强大的有监督式神经网络分类方法。作为一种最近邻原型分类器，LVQ在训练过程中通过对神经元权向量（原型向量）的不断更新，对其学习率的不断调整，能够使不同类别权向量之间的边界逐步收敛至贝叶斯分类边界。算法中，对获胜神经元（最近邻权向量）的选取是通过计算输入样本和权向量之间的距离的大小来判断的。与矢量量化（VQ）相比，LVQ最突出的特点就是其具有自适应性 
 
 

From 787173a6aa49dac4b40affa7fa77f7b75678ec3d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:34:03 +0800
Subject: [PATCH 0259/1406] change page

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From 2a44a57903934b16d1409ebf8cad4000300ba089 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:45:08 +0800
Subject: [PATCH 0260/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 79956abf..20024ada 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -13,6 +13,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="80" align="center" src="../../images/147.jpg" />
 </p>
-
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 

From 8367a2ff90119c7bf66ac78f2f53c1a65ba90aa1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:45:38 +0800
Subject: [PATCH 0261/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 20024ada..d461573e 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -10,8 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 1.向量量化
 向量量化的思路是，将高维输入空间分成若干不同的区域，对每个区域确定一个中心向量作为聚类的中心，与其处于同一区域的输入向量可用该中心向量来代表，从而形成了以各中心向量为聚类中心的点集。在图像处理领域常用各区域中心点（向量）的编码代替区域内的点来存储或传输，从而提出了各种基于向量量化的有损压缩技术，在二维输入平面上表示的中心向量分布称为Voronoi图，如图所示：
-<p align="center">
-<img width="80" align="center" src="../../images/147.jpg" />
-</p>
+
+
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 

From d15ed4d9b4cb7c21576222aeab9aabdf48d3b57e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 09:59:29 +0800
Subject: [PATCH 0262/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index d461573e..b1abc673 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -10,6 +10,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 1.向量量化
 向量量化的思路是，将高维输入空间分成若干不同的区域，对每个区域确定一个中心向量作为聚类的中心，与其处于同一区域的输入向量可用该中心向量来代表，从而形成了以各中心向量为聚类中心的点集。在图像处理领域常用各区域中心点（向量）的编码代替区域内的点来存储或传输，从而提出了各种基于向量量化的有损压缩技术，在二维输入平面上表示的中心向量分布称为Voronoi图，如图所示：
+<p align="center">
+<img width="400" align="center" src="../../images/147.jpg" />
+</p>
 
 
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。

From 32411005feef3337bbb9e79b3e144195f44cc1f8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:00:21 +0800
Subject: [PATCH 0263/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index b1abc673..83576997 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -17,3 +17,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 
+2.LVQ网络结构与工作原理
+<p align="center">
+<img width="400" align="center" src="../../images/148.jpg" />
+</p>

From fbe83c3347591dc6ff0f94db735418f370732beb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:01:27 +0800
Subject: [PATCH 0264/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 83576997..d9766f11 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -17,7 +17,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 
-2.LVQ网络结构与工作原理
+2.学习矢量量化网络结构与工作原理
 <p align="center">
 <img width="400" align="center" src="../../images/148.jpg" />
 </p>
+竞争层有m个神经元，输入层有n个神经元，两层之间完全连接。输出层每个神经元只与竞争层中的一组神经元连接，连接权重固定为1，训练过程中输入层和竞争层之间的权值逐渐被调整为聚类中心。当一个样本输入LVQ网络时，竞争层的神经元通过胜者为王学习规则产生获胜神经元，容许其输出为1，其它神经元输出为0。与获胜神经元所在组相连的输出神经元输出为1，而其它输出神经元为0，从而给出当前输入样本的模式类。将竞争层学习得到的类成为子类，而将输出层学习得到的类成为目标类。
+
+3.学习矢量量化网络学习算法

From 5873ddf1cdbde9e8c38782e74701a01597300e63 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:02:26 +0800
Subject: [PATCH 0265/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index d9766f11..97278aef 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -24,3 +24,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 竞争层有m个神经元，输入层有n个神经元，两层之间完全连接。输出层每个神经元只与竞争层中的一组神经元连接，连接权重固定为1，训练过程中输入层和竞争层之间的权值逐渐被调整为聚类中心。当一个样本输入LVQ网络时，竞争层的神经元通过胜者为王学习规则产生获胜神经元，容许其输出为1，其它神经元输出为0。与获胜神经元所在组相连的输出神经元输出为1，而其它输出神经元为0，从而给出当前输入样本的模式类。将竞争层学习得到的类成为子类，而将输出层学习得到的类成为目标类。
 
 3.学习矢量量化网络学习算法
+学习矢量量化学习规则结合了竞争学习规则和有导师学习规则，所以样本集应当为{(xi，di)}。其中di为l维，对应输出层的l个神经元，它只有一个分量为1，其他分量均为0。通常把竞争层的每个神经元指定给一个输出神经元，相应的权值为1，从而得到输出层的权值。比如某LVQ网络竞争层6个神经元，输出层3个神经元，代表3类。若将竞争层的1，3指定为第一个输出神经元，2，5指定为第二个输出神经元，3，6指定为第三个输出神经元。则竞争层到输出层的权值矩阵为:
+<p align="center">
+<img width="400" align="center" src="../../images/149.jpg" />
+</p>
+
+训练前预先定义好竞争层到输出层权重，从而指定了输出神经元类别，训练中不再改变。网络的学习通过改变输入层到竞争层的权重来进行。根据输入样本类别和获胜神经元所属类别，可判断当前分类是否正确。若分类正确，则将获胜神经元的权向量向输入向量方向调整，分类错误则向相反方向调整。
+<p align="center">
+<img width="400" align="center" src="../../images/150.jpg" />
+</p>

From 8578b80f6b31324d2eb5463d53fcacd705f88519 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:04:17 +0800
Subject: [PATCH 0266/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 97278aef..24fff54c 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -33,3 +33,18 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="400" align="center" src="../../images/150.jpg" />
 </p>
+
+学习矢量量化网络学习算法的步骤如下:
+* 初始化。竞争层各神经元权值向量随机赋值小随机数，确定初始学习速率和训练次数。
+* 输入样本向量。
+* 寻找激活神经元。
+* 根据分类是否正确按照不同规则调整获胜神经元的权值，当网络分类结果与教师信号一致时，向输入样本方向调整权值：
+
+<p align="center">
+<img width="100" align="center" src="../../images/151.jpg" />
+</p>
+
+当网络分类结果与教师信号不一致时，向输入样本反方向调整权值：
+<p align="center">
+<img width="100" align="center" src="../../images/152.jpg" />
+</p>

From 740755f8fe4c97e5c8904520c8ee2309cba8ac92 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:04:34 +0800
Subject: [PATCH 0267/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 24fff54c..33c0575c 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -41,10 +41,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 根据分类是否正确按照不同规则调整获胜神经元的权值，当网络分类结果与教师信号一致时，向输入样本方向调整权值：
 
 <p align="center">
-<img width="100" align="center" src="../../images/151.jpg" />
+<img width="300" align="center" src="../../images/151.jpg" />
 </p>
 
 当网络分类结果与教师信号不一致时，向输入样本反方向调整权值：
 <p align="center">
-<img width="100" align="center" src="../../images/152.jpg" />
+<img width="300" align="center" src="../../images/152.jpg" />
 </p>

From 93ff387a1319d68f9750ef67dff144dc01621efc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:04:50 +0800
Subject: [PATCH 0268/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 33c0575c..94815325 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -26,7 +26,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 3.学习矢量量化网络学习算法
 学习矢量量化学习规则结合了竞争学习规则和有导师学习规则，所以样本集应当为{(xi，di)}。其中di为l维，对应输出层的l个神经元，它只有一个分量为1，其他分量均为0。通常把竞争层的每个神经元指定给一个输出神经元，相应的权值为1，从而得到输出层的权值。比如某LVQ网络竞争层6个神经元，输出层3个神经元，代表3类。若将竞争层的1，3指定为第一个输出神经元，2，5指定为第二个输出神经元，3，6指定为第三个输出神经元。则竞争层到输出层的权值矩阵为:
 <p align="center">
-<img width="400" align="center" src="../../images/149.jpg" />
+<img width="300" align="center" src="../../images/149.jpg" />
 </p>
 
 训练前预先定义好竞争层到输出层权重，从而指定了输出神经元类别，训练中不再改变。网络的学习通过改变输入层到竞争层的权重来进行。根据输入样本类别和获胜神经元所属类别，可判断当前分类是否正确。若分类正确，则将获胜神经元的权向量向输入向量方向调整，分类错误则向相反方向调整。

From f5ab02d11b71b1d44baed1db6946642798d5da77 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:08:10 +0800
Subject: [PATCH 0269/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 94815325..c350dda1 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -48,3 +48,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/152.jpg" />
 </p>
+其他非激活神经元权值保持不变。
+* 更新学习速率
+<p align="center">
+<img width="300" align="center" src="../../images/153.jpg" />
+</p>
+* 当训练次数未达到设定的次数时，转到步骤输入样本向量输入下一个样本，重复各步骤直到达到设定训练次数为止。上述训练过程中，要保证η（t）为单调下降函数。

From 0d188d549f67fec0cd3936089e76666897c7303a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:11:54 +0800
Subject: [PATCH 0270/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index c350dda1..d3b66a95 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -54,3 +54,17 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/153.jpg" />
 </p>
 * 当训练次数未达到设定的次数时，转到步骤输入样本向量输入下一个样本，重复各步骤直到达到设定训练次数为止。上述训练过程中，要保证η（t）为单调下降函数。
+
+#### 结构
+学习矢量量化神经网络有三层组成：输入层，竞争层，线性输出层。
+学习矢量量化网络是SOFM网络一种有监督形式的扩展，两者有效结合可更好地发挥竞争学习和有监督学习的优点。
+
+连接方式
+输入层与竞争层之间采用全连接的方式，竞争层与线性输出层之间采用部分连接的方式。竞争层神经元个数总是大于线性输出层神经元个数，每个竞争层神经元只与一个线性输出层神经元相连接且连接权值恒为1。但是，每个线性输出层神经元可以与多个竞争层神经元相连接。竞争层神经元与线性输出层神经元的值只能是1或0。
+当某个输入模式被送至网络时，与输入模式距离最近的竞争层神经元被激活，神经元的状态为“1”，而其他竞争层神经元的状态均为“0”。因此，与被激活神经元相连接的线性输出层神经元状态也为“1”，而其他线性输出层神经元的状态均为“0”
+
+基本步骤为：
+
+初始化输入层与竞争层之间的权值W_ij及学习率η(η>0)。
+将输入向量<img width="200" align="center" src="../../images/154.jpg" />送入到输入层，并计算竞争层神经元与输入向量的距离：
+<img width="200" align="center" src="../../images/155.jpg" />

From afb043bc37ca8734e8c2b00163a3b6d19d047ec7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:13:43 +0800
Subject: [PATCH 0271/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 174 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 173 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index d3b66a95..a02f193f 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -67,4 +67,176 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 初始化输入层与竞争层之间的权值W_ij及学习率η(η>0)。
 将输入向量<img width="200" align="center" src="../../images/154.jpg" />送入到输入层，并计算竞争层神经元与输入向量的距离：
-<img width="200" align="center" src="../../images/155.jpg" />
+<img width="200" align="center" src="../../images/155.jpg" />。
+
+#### 案例
+```python
+
+function [dw,ls] = learnlv3(w,p,z,n,a,t,e,gW,gA,d,lp,ls)
+%LEARNLV2 LVQ2 weight learning function.
+%
+% Syntax
+% 
+% [dW,LS] = learnlv3(w,p,n,a,T,lp,ls,Ttrain,C)
+% info = learnlv2(code)
+%
+% Description
+%
+% LEARNLV3 is the OLVQ weight learning function.
+%
+% LEARNLV2(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,
+% W - SxR weight matrix (or Sx1 bias vector).
+% P - RxQ input vectors (or ones(1,Q)).
+% Z - SxQ weighted input vectors.
+% N - SxQ net input vectors.
+% A - SxQ output vectors.
+% T - SxQ layer target vectors.
+% E - SxQ layer error vectors.
+% gW - SxR weight gradient with respect to performance.
+% gA - SxQ output gradient with respect to performance.
+% D - SxS neuron distances.
+% LP - Learning parameters, none, LP = [].
+% LS - Learning state, initially should be = [].
+% and returns,
+% dW - SxR weight (or bias) change matrix.
+% LS - New learning state.
+%
+% Learning occurs according to LEARNLV1's learning parameter,
+% shown here with its default value.
+% LP.lr - 0.01 - Learning rate
+%
+% LEARNLV2(CODE) returns useful information for each CODE string:
+% 'pnames' - Returns names of learning parameters.
+% 'pdefaults' - Returns default learning parameters.
+% 'needg' - Returns 1 if this function uses gW or gA.
+%
+% Examples
+%
+% Here we define a sample input P, output A, weight matrix W, and
+% output gradient gA for a layer with a 2-element input and 3 neurons.
+% We also define the learning rate LR.
+%
+% p = rand(2,1);
+% w = rand(3,2);
+% n = negdist(w,p);
+% a = compet(n);
+% gA = [-1;1; 1];
+% lp.lr = 0.5;
+%
+% Since LEARNLV2 only needs these values to calculate a weight
+% change (see Algorithm below), we will use them to do so.
+%
+% dW = learnlv3(w,p,n,a,lp,Ttrain,C)
+%
+% Network Use
+%
+% You can create a standard network that uses LEARNLV2 with NEWLVQ.
+%
+% To prepare the weights of layer i of a custom network
+% to learn with LEARNLV1:
+% 1) Set NET.trainFcn to 'trainwb1'.
+% (NET.trainParam will automatically become TRAINWB1's default parameters.)
+% 2) Set NET.adaptFcn to 'adaptwb'.
+% (NET.adaptParam will automatically become TRAINWB1's default parameters.)
+% 3) Set each NET.inputWeights{i,j}.learnFcn to 'learnlv2'.
+% Set each NET.layerWeights{i,j}.learnFcn to 'learnlv2'.
+% (Each weight learning parameter property will automatically
+% be set to LEARNLV2's default parameters.)
+%
+% To train the network (or enable it to adapt):
+% 1) Set NET.trainParam (or NET.adaptParam) properties as desired.
+% 2) Call TRAIN (or ADAPT).
+%
+% Algorithm
+%
+% LEARNLV3 calculates the weight change dW for a given neuron from
+% the neuron's input P, output A, train vector target T train, output
+% conexion matrix C and learning rate LR
+% according to the OLVQ rule, given i the index of the neuron whose
+% output a(i) is 1:
+%
+% dw(i,:) = +lr*(p-w(i,:)) if C(:,i) = Ttrain
+% = -lr*(p-w(i,:)) if C(:,i) ~= Ttrain
+%
+% if C(:,i) ~= Ttrain then the index j is found of the neuron with the
+% greatest net input n(k), from the neurons whose C(:,k)=Ttrain. This
+% neuron's weights are updated as follows:
+%
+% dw(j,:) = +lr*(p-w(i,:))
+%
+% See also LEARNLV1, ADAPTWB, TRAINWB, ADAPT, TRAIN.
+
+% Mark Beale, 11-31-97
+% Copyright (c) 1992-1998 by The MathWorks, Inc.
+% $Revision: 1.1.1.1 $
+
+% FUNCTION INFO
+% =============
+if isstr(w)
+  switch lower(w)
+  case 'name'
+      dw = 'Learning Vector Quantization 3';
+  case 'pnames'
+    dw = {'lr';'window'};
+  case 'pdefaults'
+    lp.lr = 0.01;
+    lp.window = 0.25;
+    dw = lp;
+  case 'needg'
+    dw = 1;
+  otherwise
+    error('NNET:Arguments','Unrecognized code.')
+  end
+  return
+end
+
+
+% CALCULATION
+% ===========
+
+[S,R] = size(w);
+Q = size(p,2);
+pt = p';
+dw = zeros(S,R);
+% For each q...
+for q=1:Q
+
+  % Find closest neuron k1 找到获胜神经元
+  nq = n(:,q);
+  k1 = find(nq == max(nq));
+  k1 = k1(1);
+
+  % Find next closest neuron k2 次获胜神经元
+  nq(k1) = -inf;
+  k2 = find(nq == max(nq));
+  k2 = k2(1);
+
+
+  % and if x falls into the window...
+  d1 = abs(n(k1,q)); % Shorter distance
+  d2 = abs(n(k2,q)); % Greater distance
+
+  if d2/d1 > ((1-lp.window)/(1+lp.window))
+
+      % then move incorrect neuron away from input,
+      % and the correct neuron towards the input
+      ptq = pt(q,:);
+      if gA(k1,q) ~= gA(k2,q)
+          % indicate the incorrect neuron with i, the other with j
+          if gA(k1,q) ~= 0
+              i = k1;
+              j = k2;
+          else
+              i = k2;
+              j = k1;
+          end
+          dw(i,:) = dw(i,:) - lp.lr*(ptq - w(i,:));
+          dw(j,:) = dw(j,:) + lp.lr*(ptq - w(j,:));
+      else
+          dw(k1,:) = dw(k1,:) + 0.11*lp.window*(ptq-w(k1,:));
+       % dw(k2,:) = dw(k2,:) + 0.11*lp.window*(ptq-w(k2,:));
+      end
+  end
+end
+
+```

From 8a7cb43c84fe63ac4c82c3da5d719b3b8830c19e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:14:12 +0800
Subject: [PATCH 0272/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index a02f193f..69cc85f3 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -201,12 +201,12 @@ dw = zeros(S,R);
 % For each q...
 for q=1:Q
 
-  % Find closest neuron k1 找到获胜神经元
+  % Find closest neuron k1 
   nq = n(:,q);
   k1 = find(nq == max(nq));
   k1 = k1(1);
 
-  % Find next closest neuron k2 次获胜神经元
+  % Find next closest neuron k2 
   nq(k1) = -inf;
   k2 = find(nq == max(nq));
   k2 = k2(1);

From 444fa12eb885257c496d67917f022c9dd66d07b9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Jan 2018 10:18:28 +0800
Subject: [PATCH 0273/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 69cc85f3..17e495fd 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -18,6 +18,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 
 2.学习矢量量化网络结构与工作原理
+学习矢量量化神经网络有三层组成：输入层，竞争层，线性输出层。
 <p align="center">
 <img width="400" align="center" src="../../images/148.jpg" />
 </p>
@@ -55,11 +56,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 * 当训练次数未达到设定的次数时，转到步骤输入样本向量输入下一个样本，重复各步骤直到达到设定训练次数为止。上述训练过程中，要保证η（t）为单调下降函数。
 
-#### 结构
-学习矢量量化神经网络有三层组成：输入层，竞争层，线性输出层。
 学习矢量量化网络是SOFM网络一种有监督形式的扩展，两者有效结合可更好地发挥竞争学习和有监督学习的优点。
 
-连接方式
+连接方式：
+
 输入层与竞争层之间采用全连接的方式，竞争层与线性输出层之间采用部分连接的方式。竞争层神经元个数总是大于线性输出层神经元个数，每个竞争层神经元只与一个线性输出层神经元相连接且连接权值恒为1。但是，每个线性输出层神经元可以与多个竞争层神经元相连接。竞争层神经元与线性输出层神经元的值只能是1或0。
 当某个输入模式被送至网络时，与输入模式距离最近的竞争层神经元被激活，神经元的状态为“1”，而其他竞争层神经元的状态均为“0”。因此，与被激活神经元相连接的线性输出层神经元状态也为“1”，而其他线性输出层神经元的状态均为“0”
 
@@ -69,7 +69,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 将输入向量<img width="200" align="center" src="../../images/154.jpg" />送入到输入层，并计算竞争层神经元与输入向量的距离：
 <img width="200" align="center" src="../../images/155.jpg" />。
 
-#### 案例
+#### 应用案例
+
 ```python
 
 function [dw,ls] = learnlv3(w,p,z,n,a,t,e,gW,gA,d,lp,ls)

From 775dc15afaeeda4a733eb7a843abe264cb809560 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:06:48 +0800
Subject: [PATCH 0274/1406] change page

---
 assets/src/BA/BA.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/BA/BA.0.4.md

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
new file mode 100644
index 00000000..93b3f84d
--- /dev/null
+++ b/assets/src/BA/BA.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 自组织映射算法（SOM）

From 76f57adaa5c7269dd60098cb289df63fe438472f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:09:11 +0800
Subject: [PATCH 0275/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f80f8b4c..f237bc93 100644
--- a/README.md
+++ b/README.md
@@ -74,7 +74,7 @@
  * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
      * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
-     * [自组织映射算法（SOM）]()
+     * [自组织映射算法（SOM）](http://www.infoq.com/cn/articles/etcd-interpretation-application-scenario-implement-principle)
      * [局部加权学习算法（LWL）]()
  * [正则化算法]()    
      * [岭回归（Ridge Regression）]()

From b9d7f80f5b6815e27601497ff6f73d53b5547994 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:10:50 +0800
Subject: [PATCH 0276/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f237bc93..8015a352 100644
--- a/README.md
+++ b/README.md
@@ -74,7 +74,7 @@
  * [基于实例的学习算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.1.md) 
      * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
-     * [自组织映射算法（SOM）](http://www.infoq.com/cn/articles/etcd-interpretation-application-scenario-implement-principle)
+     * [自组织映射算法（SOM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.4.md)
      * [局部加权学习算法（LWL）]()
  * [正则化算法]()    
      * [岭回归（Ridge Regression）]()

From 34619e6832b26a8f8172189ccf2d9d8d34137777 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:16:11 +0800
Subject: [PATCH 0277/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index 93b3f84d..727b187b 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -3,3 +3,9 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 自组织映射算法（SOM）
+
+自组织映射（SOM）或自组织特征映射（SOFM）是一种使用非监督式学习来产生训练样本的输入空间的一个低维（通常是二维）离散化的表示的人工神经网络（ANN）。自组织映射与其他人工神经网络的不同之处在于它使用一个邻近函数来保持输入控件的拓扑性质。
+
+自组织映射（SOM）是一种非监督学习，一个常见的非监督式学习是数据聚类。在人工神经网络中，自组织映射（SOM）和适应性共振理论（ART）则是最常用的非监督式学习。
+
+非监督式学习是一种机器学习的方式，并不需要人力来输入标签。它是监督式学习和强化学习等策略之外的一种选择。在监督式学习中，典型的任务是分类和回归分析，且需要使用到人工预先准备好的范例(base)。

From 416c29c01eb68e2c3594c56244dde6174f793953 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:16:39 +0800
Subject: [PATCH 0278/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index 727b187b..deb3975f 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -9,3 +9,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 自组织映射（SOM）是一种非监督学习，一个常见的非监督式学习是数据聚类。在人工神经网络中，自组织映射（SOM）和适应性共振理论（ART）则是最常用的非监督式学习。
 
 非监督式学习是一种机器学习的方式，并不需要人力来输入标签。它是监督式学习和强化学习等策略之外的一种选择。在监督式学习中，典型的任务是分类和回归分析，且需要使用到人工预先准备好的范例(base)。
+
+自组织映射中学习的目标是使网络的不同部分对输入模式有相似的响应。这部分的灵感是来自于人类大脑皮层的不同部分处理视觉、听觉或其他感官信息的方式。
+
+自组织映射的训练实例。蓝色斑点是训练数据的分布，而小白斑点是从该分布走出的目前的训练数据。起初（左图）SOM节点处在数据空间的任意位置。选择离训练数据最近的（用黄色高亮的）节点。它会向着训练数据移动，网格上它的邻居节点也会（在较小程度上）如此移动。经过多次迭代后的网格会趋于近似的数据分布。
+
+
+神经元的权重初始化为小随机值或均匀采样自两个最大的主成分特征向量范围。用后一种方法初始化，学习的速率就会更快，因为初始的权重已经是SOM权重的一个很好的近似了。
+
+必须提供给网络大量的能够实例向量来尽可能近地表示映射中期望的那些类型的向量。这些例子通常在迭代中数次使用。

From 054c697d5e970dec927e3f71d271e1c8d1a80e13 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:19:15 +0800
Subject: [PATCH 0279/1406] change page of BA

---
 assets/images/158.jpg   | Bin 0 -> 43671 bytes
 assets/src/BA/BA.0.4.md |   6 +++++-
 2 files changed, 5 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/158.jpg

diff --git a/assets/images/158.jpg b/assets/images/158.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..a40fd9927691b3a2a97ed323503032bdeaa3284b
GIT binary patch
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diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index deb3975f..36a8b7e1 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -12,7 +12,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 自组织映射中学习的目标是使网络的不同部分对输入模式有相似的响应。这部分的灵感是来自于人类大脑皮层的不同部分处理视觉、听觉或其他感官信息的方式。
 
-自组织映射的训练实例。蓝色斑点是训练数据的分布，而小白斑点是从该分布走出的目前的训练数据。起初（左图）SOM节点处在数据空间的任意位置。选择离训练数据最近的（用黄色高亮的）节点。它会向着训练数据移动，网格上它的邻居节点也会（在较小程度上）如此移动。经过多次迭代后的网格会趋于近似的数据分布。
+自组织映射的训练实例。蓝色斑点是训练数据的分布，而小白斑点是从该分布走出的目前的训练数据。起初SOM节点处在数据空间的任意位置。选择离训练数据最近的（用黄色高亮的）节点。它会向着训练数据移动，网格上它的邻居节点也会（在较小程度上）如此移动。经过多次迭代后的网格会趋于近似的数据分布。
+
+<p align="center">
+<img width="200" align="center" src="../../images/158.jpg" />
+</p>
 
 
 神经元的权重初始化为小随机值或均匀采样自两个最大的主成分特征向量范围。用后一种方法初始化，学习的速率就会更快，因为初始的权重已经是SOM权重的一个很好的近似了。

From 2beeb149e7a77fe3da4a0bdbd3a4750533ff8d36 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:20:50 +0800
Subject: [PATCH 0280/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index 36a8b7e1..9df7a87d 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -12,12 +12,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 自组织映射中学习的目标是使网络的不同部分对输入模式有相似的响应。这部分的灵感是来自于人类大脑皮层的不同部分处理视觉、听觉或其他感官信息的方式。
 
-自组织映射的训练实例。蓝色斑点是训练数据的分布，而小白斑点是从该分布走出的目前的训练数据。起初SOM节点处在数据空间的任意位置。选择离训练数据最近的（用黄色高亮的）节点。它会向着训练数据移动，网格上它的邻居节点也会（在较小程度上）如此移动。经过多次迭代后的网格会趋于近似的数据分布。
-
 <p align="center">
-<img width="200" align="center" src="../../images/158.jpg" />
+<img width="400" align="center" src="../../images/158.jpg" />
 </p>
 
+自组织映射的训练实例。蓝色斑点是训练数据的分布，而小白斑点是从该分布走出的目前的训练数据。起初SOM节点处在数据空间的任意位置。选择离训练数据最近的（用黄色高亮的）节点。它会向着训练数据移动，网格上它的邻居节点也会（在较小程度上）如此移动。经过多次迭代后的网格会趋于近似的数据分布。
+
+
 
 神经元的权重初始化为小随机值或均匀采样自两个最大的主成分特征向量范围。用后一种方法初始化，学习的速率就会更快，因为初始的权重已经是SOM权重的一个很好的近似了。
 

From b29f686eebc7f7fe42ed5d031756766f5ea3a1c2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:21:49 +0800
Subject: [PATCH 0281/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index 9df7a87d..6b100902 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -23,3 +23,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 神经元的权重初始化为小随机值或均匀采样自两个最大的主成分特征向量范围。用后一种方法初始化，学习的速率就会更快，因为初始的权重已经是SOM权重的一个很好的近似了。
 
 必须提供给网络大量的能够实例向量来尽可能近地表示映射中期望的那些类型的向量。这些例子通常在迭代中数次使用。
+
+训练采用竞争性学习。当训练样本提供给网络的时候，就会计算它与每个权重之间的欧氏距离。权重向量与输入最相似的神经元称作最佳匹配单元（BMU）。SOM栅格中BMU的权重以及与其邻近的神经元会向着输入向量调整。从BMU变化的量会随着（栅格中）时间和距离而降低。拥有权值 Wv(s) 的神经元v的更新公式为
+
+Wv(s + 1) = Wv(s) + Θ(u, v, s) α(s)(D(t) - Wv(s)),

From a57eb9e5d28d804a376ddbe0328d0a1f3d7be537 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:22:40 +0800
Subject: [PATCH 0282/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index 6b100902..e78b40a6 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -27,3 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 训练采用竞争性学习。当训练样本提供给网络的时候，就会计算它与每个权重之间的欧氏距离。权重向量与输入最相似的神经元称作最佳匹配单元（BMU）。SOM栅格中BMU的权重以及与其邻近的神经元会向着输入向量调整。从BMU变化的量会随着（栅格中）时间和距离而降低。拥有权值 Wv(s) 的神经元v的更新公式为
 
 Wv(s + 1) = Wv(s) + Θ(u, v, s) α(s)(D(t) - Wv(s)),
+
+其中 s 为步长指数，t 是训练样本的指数，D(t) 是输入向量，u 是 D(t) 的BMU指数，α(s) 是一个单调递减的学习系数；Θ(u, v, s) 是在步长为 s 下给出神经元 u 和神经元 v 之间距离的邻近函数。 根据实现的不同，t 可以系统地（ 0, 1, 2...T-1，然后重复，T 为训练样本的大小），也可以随机从数据集中取出（Bootstrap抽样），或采用其他一些抽样方法（如jackknifing）。
+
+

From 82667a52b7a18e25c4b1eff961f6629003fc7861 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:23:20 +0800
Subject: [PATCH 0283/1406] Update BA.0.4.md

---
 assets/src/BA/BA.0.4.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BA/BA.0.4.md b/assets/src/BA/BA.0.4.md
index e78b40a6..9f7c74e7 100644
--- a/assets/src/BA/BA.0.4.md
+++ b/assets/src/BA/BA.0.4.md
@@ -30,4 +30,10 @@ Wv(s + 1) = Wv(s) + Θ(u, v, s) α(s)(D(t) - Wv(s)),
 
 其中 s 为步长指数，t 是训练样本的指数，D(t) 是输入向量，u 是 D(t) 的BMU指数，α(s) 是一个单调递减的学习系数；Θ(u, v, s) 是在步长为 s 下给出神经元 u 和神经元 v 之间距离的邻近函数。 根据实现的不同，t 可以系统地（ 0, 1, 2...T-1，然后重复，T 为训练样本的大小），也可以随机从数据集中取出（Bootstrap抽样），或采用其他一些抽样方法（如jackknifing）。
 
+邻近函数Θ(u, v, s)取决于BMU（神经元u）与神经元v之间的栅格距离。在最简单的形式中，对所有足够接近BMU的神经元都是1，其余都是0，但高斯函数也是一种常见的选择。不管函数形式如何，邻近函数都会随着时间收缩。 在起初邻域范围很大的时候，自组织发生在全局范围内。当邻域范围缩小到仅有两个神经元时，权值会收敛于局部估计值。在一些实现中，学习系数α会随着增加s而平稳减小，另一些实现（特别是t扫描训练数据集的情况）中步进式地下降，每 T 步一次。
+
+对每个输入向量这个过程都会重复（通常很多次）循环λ。该网络把输入数据集中的类别或模式与相关联的输出节点拉近。如果可以重命名这些模式，这些名称就会附加到已训练的网络中的相关节点中。
+
+在映射中，会有一个单一“获胜”神经元：该神经元的权重向量与输入向量最接近。这可以很容易由计算输入向量和权值向量的欧氏距离确定。
+
 

From f390a8dcf295a7ecc9868284c02b94dc51a54f40 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 26 Jan 2018 09:30:08 +0800
Subject: [PATCH 0284/1406] change page

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 8015a352..03dc6d69 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,7 @@
 
  * [深度神经网络](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.01.md)
  * [深度学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.02.md)
+ * [深度学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.03.md)
  * [深度学习的应用案例]()
  * [深度学习所需要的数据]()
 

From 1a5c3aea60f1510b6959cda0076187eddc2380b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:20:11 +0800
Subject: [PATCH 0285/1406] change page of BA

---
 README.md               | 2 +-
 assets/src/BA/BA.0.5.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/BA/BA.0.5.md

diff --git a/README.md b/README.md
index 03dc6d69..1f0f14c6 100644
--- a/README.md
+++ b/README.md
@@ -76,7 +76,7 @@
      * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
      * [自组织映射算法（SOM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.4.md)
-     * [局部加权学习算法（LWL）]()
+     * [局部加权学习算法（LWL）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
  * [正则化算法]()    
      * [岭回归（Ridge Regression）]()
      * [LASSO（Least Absolute Shrinkage and Selection Operator）]()
diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
new file mode 100644
index 00000000..5e74fbbd
--- /dev/null
+++ b/assets/src/BA/BA.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 局部加权学习算法（LWL）

From 8f23a1ff6b4caff72ea7230d851f8085c1b2bdee Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:23:45 +0800
Subject: [PATCH 0286/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 5e74fbbd..33e03792 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -2,4 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 局部加权学习算法（LWL）
+#### 局部加权学习算法（LWR）
+
+局部加权回归（LWR）是非参数学习方法。 首先参数学习方法是这样一种方法：在训练完成所有数据后得到一系列训练参数，然后根据训练参数来预测新样本的值，这时不再依赖之前的训练数据了，参数值是确定的。而非参数学习方法是这样一种算法：在预测新样本值时候每次都会重新训练数据得到新的参数值，也就是说每次预测新样本都会依赖训练数据集合，所以每次得到的参数值是不确定的。

From 33738fd31effdec2f03b78253929d75171faf960 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:24:21 +0800
Subject: [PATCH 0287/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1f0f14c6..f8a87fc3 100644
--- a/README.md
+++ b/README.md
@@ -76,7 +76,7 @@
      * [K-近邻算法（KNN）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.2.md)
      * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
      * [自组织映射算法（SOM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.4.md)
-     * [局部加权学习算法（LWL）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
+     * [局部加权学习算法（LWR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
  * [正则化算法]()    
      * [岭回归（Ridge Regression）]()
      * [LASSO（Least Absolute Shrinkage and Selection Operator）]()

From 8e2f0dc4b7924124577e332b75f95c8b9b2fb078 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:48:43 +0800
Subject: [PATCH 0288/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 33e03792..eef0d383 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -5,3 +5,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 局部加权学习算法（LWR）
 
 局部加权回归（LWR）是非参数学习方法。 首先参数学习方法是这样一种方法：在训练完成所有数据后得到一系列训练参数，然后根据训练参数来预测新样本的值，这时不再依赖之前的训练数据了，参数值是确定的。而非参数学习方法是这样一种算法：在预测新样本值时候每次都会重新训练数据得到新的参数值，也就是说每次预测新样本都会依赖训练数据集合，所以每次得到的参数值是不确定的。
+局部加权回归（LWR）是我们遇到的第一个non-parametric（非参数）学习算法，而线性回归则是我们遇到的以一个parametric（参数）学习算法。因为参数学习算法它有固定的明确的参数，所以参数一旦确定，就不会改变了，我们不需要在保留训练集中的训练样本。而非参数学习算法，每进行一次预测，就需要重新学习一组，是变化的，所以需要一直保留训练样本。因而，当训练集的容量较大时，非参数学习算法需要占用更多的存储空间，计算速度也较慢。所以有得必有失，效果好了，计算速度却降下来了。

From 80cd3d6ae4c51406ea90985dfc56aefc1702ed25 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:52:37 +0800
Subject: [PATCH 0289/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index eef0d383..142d64a5 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -6,3 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 局部加权回归（LWR）是非参数学习方法。 首先参数学习方法是这样一种方法：在训练完成所有数据后得到一系列训练参数，然后根据训练参数来预测新样本的值，这时不再依赖之前的训练数据了，参数值是确定的。而非参数学习方法是这样一种算法：在预测新样本值时候每次都会重新训练数据得到新的参数值，也就是说每次预测新样本都会依赖训练数据集合，所以每次得到的参数值是不确定的。
 局部加权回归（LWR）是我们遇到的第一个non-parametric（非参数）学习算法，而线性回归则是我们遇到的以一个parametric（参数）学习算法。因为参数学习算法它有固定的明确的参数，所以参数一旦确定，就不会改变了，我们不需要在保留训练集中的训练样本。而非参数学习算法，每进行一次预测，就需要重新学习一组，是变化的，所以需要一直保留训练样本。因而，当训练集的容量较大时，非参数学习算法需要占用更多的存储空间，计算速度也较慢。所以有得必有失，效果好了，计算速度却降下来了。
+
+```python
+
+```

From c53f6e09fcdbb5445cc6ad4d18b968df83b69532 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:53:35 +0800
Subject: [PATCH 0290/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 138 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 138 insertions(+)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 142d64a5..41413a13 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -9,4 +9,142 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ```python
 
+using namespace std;  
+  
+const int Number = 6;  
+const int Dimesion = 3;  
+const float learningRate=0.001;       
+const float errorThr=1; //variance threshold  
+const int MAX=1000;     //Max times of iteration  
+  
+typedef struct Data{  
+    float vectorComponent[Dimesion];  
+}vectorData;  
+  
+vectorData x[Number] = {  
+    {1,1,8},  
+    {1,1,3},  
+    {1,1,6},  
+    {1,2,3},  
+    {1,2,1},  
+    {1,2,2},  
+};  
+float y[Number]={2,10,5,13,5,8};  
+/lwr(局部线性回归)  
+float weightValue(vectorData xi,vectorData x){  
+    float weight = 0.0;  
+    for(int i=0;i<Dimesion;i++){  
+        weight+=pow(xi.vectorComponent[i]-x.vectorComponent[i],2);  
+    }  
+    float tempWeight = exp(-(weight/(2*36)));  
+    if(tempWeight<0.02)  
+        tempWeight = 0.0;  
+    return tempWeight;  
+}  
+  
+float multiPly(vectorData x1,vectorData x2){  
+    float temp = 0.0;  
+    for(int i=0;i<Dimesion;i++){  
+        temp += x1.vectorComponent[i]*x2.vectorComponent[i];  
+    }  
+    return temp;  
+}  
+  
+vectorData addVectorData(vectorData x1,vectorData x2){  
+    vectorData temp;  
+    for(int i=0;i<Dimesion;i++)  
+        temp.vectorComponent[i] = x1.vectorComponent[i]+x2.vectorComponent[i];  
+    return temp;  
+}  
+  
+vectorData minusVectorData(vectorData x1,vectorData x2){  
+    vectorData temp;  
+    for(int i=0;i<Dimesion;i++)  
+        temp.vectorComponent[i] = x1.vectorComponent[i]-x2.vectorComponent[i];  
+    return temp;  
+}  
+  
+vectorData numberMultiVectorData(float para,vectorData x1){  
+    vectorData temp;  
+    for(int i=0;i<Dimesion;i++)  
+        temp.vectorComponent[i] = x1.vectorComponent[i]*para;  
+    return temp;  
+}  
+float costFunction(vectorData parameter[],vectorData inputData[],float inputResultData[],vectorData object){  
+    float costValue = 0.0;  
+    float tempValue = 0.0;  
+    float weightedValue = 0.0;  
+    for(int i=0;i<Number;i++){  
+        tempValue = 0.0;  
+          
+        //consider all the parameters although most of them is zero  
+        for(int j=0;j<Number;j++)  
+            tempValue += multiPly(parameter[j],inputData[i]);  
+        costValue += weightValue(inputData[i],object)*pow((inputResultData[i]-tempValue),2);      
+    }  
+  
+    return (costValue/2*4);  
+}  
+  
+  
+int LocallyWeightedAgression(vectorData parameter[],vectorData inputData[],float resultData[],vectorData objectVector){  
+    float tempValue = 0.0;  
+    float errorCost = 0.0;  
+    float weightedValue = 0.0;  
+    errorCost=costFunction(parameter,inputData,resultData,objectVector);  
+    if(errorCost<errorThr)  
+        return 1;  
+    for(int iteration=0;iteration<MAX;iteration++){  
+  
+        //stochastic  
+        for(int i=0;i<Number;i++){  
+            //calculate the h(x)  
+            weightedValue = weightValue(inputData[i],objectVector);  
+            tempValue=0.0;  
+            for(int j=0;j<Number;j++)  
+                tempValue+=multiPly(parameter[j],inputData[i]);  
+            //update the parameter by stochastic(随机梯度下降)  
+            printf("the next parameter is ");  
+            for(int ii=0;ii<Number;ii++){  
+                parameter[ii] = addVectorData(parameter[ii],numberMultiVectorData(weightedValue*learningRate*(resultData[i]-tempValue),inputData[i]));  
+                if(multiPly(parameter[ii],parameter[ii])!=0){  
+                    for(int jj=0;jj<Dimesion;jj++){  
+                        printf("%f ",parameter[ii].vectorComponent[jj]);  
+                    }  
+                }  
+            }  
+            printf("\n");  
+            errorCost=costFunction(parameter,inputData,resultData,objectVector);  
+            printf("error cost is %f\n",errorCost);  
+            if(errorCost<errorThr)  
+                break;  
+        }//end stochastic one time  
+  
+    }//end when the iteration becomes MAX   
+  
+    //calculate the object vector  
+    float resultValue = 0.0;  
+    for(int i=0;i<Number;i++){  
+        resultValue += weightValue(inputData[i],objectVector)*multiPly(parameter[i],objectVector);  
+    }  
+    printf("result value is %f \n",resultValue);  
+    return 1;  
+}  
+  
+int testLWA(){  
+    vectorData objectData = {1,1.5,1.5};  
+    vectorData localParameter[Number] = {0.0};  
+    LocallyWeightedAgression(localParameter,x,y,objectData);  
+    return 1;  
+}  
+int main(){  
+  //  DescendAlgorithm(parameter,x,y);  
+    //clearParameter(parameter);  
+    //Stochastic(parameter,x,y);  
+    //float ForTestData[] = {1,10,20};  
+    //testData(ForTestData);  
+    testLWA();  
+    system("pause");  
+    return 1;  
+}  
 ```

From 59be501a7f1b08ed7b4b97ec7a55e4d72c483646 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 09:56:48 +0800
Subject: [PATCH 0291/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 200 +++++++++++++---------------------------
 1 file changed, 62 insertions(+), 138 deletions(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 41413a13..ed3ece5c 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -8,143 +8,67 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 局部加权回归（LWR）是我们遇到的第一个non-parametric（非参数）学习算法，而线性回归则是我们遇到的以一个parametric（参数）学习算法。因为参数学习算法它有固定的明确的参数，所以参数一旦确定，就不会改变了，我们不需要在保留训练集中的训练样本。而非参数学习算法，每进行一次预测，就需要重新学习一组，是变化的，所以需要一直保留训练样本。因而，当训练集的容量较大时，非参数学习算法需要占用更多的存储空间，计算速度也较慢。所以有得必有失，效果好了，计算速度却降下来了。
 
 ```python
+# coding: utf-8
+# linear_regression/regression.py
+
+def JLwr(theta, X, y, x, c):
+    """局部加权线性回归的代价函数计算式
+
+    Args:
+        theta: 相关系数矩阵
+        X: 样本集矩阵
+        y: 标签集矩阵
+        x: 待预测输入
+        c: tau
+    Returns:
+        预测代价
+    """
+    m,n = X.shape
+    summerize = 0
+    for i in range(m):
+        diff = (X[i]-x)*(X[i]-x).T
+        w = np.exp(-diff/(2*c*c))
+        predictDiff = np.power(y[i] - X[i]*theta,2)
+        summerize = summerize + w*predictDiff
+    return summerize
+
+@exeTime
+def lwr(rate, maxLoop, epsilon, X, y, x, c=1):
+    """局部加权线性回归
+
+    Args:
+        rate: 学习率
+        maxLoop: 最大迭代次数
+        epsilon: 预测精度
+        X: 输入样本
+        y: 标签向量
+        x: 待预测向量
+        c: tau
+    """
+    m,n = X.shape
+    # 初始化theta
+    theta = np.zeros((n,1))
+    count = 0
+    converged = False
+    error = float('inf')
+    errors = []
+    thetas = {}
+    for j in range(n):
+        thetas[j] = [theta[j,0]]
+    # 执行批量梯度下降
+    while count<=maxLoop:
+        if(converged):
+            break
+        count = count + 1
+        for j in range(n):
+            deriv = (y-X*theta).T*X[:, j]/m
+            theta[j,0] = theta[j,0]+rate*deriv
+            thetas[j].append(theta[j,0])
+        error = JLwr(theta, X, y, x, c)
+        errors.append(error[0,0])
+        # 如果已经收敛
+        if(error < epsilon):
+            converged = True
+    return theta,errors,thetas
 
-using namespace std;  
-  
-const int Number = 6;  
-const int Dimesion = 3;  
-const float learningRate=0.001;       
-const float errorThr=1; //variance threshold  
-const int MAX=1000;     //Max times of iteration  
-  
-typedef struct Data{  
-    float vectorComponent[Dimesion];  
-}vectorData;  
-  
-vectorData x[Number] = {  
-    {1,1,8},  
-    {1,1,3},  
-    {1,1,6},  
-    {1,2,3},  
-    {1,2,1},  
-    {1,2,2},  
-};  
-float y[Number]={2,10,5,13,5,8};  
-/lwr(局部线性回归)  
-float weightValue(vectorData xi,vectorData x){  
-    float weight = 0.0;  
-    for(int i=0;i<Dimesion;i++){  
-        weight+=pow(xi.vectorComponent[i]-x.vectorComponent[i],2);  
-    }  
-    float tempWeight = exp(-(weight/(2*36)));  
-    if(tempWeight<0.02)  
-        tempWeight = 0.0;  
-    return tempWeight;  
-}  
-  
-float multiPly(vectorData x1,vectorData x2){  
-    float temp = 0.0;  
-    for(int i=0;i<Dimesion;i++){  
-        temp += x1.vectorComponent[i]*x2.vectorComponent[i];  
-    }  
-    return temp;  
-}  
-  
-vectorData addVectorData(vectorData x1,vectorData x2){  
-    vectorData temp;  
-    for(int i=0;i<Dimesion;i++)  
-        temp.vectorComponent[i] = x1.vectorComponent[i]+x2.vectorComponent[i];  
-    return temp;  
-}  
-  
-vectorData minusVectorData(vectorData x1,vectorData x2){  
-    vectorData temp;  
-    for(int i=0;i<Dimesion;i++)  
-        temp.vectorComponent[i] = x1.vectorComponent[i]-x2.vectorComponent[i];  
-    return temp;  
-}  
-  
-vectorData numberMultiVectorData(float para,vectorData x1){  
-    vectorData temp;  
-    for(int i=0;i<Dimesion;i++)  
-        temp.vectorComponent[i] = x1.vectorComponent[i]*para;  
-    return temp;  
-}  
-float costFunction(vectorData parameter[],vectorData inputData[],float inputResultData[],vectorData object){  
-    float costValue = 0.0;  
-    float tempValue = 0.0;  
-    float weightedValue = 0.0;  
-    for(int i=0;i<Number;i++){  
-        tempValue = 0.0;  
-          
-        //consider all the parameters although most of them is zero  
-        for(int j=0;j<Number;j++)  
-            tempValue += multiPly(parameter[j],inputData[i]);  
-        costValue += weightValue(inputData[i],object)*pow((inputResultData[i]-tempValue),2);      
-    }  
-  
-    return (costValue/2*4);  
-}  
-  
-  
-int LocallyWeightedAgression(vectorData parameter[],vectorData inputData[],float resultData[],vectorData objectVector){  
-    float tempValue = 0.0;  
-    float errorCost = 0.0;  
-    float weightedValue = 0.0;  
-    errorCost=costFunction(parameter,inputData,resultData,objectVector);  
-    if(errorCost<errorThr)  
-        return 1;  
-    for(int iteration=0;iteration<MAX;iteration++){  
-  
-        //stochastic  
-        for(int i=0;i<Number;i++){  
-            //calculate the h(x)  
-            weightedValue = weightValue(inputData[i],objectVector);  
-            tempValue=0.0;  
-            for(int j=0;j<Number;j++)  
-                tempValue+=multiPly(parameter[j],inputData[i]);  
-            //update the parameter by stochastic(随机梯度下降)  
-            printf("the next parameter is ");  
-            for(int ii=0;ii<Number;ii++){  
-                parameter[ii] = addVectorData(parameter[ii],numberMultiVectorData(weightedValue*learningRate*(resultData[i]-tempValue),inputData[i]));  
-                if(multiPly(parameter[ii],parameter[ii])!=0){  
-                    for(int jj=0;jj<Dimesion;jj++){  
-                        printf("%f ",parameter[ii].vectorComponent[jj]);  
-                    }  
-                }  
-            }  
-            printf("\n");  
-            errorCost=costFunction(parameter,inputData,resultData,objectVector);  
-            printf("error cost is %f\n",errorCost);  
-            if(errorCost<errorThr)  
-                break;  
-        }//end stochastic one time  
-  
-    }//end when the iteration becomes MAX   
-  
-    //calculate the object vector  
-    float resultValue = 0.0;  
-    for(int i=0;i<Number;i++){  
-        resultValue += weightValue(inputData[i],objectVector)*multiPly(parameter[i],objectVector);  
-    }  
-    printf("result value is %f \n",resultValue);  
-    return 1;  
-}  
-  
-int testLWA(){  
-    vectorData objectData = {1,1.5,1.5};  
-    vectorData localParameter[Number] = {0.0};  
-    LocallyWeightedAgression(localParameter,x,y,objectData);  
-    return 1;  
-}  
-int main(){  
-  //  DescendAlgorithm(parameter,x,y);  
-    //clearParameter(parameter);  
-    //Stochastic(parameter,x,y);  
-    //float ForTestData[] = {1,10,20};  
-    //testData(ForTestData);  
-    testLWA();  
-    system("pause");  
-    return 1;  
-}  
 ```

From dfe54b8c2220498400c3a4e41391609eee321e5d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 10:00:42 +0800
Subject: [PATCH 0292/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 76 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index ed3ece5c..67dba3d1 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -72,3 +72,79 @@ def lwr(rate, maxLoop, epsilon, X, y, x, c=1):
     return theta,errors,thetas
 
 ```
+
+#### 结果
+
+```python
+# coding: utf-8
+# linear_regression/test_lwr.py
+import regression
+import matplotlib.pyplot as plt
+import matplotlib.ticker as mtick
+import numpy as np
+
+if __name__ == "__main__":
+    srcX, y = regression.loadDataSet('data/lwr.txt');
+
+    m,n = srcX.shape
+    srcX = np.concatenate((srcX[:, 0], np.power(srcX[:, 0],2)), axis=1)
+    # 特征缩放
+    X = regression.standardize(srcX.copy())
+    X = np.concatenate((np.ones((m,1)), X), axis=1)
+
+    rate = 0.1
+    maxLoop = 1000
+    epsilon = 0.01
+
+    predicateX = regression.standardize(np.matrix([[8, 64]]))
+
+    predicateX = np.concatenate((np.ones((1,1)), predicateX), axis=1)
+
+    result, t = regression.lwr(rate, maxLoop, epsilon, X, y, predicateX, 1)
+    theta, errors, thetas = result
+
+    result2, t = regression.lwr(rate, maxLoop, epsilon, X, y, predicateX, 0.1)
+    theta2, errors2, thetas2 = result2
+
+
+    # 打印特征点
+    fittingFig = plt.figure()
+    title = 'polynomial with bgd: rate=%.2f, maxLoop=%d, epsilon=%.3f'%(rate,maxLoop,epsilon)
+    ax = fittingFig.add_subplot(111, title=title)
+    trainingSet = ax.scatter(srcX[:, 0].flatten().A[0], y[:,0].flatten().A[0])
+
+    print theta
+    print theta2
+
+    # 打印拟合曲线
+    xx = np.linspace(1, 7, 50)
+    xx2 = np.power(xx,2)
+    yHat1 = []
+    yHat2 = []
+    for i in range(50):
+        normalizedSize = (xx[i]-xx.mean())/xx.std(0)
+        normalizedSize2 = (xx2[i]-xx2.mean())/xx2.std(0)
+        x = np.matrix([[1,normalizedSize, normalizedSize2]])
+        yHat1.append(regression.h(theta, x.T))
+        yHat2.append(regression.h(theta2, x.T))
+    fittingLine1, = ax.plot(xx, yHat1, color='g')
+    fittingLine2, = ax.plot(xx, yHat2, color='r')
+
+    ax.set_xlabel('temperature')
+    ax.set_ylabel('yield')
+
+    plt.legend([trainingSet, fittingLine1, fittingLine2], ['Training Set', r'LWR with $\tau$=1', r'LWR with $\tau$=0.1'])
+    plt.show()
+
+    # 打印误差曲线
+    errorsFig = plt.figure()
+    ax = errorsFig.add_subplot(111)
+    ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.2e'))
+
+    ax.plot(range(len(errors)), errors)
+    ax.set_xlabel('Number of iterations')
+    ax.set_ylabel('Cost J')
+
+    plt.show()
+```
+

From bbd9d803f94131dec83b4e877e7e2c9bf5ddb86d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 12:26:57 +0800
Subject: [PATCH 0293/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 67dba3d1..5ec2a6a7 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -147,4 +147,4 @@ if __name__ == "__main__":
 
     plt.show()
 ```
-
+最后，我们分别对ττ取值  0.10.1  和  11 ，得到了不同的拟合曲线：

From 016c8a43e32ac6266c82706760ffbf35aff988ef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 12:28:38 +0800
Subject: [PATCH 0294/1406] change page BA

---
 assets/images/159.jpg   | Bin 0 -> 86816 bytes
 assets/src/BA/BA.0.5.md |   4 ++++
 2 files changed, 4 insertions(+)
 create mode 100644 assets/images/159.jpg

diff --git a/assets/images/159.jpg b/assets/images/159.jpg
new file mode 100644
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literal 0
HcmV?d00001

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 5ec2a6a7..99f7060e 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -148,3 +148,7 @@ if __name__ == "__main__":
     plt.show()
 ```
 最后，我们分别对ττ取值  0.10.1  和  11 ，得到了不同的拟合曲线：
+<p align="center">
+<img width="50" align="center" src="../../images/159.jpg" />
+</p>
+

From a6d405932e66b901d7a94be50663bd433a0ce412 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jan 2018 12:31:13 +0800
Subject: [PATCH 0295/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 99f7060e..12ba7b86 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -149,6 +149,6 @@ if __name__ == "__main__":
 ```
 最后，我们分别对ττ取值  0.10.1  和  11 ，得到了不同的拟合曲线：
 <p align="center">
-<img width="50" align="center" src="../../images/159.jpg" />
+<img width="400" align="center" src="../../images/159.jpg" />
 </p>
 

From f125cbe697d7190e5c2c90493b3164b5888175cb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 28 Jan 2018 09:10:32 +0800
Subject: [PATCH 0296/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 12ba7b86..b6a1f210 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -7,6 +7,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 局部加权回归（LWR）是非参数学习方法。 首先参数学习方法是这样一种方法：在训练完成所有数据后得到一系列训练参数，然后根据训练参数来预测新样本的值，这时不再依赖之前的训练数据了，参数值是确定的。而非参数学习方法是这样一种算法：在预测新样本值时候每次都会重新训练数据得到新的参数值，也就是说每次预测新样本都会依赖训练数据集合，所以每次得到的参数值是不确定的。
 局部加权回归（LWR）是我们遇到的第一个non-parametric（非参数）学习算法，而线性回归则是我们遇到的以一个parametric（参数）学习算法。因为参数学习算法它有固定的明确的参数，所以参数一旦确定，就不会改变了，我们不需要在保留训练集中的训练样本。而非参数学习算法，每进行一次预测，就需要重新学习一组，是变化的，所以需要一直保留训练样本。因而，当训练集的容量较大时，非参数学习算法需要占用更多的存储空间，计算速度也较慢。所以有得必有失，效果好了，计算速度却降下来了。
 
+
+
+####
 ```python
 # coding: utf-8
 # linear_regression/regression.py

From 504e60e7a110761dbfde3ac3ef15653943636f49 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 28 Jan 2018 09:10:50 +0800
Subject: [PATCH 0297/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index b6a1f210..2b71fad3 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -9,7 +9,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 
-####
+#### 应用案例
+
 ```python
 # coding: utf-8
 # linear_regression/regression.py

From d9e1a90910422a708b7bc6d3cd340ab59b263cf2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:10:12 +0800
Subject: [PATCH 0298/1406] Update BA.0.5.md

---
 assets/src/BA/BA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BA/BA.0.5.md b/assets/src/BA/BA.0.5.md
index 2b71fad3..9ad2127c 100644
--- a/assets/src/BA/BA.0.5.md
+++ b/assets/src/BA/BA.0.5.md
@@ -153,6 +153,6 @@ if __name__ == "__main__":
 ```
 最后，我们分别对ττ取值  0.10.1  和  11 ，得到了不同的拟合曲线：
 <p align="center">
-<img width="400" align="center" src="../../images/159.jpg" />
+<img width="600" align="center" src="../../images/159.jpg" />
 </p>
 

From 4e1b855f7daf24de4186cca95c7f1b44c8a08ccf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:15:50 +0800
Subject: [PATCH 0299/1406] change page

---
 assets/src/RGN/RGN.0.1.md | 10 ++++++++++
 1 file changed, 10 insertions(+)
 create mode 100644 assets/src/RGN/RGN.0.1.md

diff --git a/assets/src/RGN/RGN.0.1.md b/assets/src/RGN/RGN.0.1.md
new file mode 100644
index 00000000..1eda376b
--- /dev/null
+++ b/assets/src/RGN/RGN.0.1.md
@@ -0,0 +1,10 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 正则化算法
+
+* 岭回归（Ridge Regression）
+* LASSO（Least Absolute Shrinkage and Selection Operator）
+* Elastic Net
+* 最小角回归（LARS）

From 2bc9c57376b6aec3dd3cb4f29e39c9d164ec552b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:16:32 +0800
Subject: [PATCH 0300/1406] change page of RGN

---
 assets/src/RGN/RGN.0.2.md | 10 ++++++++++
 1 file changed, 10 insertions(+)
 create mode 100644 assets/src/RGN/RGN.0.2.md

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
new file mode 100644
index 00000000..1eda376b
--- /dev/null
+++ b/assets/src/RGN/RGN.0.2.md
@@ -0,0 +1,10 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 正则化算法
+
+* 岭回归（Ridge Regression）
+* LASSO（Least Absolute Shrinkage and Selection Operator）
+* Elastic Net
+* 最小角回归（LARS）

From f96c2e0fdf012eef627fa82e45d612a5d6879170 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:17:47 +0800
Subject: [PATCH 0301/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f8a87fc3..43f45251 100644
--- a/README.md
+++ b/README.md
@@ -77,7 +77,7 @@
      * [学习矢量化（LVQ）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.3.md)
      * [自组织映射算法（SOM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.4.md)
      * [局部加权学习算法（LWR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
- * [正则化算法]()    
+ * [正则化算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.1.md)    
      * [岭回归（Ridge Regression）]()
      * [LASSO（Least Absolute Shrinkage and Selection Operator）]()
      * [Elastic Net]()

From 13535fccf95cc585a441e17564e872e78cfe966a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:18:06 +0800
Subject: [PATCH 0302/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 43f45251..7ce90aed 100644
--- a/README.md
+++ b/README.md
@@ -78,7 +78,7 @@
      * [自组织映射算法（SOM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.4.md)
      * [局部加权学习算法（LWR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
  * [正则化算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.1.md)    
-     * [岭回归（Ridge Regression）]()
+     * [岭回归（Ridge Regression）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.2.md)
      * [LASSO（Least Absolute Shrinkage and Selection Operator）]()
      * [Elastic Net]()
      * [最小角回归（LARS）]()

From 62dc4442177b5b3ad787e8302c5da4fa7a6c0cb7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:18:20 +0800
Subject: [PATCH 0303/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 1eda376b..5b0462bc 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,7 +4,3 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 正则化算法
 
-* 岭回归（Ridge Regression）
-* LASSO（Least Absolute Shrinkage and Selection Operator）
-* Elastic Net
-* 最小角回归（LARS）

From 8fbb5b58d05ede5a077ea2759559c96bbefc9bdc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:18:31 +0800
Subject: [PATCH 0304/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 5b0462bc..d25cb298 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -2,5 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 正则化算法
+#### 岭回归（Ridge Regression）
 

From bb9cfa1956160696dbc548ccb821d0fa74f5ea5f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:20:30 +0800
Subject: [PATCH 0305/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index d25cb298..14a62be5 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 岭回归（Ridge Regression）
 
+在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
+

From ad2d645a18a72c1b8f40fbb5cf48f48ef80af2d1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:25:42 +0800
Subject: [PATCH 0306/1406] Update RGN.0.1.md

---
 assets/src/RGN/RGN.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.1.md b/assets/src/RGN/RGN.0.1.md
index 1eda376b..fcb5a03f 100644
--- a/assets/src/RGN/RGN.0.1.md
+++ b/assets/src/RGN/RGN.0.1.md
@@ -4,6 +4,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 正则化算法
 
+监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据，
+
 * 岭回归（Ridge Regression）
 * LASSO（Least Absolute Shrinkage and Selection Operator）
 * Elastic Net

From b70ffda07b03ee9ef9db01e9563764b934e5966e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:26:37 +0800
Subject: [PATCH 0307/1406] Update RGN.0.1.md

---
 assets/src/RGN/RGN.0.1.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.1.md b/assets/src/RGN/RGN.0.1.md
index fcb5a03f..614daf8f 100644
--- a/assets/src/RGN/RGN.0.1.md
+++ b/assets/src/RGN/RGN.0.1.md
@@ -4,7 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 正则化算法
 
-监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据，
+监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据,但是我们在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
+
+正则化算法包括：
 
 * 岭回归（Ridge Regression）
 * LASSO（Least Absolute Shrinkage and Selection Operator）

From 0a5b74c8f4f423788ba50c6ab8a38d9211fe2b5f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:28:16 +0800
Subject: [PATCH 0308/1406] Update RGN.0.1.md

---
 assets/src/RGN/RGN.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.1.md b/assets/src/RGN/RGN.0.1.md
index 614daf8f..540d4d8f 100644
--- a/assets/src/RGN/RGN.0.1.md
+++ b/assets/src/RGN/RGN.0.1.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 正则化算法
 
-监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据,但是我们在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
+监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据,而规则化参数是防止我们的模型过分拟合我们的训练数据。但是我们在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
 
 正则化算法包括：
 

From c8f4e2d53a4b2d697d85d46c79ecc619512c92b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:29:12 +0800
Subject: [PATCH 0309/1406] Update RGN.0.1.md

---
 assets/src/RGN/RGN.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.1.md b/assets/src/RGN/RGN.0.1.md
index 540d4d8f..780a5a16 100644
--- a/assets/src/RGN/RGN.0.1.md
+++ b/assets/src/RGN/RGN.0.1.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 正则化算法
 
-监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据,而规则化参数是防止我们的模型过分拟合我们的训练数据。但是我们在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
+监督机器学习问题就是“minimizeyour error while regularizing your parameters”，在规则化参数的同时最小化误差。最小化误差是为了让我们的模型拟合我们的训练数据,而规则化参数是防止我们的模型过分拟合我们的训练数据。
 
 正则化算法包括：
 

From 4b195e0bb86505eed9f784348028966b61523c02 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Jan 2018 09:29:38 +0800
Subject: [PATCH 0310/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 14a62be5..2f921708 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,5 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 岭回归（Ridge Regression）
 
-在线性回归模型中提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。
+在线性回归模型中我们提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。而归就是一种正则化方法，通过在损失函数中添加L2范数惩罚项，来控制线性模型的复杂程度，从而使得模型更稳健。
+
 

From 9b462d50d7bd7f6d802073b3191910ee85d51305 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:23:22 +0800
Subject: [PATCH 0311/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 2f921708..f38a6c81 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,6 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 岭回归（Ridge Regression）
 
+
 在线性回归模型中我们提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。而归就是一种正则化方法，通过在损失函数中添加L2范数惩罚项，来控制线性模型的复杂程度，从而使得模型更稳健。
 
 

From c487025af1240ded0a39e83275d13afae5b9a5da Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:26:30 +0800
Subject: [PATCH 0312/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index f38a6c81..157073a8 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,7 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 岭回归（Ridge Regression）
 
-
-在线性回归模型中我们提到了正则化，所谓正则化就是对模型的参数添加一些先验假设，控制模型空间，以达到使得模糊复杂度较小的目的。而归就是一种正则化方法，通过在损失函数中添加L2范数惩罚项，来控制线性模型的复杂程度，从而使得模型更稳健。
-
+岭回归(ridge regression)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
 

From 56fd875819fda35226823b21225649e58af32920 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:28:23 +0800
Subject: [PATCH 0313/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 157073a8..7c2cc1e4 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -4,5 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 岭回归（Ridge Regression）
 
-岭回归(ridge regression)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
-
+岭回归(ridge regression, Tikhonov regularization)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。

From 40d32d2014adaefa6d65bed00c538df9274cde23 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:29:04 +0800
Subject: [PATCH 0314/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 7c2cc1e4..120e5648 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 岭回归（Ridge Regression）
 
 岭回归(ridge regression, Tikhonov regularization)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
+
+岭回归，又称脊回归、吉洪诺夫正则化（Tikhonov regularization），是对不适定问题（ill-posed problem)进行回归分析时最经常使用的一种正则化方法。

From 59c3b29ba94e86c882985a9634f924f7aaeb3a1a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:34:36 +0800
Subject: [PATCH 0315/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 120e5648..d14718f5 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -7,3 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归(ridge regression, Tikhonov regularization)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
 
 岭回归，又称脊回归、吉洪诺夫正则化（Tikhonov regularization），是对不适定问题（ill-posed problem)进行回归分析时最经常使用的一种正则化方法。
+对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。

From 8ed4d1865d0ed0048a3e22b84f077e0135126595 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:34:51 +0800
Subject: [PATCH 0316/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index d14718f5..00a6d037 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -7,4 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归(ridge regression, Tikhonov regularization)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
 
 岭回归，又称脊回归、吉洪诺夫正则化（Tikhonov regularization），是对不适定问题（ill-posed problem)进行回归分析时最经常使用的一种正则化方法。
-对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。
+对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：

From cfb82daed94a3bba95960c0d99438e6289f2c4d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:39:42 +0800
Subject: [PATCH 0317/1406] change page of RGN

---
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 assets/src/RGN/RGN.0.2.md |   7 ++++++-
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diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 00a6d037..691f7d94 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -7,4 +7,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归(ridge regression, Tikhonov regularization)是一种专用于共线性数据分析的有偏估计回归方法，实质上是一种改良的最小二乘估计法，通过放弃最小二乘法的无偏性，以损失部分信息、降低精度为代价获得回归系数更为符合实际、更可靠的回归方法，对病态数据的拟合要强于最小二乘法。
 
 岭回归，又称脊回归、吉洪诺夫正则化（Tikhonov regularization），是对不适定问题（ill-posed problem)进行回归分析时最经常使用的一种正则化方法。
-对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：
+对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。
+
+回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：
+<p align="center">
+<img width="100" align="center" src="../../images/160.jpg" />
+</p>

From cdf570ba73807f7f9efbb5c01150e0b6a83c3e59 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:40:19 +0800
Subject: [PATCH 0318/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 691f7d94..be38e786 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -11,5 +11,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：
 <p align="center">
-<img width="100" align="center" src="../../images/160.jpg" />
+<img width="70" align="center" src="../../images/160.jpg" />
 </p>

From d602a03a150198b7a19f4854e8b85e5534167dd4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:40:42 +0800
Subject: [PATCH 0319/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index be38e786..812dc6c1 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -13,3 +13,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="70" align="center" src="../../images/160.jpg" />
 </p>
+采用最小二乘法，定义损失函数为残差的平方，最小化损失函数:
+<p align="center">
+<img width="70" align="center" src="../../images/161.jpg" />
+</p>

From afc96d02e19979e39e01756562fe591ae55b7371 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:41:21 +0800
Subject: [PATCH 0320/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 812dc6c1..4e3c8c85 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -17,3 +17,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="70" align="center" src="../../images/161.jpg" />
 </p>
+也可以采用梯度下降法进行求解优化，也可以采用如下公式进行直接求解
+<p align="center">
+<img width="70" align="center" src="../../images/162.jpg" />
+</p>

From 6aed8f0643cd072b6d55baeba8de2c00aa779cf9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:41:37 +0800
Subject: [PATCH 0321/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 4e3c8c85..35269e96 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -19,5 +19,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 也可以采用梯度下降法进行求解优化，也可以采用如下公式进行直接求解
 <p align="center">
-<img width="70" align="center" src="../../images/162.jpg" />
+<img width="100" align="center" src="../../images/162.jpg" />
 </p>

From 8e4dcefb71bfbab0a104e20e7cf1e86a3f4598fa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:43:16 +0800
Subject: [PATCH 0322/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 35269e96..f4ad306f 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -21,3 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="100" align="center" src="../../images/162.jpg" />
 </p>
+当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="100" align="center" src="../../images/163.jpg" />的行列式接近于0，即<img width="100" align="center" src="../../images/163.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/164.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。

From 0cb14d05a19d0d3b13bf225167fdc1f1aa67f42b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:44:14 +0800
Subject: [PATCH 0323/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index f4ad306f..419b3234 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -17,8 +17,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="70" align="center" src="../../images/161.jpg" />
 </p>
-也可以采用梯度下降法进行求解优化，也可以采用如下公式进行直接求解
+也可以采用梯度下降法进行求解优化，也可以采用如下公式进行直接求解：
+
 <p align="center">
 <img width="100" align="center" src="../../images/162.jpg" />
 </p>
-当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="100" align="center" src="../../images/163.jpg" />的行列式接近于0，即<img width="100" align="center" src="../../images/163.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/164.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。
+
+当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="100" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="100" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。

From 737675dd89f37bd9b6195e997c2d057adcaaa4eb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:44:38 +0800
Subject: [PATCH 0324/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 419b3234..5097f81c 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -23,4 +23,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="100" align="center" src="../../images/162.jpg" />
 </p>
 
-当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="100" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="100" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。
+当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="70" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="70" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。

From 637ee972afd2d98edd3b61f6c6c0fdf6df06cd55 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:45:01 +0800
Subject: [PATCH 0325/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 5097f81c..ea263b88 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -23,4 +23,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="100" align="center" src="../../images/162.jpg" />
 </p>
 
-当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="70" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="70" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="100" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。
+当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="50" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="50" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="50" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。

From 403ff555cc3d36ba78591bbd50f1e18769d3716e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:45:58 +0800
Subject: [PATCH 0326/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index ea263b88..4121a128 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：
 <p align="center">
-<img width="70" align="center" src="../../images/160.jpg" />
+<img width="50" align="center" src="../../images/160.jpg" />
 </p>
 采用最小二乘法，定义损失函数为残差的平方，最小化损失函数:
 <p align="center">
@@ -23,4 +23,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="100" align="center" src="../../images/162.jpg" />
 </p>
 
-当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="50" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="50" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="50" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。
+当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="40" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="40" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="50" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。

From 3c6ca38b4ab434ebdd06c9da8d07dc7310d06d7d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:47:48 +0800
Subject: [PATCH 0327/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 4121a128..6dde3e90 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -24,3 +24,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 当X不是列满秩时，或者某些列之间的线性相关性比较大时，<img width="40" align="center" src="../../images/164.jpg" />的行列式接近于0，即<img width="40" align="center" src="../../images/164.jpg" />接近于奇异，上述问题变为一个不适定问题，此时，计算<img width="50" align="center" src="../../images/165.jpg" />时误差会很大，传统的最小二乘法缺乏稳定性与可靠性。
+
+因而，我们需要将不适定问题转化为适定问题：我们为上述损失函数加上一个正则化项，变为
+<p align="center">
+<img width="100" align="center" src="../../images/166.jpg" />
+</p>

From 0e250b61818f754705671bb32d725b40180cd765 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:48:51 +0800
Subject: [PATCH 0328/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 6dde3e90..e15f5cb9 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -29,3 +29,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="100" align="center" src="../../images/166.jpg" />
 </p>
+
+其中，我们定义<img width="100" align="center" src="../../images/167.jpg" />，于是：
+<p align="center">
+<img width="100" align="center" src="../../images/168.jpg" />
+</p>

From 9550b9cdd0d475f3aa1a0c09732a063e2017cf7a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:49:11 +0800
Subject: [PATCH 0329/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index e15f5cb9..0a68e1ca 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -27,10 +27,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 因而，我们需要将不适定问题转化为适定问题：我们为上述损失函数加上一个正则化项，变为
 <p align="center">
-<img width="100" align="center" src="../../images/166.jpg" />
+<img width="200" align="center" src="../../images/166.jpg" />
 </p>
 
-其中，我们定义<img width="100" align="center" src="../../images/167.jpg" />，于是：
+其中，我们定义<img width="40" align="center" src="../../images/167.jpg" />，于是：
 <p align="center">
-<img width="100" align="center" src="../../images/168.jpg" />
+<img width="300" align="center" src="../../images/168.jpg" />
 </p>

From 791440ee704d94be4e379ec1e0b838bbe4d78eda Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:49:46 +0800
Subject: [PATCH 0330/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 0a68e1ca..08a0986b 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -32,5 +32,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 其中，我们定义<img width="40" align="center" src="../../images/167.jpg" />，于是：
 <p align="center">
-<img width="300" align="center" src="../../images/168.jpg" />
+<img width="200" align="center" src="../../images/168.jpg" />
 </p>
+其中I是单位矩阵。

From b52b0c27e8c770b86cc3280aa91101c46525a8f6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:53:49 +0800
Subject: [PATCH 0331/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 08a0986b..06988d92 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -35,3 +35,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/168.jpg" />
 </p>
 其中I是单位矩阵。
+
+随着的<img width="30" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="30" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="30" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="30" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="30" align="center" src="../../images/169.jpg" />值了。
+岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。

From 0a4d7313eda7371b442c57b4991cc358361da245 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:54:19 +0800
Subject: [PATCH 0332/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 06988d92..6ca3eaa7 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -36,5 +36,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 其中I是单位矩阵。
 
-随着的<img width="30" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="30" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="30" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="30" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="30" align="center" src="../../images/169.jpg" />值了。
+随着的<img width="20" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="30" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="20" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="20" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="20" align="center" src="../../images/169.jpg" />值了。
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。

From 8ed790cf0cb4b822d3365cdafacd8be35832c622 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 09:55:23 +0800
Subject: [PATCH 0333/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 6ca3eaa7..51c2f269 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -36,5 +36,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 其中I是单位矩阵。
 
-随着的<img width="20" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="30" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="20" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="20" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="20" align="center" src="../../images/169.jpg" />值了。
+随着的<img width="10" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="40" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="10" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="10" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="10" align="center" src="../../images/169.jpg" />值了。
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。

From c006e4806050b9b6f7a8dde6af1dca60051863bf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 10:12:02 +0800
Subject: [PATCH 0334/1406] change page of RGN

---
 assets/images/163.jpg | Bin 635 -> 239 bytes
 assets/images/172.jpg | Bin 239 -> 0 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 assets/images/172.jpg

diff --git a/assets/images/163.jpg b/assets/images/163.jpg
index 1806d7dbb72395e4ba98f6c94d4a43fa0b06e525..cf4229492bbd2b0775b9983d9b318a4b1b7721a9 100644
GIT binary patch
delta 174
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zRN{=}4|#(R<_t$~>KV*QODIi95K1UZUr~^dFr#u?Lt`kT1~bbZ?gJvs$<{4tkqivm
Yo=Gf<tO>IPx`4sc)z5`xol`;+0Q3?#c>n+a

delta 573
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From 7c4b14f34fe55b34768ee8386eaef1bf5aaafae8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 10:13:32 +0800
Subject: [PATCH 0335/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 51c2f269..90c5b6c4 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -36,5 +36,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 其中I是单位矩阵。
 
-随着的<img width="10" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="40" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="10" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="10" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="10" align="center" src="../../images/169.jpg" />值了。
+随着的<img width="10" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="10" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="10" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="10" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="10" align="center" src="../../images/169.jpg" />值了。
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。

From f7813bb648665aa49ef055fb69e437995a40cc3a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 18:55:39 +0800
Subject: [PATCH 0336/1406] change page

---
 assets/src/RGN/RGN.0.3.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/RGN/RGN.0.3.md

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
new file mode 100644
index 00000000..e9791330
--- /dev/null
+++ b/assets/src/RGN/RGN.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### Lasso算法(least absolute shrinkage and selection operator)

From 4599fe22ae0da3e4a831a9322d3f057842fde628 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 18:56:30 +0800
Subject: [PATCH 0337/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 7ce90aed..94d56827 100644
--- a/README.md
+++ b/README.md
@@ -79,7 +79,7 @@
      * [局部加权学习算法（LWR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BA/BA.0.5.md)
  * [正则化算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.1.md)    
      * [岭回归（Ridge Regression）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.2.md)
-     * [LASSO（Least Absolute Shrinkage and Selection Operator）]()
+     * [LASSO（Least Absolute Shrinkage and Selection Operator）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.3.md)
      * [Elastic Net]()
      * [最小角回归（LARS）]()
  * [决策树算法]()

From 48134e014e00f5be68c82918e4c0e2338c4bd6f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 19:01:50 +0800
Subject: [PATCH 0338/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 90c5b6c4..1f298ce9 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -38,3 +38,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 随着的<img width="10" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="10" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="10" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="10" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="10" align="center" src="../../images/169.jpg" />值了。
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。
+
+#### 应用案例

From 622cce660e1c1994f31a12302c1510fd46d311e2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 30 Jan 2018 19:02:17 +0800
Subject: [PATCH 0339/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 1f298ce9..45c3fe7f 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -39,4 +39,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 随着的<img width="10" align="center" src="../../images/169.jpg" />增大，<img width="30" align="center" src="../../images/170.jpg" />各元素<img width="30" align="center" src="../../images/171.jpg" />的绝对值均趋于不断变小，它们相对于正确值<img width="10" align="center" src="../../images/163.jpg" />的偏差也越来越大。<img width="10" align="center" src="../../images/169.jpg" />趋于无穷大时，<img width="30" align="center" src="../../images/170.jpg" />趋于0。其中，<img width="30" align="center" src="../../images/170.jpg" />随<img width="10" align="center" src="../../images/169.jpg" />的改变而变化的轨迹，就称为岭迹。实际计算中可选非常多的  值，做出一个岭迹图，看看这个图在取哪个值的时候变稳定了，那就确定<img width="10" align="center" src="../../images/169.jpg" />值了。
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。
 
+
 #### 应用案例

From 1842401db2132629306a7dca304b57ebe47e7a3f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:22:34 +0800
Subject: [PATCH 0340/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 45c3fe7f..eef98d69 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -41,3 +41,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 应用案例
+

From a63ed120385fa58299337fbb91868bcadcb419fd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:24:29 +0800
Subject: [PATCH 0341/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index eef98d69..73aa948c 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -9,6 +9,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归，又称脊回归、吉洪诺夫正则化（Tikhonov regularization），是对不适定问题（ill-posed problem)进行回归分析时最经常使用的一种正则化方法。
 对于有些矩阵，矩阵中某个元素的一个很小的变动，会引起最后计算结果误差很大，这种矩阵称为“病态矩阵”。有些时候不正确的计算方法也会使一个正常的矩阵在运算中表现出病态。对于高斯消去法来说，如果主元（即对角线上的元素）上的元素很小，在计算时就会表现出病态的特征。
 
+岭回归分析核心思想是采用最小二乘法原理来求解回归系数，最小二乘法思想背景：1801年，意大利天文学家朱赛普·皮亚齐发现了第一颗小行星谷神星。经过40天的跟踪观测后，由于谷神星运行至太阳背后，使得皮亚齐失去了谷神星的位置。随后全世界的科学家利用皮亚齐的观测数据开始寻找谷神星，但是根据大多数人计算的结果来寻找谷神星都没有结果。时年24岁的高斯计算了谷神星的轨道并进行了分析。奥地利天文学家海因里希·奥伯斯根据高斯计算出来的轨道重新发现了谷神星。
+
+高斯使用的最小二乘法的方法发表于1809年他的著作《天体运动论》中，而法国科学家勒让德于1806年独立发现“最小二乘法”，但因不为世人所知而默默无闻。两人曾为谁最早创立最小二乘法原理发生争执。
+
+1829年，高斯提供了最小二乘法的优化效果强于其他方法的证明，见高斯-马尔可夫定理。
+
+
 回归分析中常用的最小二乘法是一种无偏估计。对于一个适定问题，X通常是列满秩的：
 <p align="center">
 <img width="50" align="center" src="../../images/160.jpg" />

From 2498b519441edd760f8ac9cb0c2d4bd5a6750007 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:25:10 +0800
Subject: [PATCH 0342/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 73aa948c..cb3bc539 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -47,5 +47,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归是对最小二乘回归的一种补充，它损失了无偏性，来换取高的数值稳定性，从而得到较高的计算精度。
 
 
-#### 应用案例
+#### 相关应用
+岭回归是在自变量组成的信息矩阵的主对角线元素上人为的加入一个非负因子k，使得矩阵行列式不为零，以降低对回归系数估计的误差，提高估计精确度以及模型的平稳性。它是最小二乘法的补充，岭回归可以修复病态矩阵，达到较好的效果。
 
+近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。

From 70c47faa0b2e7ab9b4bdd5b41c88c1e5e18ddfc4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:25:33 +0800
Subject: [PATCH 0343/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index cb3bc539..a08c6d1c 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -51,3 +51,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 岭回归是在自变量组成的信息矩阵的主对角线元素上人为的加入一个非负因子k，使得矩阵行列式不为零，以降低对回归系数估计的误差，提高估计精确度以及模型的平稳性。它是最小二乘法的补充，岭回归可以修复病态矩阵，达到较好的效果。
 
 近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。
+
+
+#### 优缺点

From a1af06bc6e4015bdcc6cbd78a7d1f9cadd5ae968 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:27:31 +0800
Subject: [PATCH 0344/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index a08c6d1c..d7f36285 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -54,3 +54,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 优缺点
+优点：可对变量之间共线性比较严重或病态数据偏多的数据类型作回归分析，对这类数据作回归得到的回归系数更符合实际，更可靠。另外，岭回归能让估计参数的波动范围变小，变的更稳定。
+
+缺点：对系数的估计时，会损失部分信息、降低精度。同时岭回归方程的R平方值会稍低于普通的回归方法。

From 663199aa66f7610387d2fc8e40a1a1e683c34cd3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:33:32 +0800
Subject: [PATCH 0345/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index e9791330..d207c61c 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Lasso算法(least absolute shrinkage and selection operator)
+
+Lasso算法（least absolute shrinkage and selection operator，又译最小绝对值收敛和选择算子、套索算法）是一种同时进行特征选择和正则化（数学）的回归分析方法，旨在增强统计模型的预测准确性和可解释性，最初由斯坦福大学统计学教授Robert Tibshirani于1996年基于Leo Breiman的非负参数推断(Nonnegative Garrote, NNG)提出[1][2]。Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。

From 6ea530968bb79a4dc9f86122420dff92a7b4559a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 31 Jan 2018 09:49:10 +0800
Subject: [PATCH 0346/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index d207c61c..79bb0316 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -4,4 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Lasso算法(least absolute shrinkage and selection operator)
 
-Lasso算法（least absolute shrinkage and selection operator，又译最小绝对值收敛和选择算子、套索算法）是一种同时进行特征选择和正则化（数学）的回归分析方法，旨在增强统计模型的预测准确性和可解释性，最初由斯坦福大学统计学教授Robert Tibshirani于1996年基于Leo Breiman的非负参数推断(Nonnegative Garrote, NNG)提出[1][2]。Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。
+Lasso算法（least absolute shrinkage and selection operator，又译最小绝对值收敛和选择算子、套索算法）是一种同时进行特征选择和正则化（数学）的回归分析方法，旨在增强统计模型的预测准确性和可解释性，最初由斯坦福大学统计学教授Robert Tibshirani于1996年基于Leo Breiman的非负参数推断(Nonnegative Garrote, NNG)提出[1][2]。
+
+Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。

From a91af1e8795662dfeb73bf185baff264d4b836b4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:04:50 +0800
Subject: [PATCH 0347/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index d7f36285..5064ad10 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -52,6 +52,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。
 
+```python
+```
+
 
 #### 优缺点
 优点：可对变量之间共线性比较严重或病态数据偏多的数据类型作回归分析，对这类数据作回归得到的回归系数更符合实际，更可靠。另外，岭回归能让估计参数的波动范围变小，变的更稳定。

From 391c3ec9bbfabe1ad2b94e3701f1265ef9279330 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:06:35 +0800
Subject: [PATCH 0348/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 5064ad10..fd1f52d6 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -52,10 +52,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。
 
-```python
-```
-
-
 #### 优缺点
 优点：可对变量之间共线性比较严重或病态数据偏多的数据类型作回归分析，对这类数据作回归得到的回归系数更符合实际，更可靠。另外，岭回归能让估计参数的波动范围变小，变的更稳定。
 

From bc4f558b5158a4e132872cc85609945b5bbad461 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:23:38 +0800
Subject: [PATCH 0349/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 79bb0316..86208359 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -6,4 +6,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 Lasso算法（least absolute shrinkage and selection operator，又译最小绝对值收敛和选择算子、套索算法）是一种同时进行特征选择和正则化（数学）的回归分析方法，旨在增强统计模型的预测准确性和可解释性，最初由斯坦福大学统计学教授Robert Tibshirani于1996年基于Leo Breiman的非负参数推断(Nonnegative Garrote, NNG)提出[1][2]。
 
-Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。
+Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。Lasso是另一种缩减方法，将回归系数收缩在一定的区域内。Lasso的主要思想是构造一个一阶惩罚函数获得一个精炼的模型, 通过最终确定一些变量的系数为0进行特征筛选。以两个变量为例，标准线性回归的cost function还是可以用二维平面的等值线表示，而约束条件则与岭回归的圆不同，Lasso的约束条件可以用方形表示，如图:
+
+
+
+
+#### 应用案例

From bee93a0a068a8b41c8694ea78714d9555a022965 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:25:17 +0800
Subject: [PATCH 0350/1406] change page of RGN

---
 assets/images/172.jpg     | Bin 0 -> 12852 bytes
 assets/src/RGN/RGN.0.3.md |   3 +++
 2 files changed, 3 insertions(+)
 create mode 100644 assets/images/172.jpg

diff --git a/assets/images/172.jpg b/assets/images/172.jpg
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diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 86208359..5d4c7872 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -8,6 +8,9 @@ Lasso算法（least absolute shrinkage and selection operator，又译最小绝
 
 Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。Lasso是另一种缩减方法，将回归系数收缩在一定的区域内。Lasso的主要思想是构造一个一阶惩罚函数获得一个精炼的模型, 通过最终确定一些变量的系数为0进行特征筛选。以两个变量为例，标准线性回归的cost function还是可以用二维平面的等值线表示，而约束条件则与岭回归的圆不同，Lasso的约束条件可以用方形表示，如图:
 
+<p align="center">
+<img width="300" align="center" src="../../images/172.jpg" />
+</p>
 
 
 

From 33cab7557197547801b1ec5a3e45adec6d6121c1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:26:45 +0800
Subject: [PATCH 0351/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 5d4c7872..8a15305f 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -6,7 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 Lasso算法（least absolute shrinkage and selection operator，又译最小绝对值收敛和选择算子、套索算法）是一种同时进行特征选择和正则化（数学）的回归分析方法，旨在增强统计模型的预测准确性和可解释性，最初由斯坦福大学统计学教授Robert Tibshirani于1996年基于Leo Breiman的非负参数推断(Nonnegative Garrote, NNG)提出[1][2]。
 
-Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。Lasso是另一种缩减方法，将回归系数收缩在一定的区域内。Lasso的主要思想是构造一个一阶惩罚函数获得一个精炼的模型, 通过最终确定一些变量的系数为0进行特征筛选。以两个变量为例，标准线性回归的cost function还是可以用二维平面的等值线表示，而约束条件则与岭回归的圆不同，Lasso的约束条件可以用方形表示，如图:
+Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示了很多估计量的重要性质，如估计量与岭回归（Ridge regression，也叫Tikhonov regularization）和最佳子集选择的关系，Lasso系数估计值(estimate)和软阈值（soft thresholding）之间的联系。它也揭示了当协变量共线时，Lasso系数估计值不一定唯一（类似标准线性回归）。Lasso是一种缩减方法，将回归系数收缩在一定的区域内。Lasso的主要思想是构造一个一阶惩罚函数获得一个精确的模型, 通过最终确定一些变量的系数为0进行特征筛选。以两个变量为例，标准线性回归的cost function还是可以用二维平面的等值线表示，而约束条件则与岭回归的圆不同，Lasso的约束条件可以用方形表示，如图:
 
 <p align="center">
 <img width="300" align="center" src="../../images/172.jpg" />

From 1e5526b3f01b5ceb258470aeb092c2fc17b9d639 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:27:20 +0800
Subject: [PATCH 0352/1406] Update RGN.0.3.md


From 5f4fde63c258116fff15f68b03b6beb2353f00bb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:28:19 +0800
Subject: [PATCH 0353/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 8a15305f..1c2ebe46 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -12,6 +12,9 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 <img width="300" align="center" src="../../images/172.jpg" />
 </p>
 
+相比圆，方形的顶点更容易与抛物面相交，顶点就意味着对应的很多系数为0，而岭回归中的圆上的任意一点都很容易与抛物面相交很难得到正好等于0的系数。这也就意味着，lasso起到了很好的筛选变量的作用。
+
+
 
 
 #### 应用案例

From e411f010fe0ae4a3b06a4d622617dba36601da2b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:30:08 +0800
Subject: [PATCH 0354/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 1c2ebe46..c8fe6677 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -15,6 +15,4 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 相比圆，方形的顶点更容易与抛物面相交，顶点就意味着对应的很多系数为0，而岭回归中的圆上的任意一点都很容易与抛物面相交很难得到正好等于0的系数。这也就意味着，lasso起到了很好的筛选变量的作用。
 
 
-
-
 #### 应用案例

From 02cd2d3aeab5d29a730398c349dca5d0b4f9c486 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Feb 2018 09:35:14 +0800
Subject: [PATCH 0355/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index c8fe6677..3b98b867 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -15,4 +15,3 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 相比圆，方形的顶点更容易与抛物面相交，顶点就意味着对应的很多系数为0，而岭回归中的圆上的任意一点都很容易与抛物面相交很难得到正好等于0的系数。这也就意味着，lasso起到了很好的筛选变量的作用。
 
 
-#### 应用案例

From 6e9a450f266676aaaccf486ac71b1bb38255e0ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:23:01 +0800
Subject: [PATCH 0356/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 3b98b867..d6252c61 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -14,4 +14,8 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 
 相比圆，方形的顶点更容易与抛物面相交，顶点就意味着对应的很多系数为0，而岭回归中的圆上的任意一点都很容易与抛物面相交很难得到正好等于0的系数。这也就意味着，lasso起到了很好的筛选变量的作用。
 
+#### 应用案例
 
+```python
+
+```

From 2a70cdd24462d92b5a69825df35bc12ad8b1f3a5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:23:11 +0800
Subject: [PATCH 0357/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index d6252c61..1727ca7c 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -16,6 +16,7 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 
 #### 应用案例
 
+
 ```python
 
 ```

From 59691daf1a09d751258c638c1a5919ec752ee233 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:23:22 +0800
Subject: [PATCH 0358/1406] Update RGN.0.3.md

---
 assets/src/RGN/RGN.0.3.md | 43 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/assets/src/RGN/RGN.0.3.md b/assets/src/RGN/RGN.0.3.md
index 1727ca7c..b38b7b41 100644
--- a/assets/src/RGN/RGN.0.3.md
+++ b/assets/src/RGN/RGN.0.3.md
@@ -18,5 +18,48 @@ Lasso算法最初用于计算最小二乘法模型，这个简单的算法揭示
 
 
 ```python
+import matplotlib.pyplot as plt
+import numpy as np
+from sklearn import datasets, linear_model, discriminant_analysis, cross_validation
 
+def load_data():
+    diabetes = datasets.load_diabetes()
+    return cross_validation.train_test_split(diabetes.data, diabetes.target, test_size=0.25, random_state=0)
+
+def test_lasso(*data):
+    X_train, X_test, y_train, y_test = data
+    lassoRegression = linear_model.Lasso()
+    lassoRegression.fit(X_train, y_train)
+    print("权重向量:%s, b的值为:%.2f" % (lassoRegression.coef_, lassoRegression.intercept_))
+    print("损失函数的值:%.2f" % np.mean((lassoRegression.predict(X_test) - y_test) ** 2))
+    print("预测性能得分: %.2f" % lassoRegression.score(X_test, y_test))
+
+#测试不同的α值对预测性能的影响
+def test_lasso_alpha(*data):
+    X_train, X_test, y_train, y_test = data
+    alphas = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000]
+    scores = []
+    for i, alpha in enumerate(alphas):
+        lassoRegression = linear_model.Lasso(alpha=alpha)
+        lassoRegression.fit(X_train, y_train)
+        scores.append(lassoRegression.score(X_test, y_test))
+    return alphas, scores
+
+def show_plot(alphas, scores):
+    figure = plt.figure()
+    ax = figure.add_subplot(1, 1, 1)
+    ax.plot(alphas, scores)
+    ax.set_xlabel(r"$\alpha$")
+    ax.set_ylabel(r"score")
+    ax.set_xscale("log")
+    ax.set_title("Ridge")
+    plt.show()
+
+if __name__=='__main__':
+    X_train, X_test, y_train, y_test = load_data()
+    # 使用默认的alpha
+    #test_lasso(X_train, X_test, y_train, y_test)
+    # 使用自己设置的alpha
+    alphas, scores = test_lasso_alpha(X_train, X_test, y_train, y_test)
+    show_plot(alphas, scores)
 ```

From f61932fa84b4f681f41dd9575278ba2734c891f7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:24:23 +0800
Subject: [PATCH 0359/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index fd1f52d6..8e75a997 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -52,6 +52,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。
 
+#### 应用案例
+
+
 #### 优缺点
 优点：可对变量之间共线性比较严重或病态数据偏多的数据类型作回归分析，对这类数据作回归得到的回归系数更符合实际，更可靠。另外，岭回归能让估计参数的波动范围变小，变的更稳定。
 

From ff29310d8557fb1882b6bf8dcbfad8a88f250da2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:24:40 +0800
Subject: [PATCH 0360/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index 8e75a997..ce0f4c76 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -53,7 +53,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 近年来，岭回归在经济、工业生产、工程技术、环境保护等方面已有一定的应用。
 
 #### 应用案例
+```python
 
+```
 
 #### 优缺点
 优点：可对变量之间共线性比较严重或病态数据偏多的数据类型作回归分析，对这类数据作回归得到的回归系数更符合实际，更可靠。另外，岭回归能让估计参数的波动范围变小，变的更稳定。

From cf191968b49cca927d53f6d09429c942ed13ec5b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:27:40 +0800
Subject: [PATCH 0361/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 47 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 46 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index ce0f4c76..dd40a7e3 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -54,7 +54,52 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用案例
 ```python
-
+import matplotlib.pyplot as plt
+import numpy as np
+from sklearn import datasets, linear_model, discriminant_analysis, cross_validation
+
+def load_data():
+    diabetes = datasets.load_diabetes()
+    return cross_validation.train_test_split(diabetes.data, diabetes.target, test_size=0.25, random_state=0)
+
+def test_ridge(*data):
+    X_train, X_test, y_train, y_test = data
+    ridgeRegression = linear_model.Ridge()
+    ridgeRegression.fit(X_train, y_train)
+    print("权重向量:%s, b的值为:%.2f" % (ridgeRegression.coef_, ridgeRegression.intercept_))
+    print("损失函数的值:%.2f" % np.mean((ridgeRegression.predict(X_test) - y_test) ** 2))
+    print("预测性能得分: %.2f" % ridgeRegression.score(X_test, y_test))
+
+#测试不同的α值对预测性能的影响
+def test_ridge_alpha(*data):
+    X_train, X_test, y_train, y_test = data
+    alphas = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000]
+    scores = []
+    for i, alpha in enumerate(alphas):
+        ridgeRegression = linear_model.Ridge(alpha=alpha)
+        ridgeRegression.fit(X_train, y_train)
+        scores.append(ridgeRegression.score(X_test, y_test))
+    return alphas, scores
+
+def show_plot(alphas, scores):
+    figure = plt.figure()
+    ax = figure.add_subplot(1, 1, 1)
+    ax.plot(alphas, scores)
+    ax.set_xlabel(r"$\alpha$")
+    ax.set_ylabel(r"score")
+    ax.set_xscale("log")
+    ax.set_title("Ridge")
+    plt.show()
+
+if __name__ == '__main__':
+    #X_train, X_test, y_train, y_test = load_data()
+    #进行训练并且预测结果
+    #test_ridge(X_train, X_test, y_train, y_test)
+
+    #使用自己设置的alpha
+    X_train, X_test, y_train, y_test = load_data()
+    alphas, scores = test_ridge_alpha(X_train, X_test, y_train, y_test)
+    show_plot(alphas, scores)
 ```
 
 #### 优缺点

From 324caf1be29b07c92f20159df95934bd36ecf003 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:28:43 +0800
Subject: [PATCH 0362/1406] Update RGN.0.2.md

---
 assets/src/RGN/RGN.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.2.md b/assets/src/RGN/RGN.0.2.md
index dd40a7e3..74fd1a51 100644
--- a/assets/src/RGN/RGN.0.2.md
+++ b/assets/src/RGN/RGN.0.2.md
@@ -93,7 +93,6 @@ def show_plot(alphas, scores):
 
 if __name__ == '__main__':
     #X_train, X_test, y_train, y_test = load_data()
-    #进行训练并且预测结果
     #test_ridge(X_train, X_test, y_train, y_test)
 
     #使用自己设置的alpha

From 224b90b614e63a137187ac587a8fef05e17592e5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:32:20 +0800
Subject: [PATCH 0363/1406] change page

---
 assets/src/RGN/RGN.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/RGN/RGN.0.4.md

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
new file mode 100644
index 00000000..2a43db13
--- /dev/null
+++ b/assets/src/RGN/RGN.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 弹性网络(Elastic Net)
\ No newline at end of file

From 3e640c3750e726ecbd47d302d35b049bda1f612e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:33:00 +0800
Subject: [PATCH 0364/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 94d56827..804ee1cb 100644
--- a/README.md
+++ b/README.md
@@ -80,7 +80,7 @@
  * [正则化算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.1.md)    
      * [岭回归（Ridge Regression）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.2.md)
      * [LASSO（Least Absolute Shrinkage and Selection Operator）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.3.md)
-     * [Elastic Net]()
+     * [Elastic Net](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
      * [最小角回归（LARS）]()
  * [决策树算法]()
      * [分类和回归树（CART）]()

From 98aa40c615ac4ec71a0707ff6a8d174bc4fe3a59 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:36:09 +0800
Subject: [PATCH 0365/1406] change page of RGN

---
 assets/src/RGN/RGN.0.5.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/RGN/RGN.0.5.md

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
new file mode 100644
index 00000000..385d2fa2
--- /dev/null
+++ b/assets/src/RGN/RGN.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 最小角回归（LARS）
\ No newline at end of file

From b0e88cc2e1b1206d97e9376d05ceb438e0ac8937 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Feb 2018 09:37:21 +0800
Subject: [PATCH 0366/1406] change page of readme

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 804ee1cb..224b36e1 100644
--- a/README.md
+++ b/README.md
@@ -80,8 +80,8 @@
  * [正则化算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.1.md)    
      * [岭回归（Ridge Regression）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.2.md)
      * [LASSO（Least Absolute Shrinkage and Selection Operator）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.3.md)
-     * [Elastic Net](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
-     * [最小角回归（LARS）]()
+     * [弹性网络(Elastic Net)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
+     * [最小角回归（LARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
  * [决策树算法]()
      * [分类和回归树（CART）]()
      * [ID3算法(Iterative Dichotomiser 3)]()

From f9047ff368f2554b572181f18adaf67d4ea83fd0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 3 Feb 2018 13:31:47 +0800
Subject: [PATCH 0367/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 2a43db13..093a4880 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -2,4 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 弹性网络(Elastic Net)
\ No newline at end of file
+x
+

From 983f7a6d2681faaba90a4d5b5465a1969fe87d72 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 3 Feb 2018 13:32:03 +0800
Subject: [PATCH 0368/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 093a4880..ac17b168 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -2,5 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-x
+
+####
 

From 9734eb1225d8e9fd1cc5ad3391aa6c5ee525cc43 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 3 Feb 2018 13:32:28 +0800
Subject: [PATCH 0369/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index ac17b168..55afa786 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -3,5 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
-####
+#### 弹性网络(Elastic Net)
 

From 5f1a27f2850548433c012250092de1093b186515 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 4 Feb 2018 15:35:07 +0800
Subject: [PATCH 0370/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 385d2fa2..974b2cb0 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 最小角回归（LARS）
\ No newline at end of file
+#### 

From 052b01c7b6eee087e6ead863d4d66f9524739ac6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 4 Feb 2018 15:35:15 +0800
Subject: [PATCH 0371/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 974b2cb0..a045b514 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 
+#### 最小角回归（LARS）

From 755cc6294107db6510ffee92655b336a64367526 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Feb 2018 09:12:00 +0800
Subject: [PATCH 0372/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 55afa786..055a901f 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,3 +5,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
+Elasticnet是一不断叠代的方法。第一个式子是绳上的点每一次叠代改变的量，第一项是吸引力，第二项就是张力。第二个方程式是城市Xi对点Yj的影响。

From 36e83c7608d1515afabba3d786601c5ec4b587ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Feb 2018 09:12:55 +0800
Subject: [PATCH 0373/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 055a901f..f53bf3da 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,4 +5,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
-Elasticnet是一不断叠代的方法。第一个式子是绳上的点每一次叠代改变的量，第一项是吸引力，第二项就是张力。第二个方程式是城市Xi对点Yj的影响。
+Elasticnet是一不断叠代的方法。

From dbe8da60025447e2ee449578f3d2c1d3bad9f040 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Feb 2018 09:14:14 +0800
Subject: [PATCH 0374/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index f53bf3da..85d59a73 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -6,3 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 弹性网络(Elastic Net)
 
 Elasticnet是一不断叠代的方法。
+弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。

From 3eac8175c9e328e3d41037b14857d03681f0e023 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:15:23 +0800
Subject: [PATCH 0375/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 85d59a73..70d302e2 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,5 +5,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
+弹性网络 是一种使用 L1， L2 范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso 一样，但是它仍然保持 一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。
+
 Elasticnet是一不断叠代的方法。
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
+

From f64496bc5f824dcf75ee5dc261316e4d7a1ac810 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:15:36 +0800
Subject: [PATCH 0376/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 70d302e2..574ecc39 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,8 +5,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
-弹性网络 是一种使用 L1， L2 范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso 一样，但是它仍然保持 一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。
-
-Elasticnet是一不断叠代的方法。
+弹性网络 是一种使用 L1， L2 范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso 一样，但是它仍然保持 一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。Elasticnet是一不断叠代的方法。
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From 9727234569148b0239aed1d7cb96a80f1f9377c2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:15:55 +0800
Subject: [PATCH 0377/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 574ecc39..b10cc89a 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -6,5 +6,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 弹性网络(Elastic Net)
 
 弹性网络 是一种使用 L1， L2 范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso 一样，但是它仍然保持 一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。Elasticnet是一不断叠代的方法。
+
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From 2ed9f541c9e35e72e1e8256a37725aa41962c866 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:17:01 +0800
Subject: [PATCH 0378/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index b10cc89a..7d46cb0d 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
-弹性网络 是一种使用 L1， L2 范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso 一样，但是它仍然保持 一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。Elasticnet是一不断叠代的方法。
+弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。弹性网络是一不断叠代的方法。
 
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From 3115be3de16690fda7b85e920ec2f142e0ecb67d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:17:18 +0800
Subject: [PATCH 0379/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 7d46cb0d..77c18354 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
-弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制 L1 和 L2 的凸组合。弹性网络是一不断叠代的方法。
+弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
 
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From 47015584a4079e084d7f901dbaa44ebfc58365ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:18:05 +0800
Subject: [PATCH 0380/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 77c18354..29e32b6c 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 弹性网络(Elastic Net)
 
-弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型。 这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像 Ridge 的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
+弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型.这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像Ridge的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
 
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From 27acb4fde0596ddc00a121368a786fd9eedb3774 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:18:28 +0800
Subject: [PATCH 0381/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 29e32b6c..9a9e1ff7 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -7,5 +7,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型.这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像Ridge的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
 
+弹性网络在很多特征互相联系的情况下是非常有用的。Lasso 很可能只随机考虑这些特征中的一个，而弹性网络更倾向于选择两个。
+
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 

From c2c6c6ed0ac46c687f68c6c6db001e5c84c28d77 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:18:49 +0800
Subject: [PATCH 0382/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 9a9e1ff7..8bbaaafc 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -11,3 +11,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 
+在实践中，Lasso 和 Ridge 之间权衡的一个优势是它允许在循环过程（Under rotate）中继承 Ridge 的稳定性。
+
+在这里，最小化的目标函数是:

From 9fd5c695ed7ea9555c701243e7fbfe1167bd866f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:19:14 +0800
Subject: [PATCH 0383/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 8bbaaafc..b914494f 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -7,10 +7,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型.这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像Ridge的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
 
-弹性网络在很多特征互相联系的情况下是非常有用的。Lasso 很可能只随机考虑这些特征中的一个，而弹性网络更倾向于选择两个。
-
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 
+弹性网络在很多特征互相联系的情况下是非常有用的。Lasso 很可能只随机考虑这些特征中的一个，而弹性网络更倾向于选择两个。
 在实践中，Lasso 和 Ridge 之间权衡的一个优势是它允许在循环过程（Under rotate）中继承 Ridge 的稳定性。
 
 在这里，最小化的目标函数是:

From 749617b73ca2b3f3c8905c29cd6b425a882562b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:20:46 +0800
Subject: [PATCH 0384/1406] change page of RGN

---
 assets/images/173.jpg     | Bin 0 -> 1485 bytes
 assets/src/RGN/RGN.0.4.md |   5 +++++
 2 files changed, 5 insertions(+)
 create mode 100644 assets/images/173.jpg

diff --git a/assets/images/173.jpg b/assets/images/173.jpg
new file mode 100644
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diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index b914494f..7c4b40f2 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -13,3 +13,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在实践中，Lasso 和 Ridge 之间权衡的一个优势是它允许在循环过程（Under rotate）中继承 Ridge 的稳定性。
 
 在这里，最小化的目标函数是:
+<p align="center">
+<img width="300" align="center" src="../../images/173.jpg" />
+</p>
+
+

From 9525ae17d36a860084b62862b3f803ffd607db53 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:24:17 +0800
Subject: [PATCH 0385/1406] change page RGN

---
 assets/images/174.jpg     | Bin 0 -> 69850 bytes
 assets/images/175.jpg     | Bin 0 -> 56855 bytes
 assets/src/RGN/RGN.0.4.md |   4 ++++
 3 files changed, 4 insertions(+)
 create mode 100644 assets/images/174.jpg
 create mode 100644 assets/images/175.jpg

diff --git a/assets/images/174.jpg b/assets/images/174.jpg
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HcmV?d00001

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 7c4b40f2..7464da26 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -7,6 +7,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 弹性网络是一种使用 L1，L2范数作为先验正则项训练的线性回归模型.这种组合允许学习到一个只有少量参数是非零稀疏的模型，就像 Lasso一样，但是它仍然保持一些像Ridge的正则性质。我们可利用 l1_ratio 参数控制L1和L2的凸组合。弹性网络是一不断叠代的方法。
 
+<p align="center">
+<img width="300" align="center" src="../../images/174.jpg" />
+<img width="300" align="center" src="../../images/175.jpg" />
+</p>
 弹性网络最妙的地方是它永远可以产生有效解。由于它不会产生交叉的路径，所以产生的解都相当不错。举例来说，对一个随机产生的50个城市的推销员问题，弹性网络的解只有比德宾和威尔萧的论文中所提的最具竞争力的演算法长2%（什么是最具竞争力的演算法？有人说是林－克尼根（Lin-Kernighan）演算法，也有人说是SA+OP）。但是弹性网络最吸引人的地方不在它的有效解，而在它收敛的速度。许多人试着去改善弹性网络收敛的速度，都有不错的结果。举例来说，柏尔（Burr）所提出的改良版可令50个城市的推销员问题的收敛次数由1250大幅降为30次。一个最佳化的弹性网络的速度会比林－克尼根快两倍。
 
 弹性网络在很多特征互相联系的情况下是非常有用的。Lasso 很可能只随机考虑这些特征中的一个，而弹性网络更倾向于选择两个。

From 9d7bd8b6423e637b451e1332f35527d7785a7b74 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:27:11 +0800
Subject: [PATCH 0386/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index 7464da26..b07eaab1 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -22,3 +22,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
+#### 应用案例

From a39c729a5ce3afa9bcd90a49a97b0f08c3137bdd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Feb 2018 09:27:31 +0800
Subject: [PATCH 0387/1406] Update RGN.0.4.md

---
 assets/src/RGN/RGN.0.4.md | 85 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)

diff --git a/assets/src/RGN/RGN.0.4.md b/assets/src/RGN/RGN.0.4.md
index b07eaab1..c5168890 100644
--- a/assets/src/RGN/RGN.0.4.md
+++ b/assets/src/RGN/RGN.0.4.md
@@ -23,3 +23,88 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 应用案例
+```python
+print(__doc__)
+
+# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
+# License: BSD 3 clause
+
+from itertools import cycle
+import numpy as np
+import matplotlib.pyplot as plt
+
+from sklearn.linear_model import lasso_path, enet_path
+from sklearn import datasets
+
+diabetes = datasets.load_diabetes()
+X = diabetes.data
+y = diabetes.target
+
+X /= X.std(axis=0)  # Standardize data (easier to set the l1_ratio parameter)
+
+# Compute paths
+
+eps = 5e-3  # the smaller it is the longer is the path
+
+print("Computing regularization path using the lasso...")
+alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)
+
+print("Computing regularization path using the positive lasso...")
+alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
+    X, y, eps, positive=True, fit_intercept=False)
+print("Computing regularization path using the elastic net...")
+alphas_enet, coefs_enet, _ = enet_path(
+    X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)
+
+print("Computing regularization path using the positive elastic net...")
+alphas_positive_enet, coefs_positive_enet, _ = enet_path(
+    X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)
+
+# Display results
+
+plt.figure(1)
+ax = plt.gca()
+
+colors = cycle(['b', 'r', 'g', 'c', 'k'])
+neg_log_alphas_lasso = -np.log10(alphas_lasso)
+neg_log_alphas_enet = -np.log10(alphas_enet)
+for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):
+    l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
+    l2 = plt.plot(neg_log_alphas_enet, coef_e, linestyle='--', c=c)
+
+plt.xlabel('-Log(alpha)')
+plt.ylabel('coefficients')
+plt.title('Lasso and Elastic-Net Paths')
+plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
+plt.axis('tight')
+
+
+plt.figure(2)
+ax = plt.gca()
+neg_log_alphas_positive_lasso = -np.log10(alphas_positive_lasso)
+for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):
+    l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
+    l2 = plt.plot(neg_log_alphas_positive_lasso, coef_pl, linestyle='--', c=c)
+
+plt.xlabel('-Log(alpha)')
+plt.ylabel('coefficients')
+plt.title('Lasso and positive Lasso')
+plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
+plt.axis('tight')
+
+
+plt.figure(3)
+ax = plt.gca()
+neg_log_alphas_positive_enet = -np.log10(alphas_positive_enet)
+for (coef_e, coef_pe, c) in zip(coefs_enet, coefs_positive_enet, colors):
+    l1 = plt.plot(neg_log_alphas_enet, coef_e, c=c)
+    l2 = plt.plot(neg_log_alphas_positive_enet, coef_pe, linestyle='--', c=c)
+
+plt.xlabel('-Log(alpha)')
+plt.ylabel('coefficients')
+plt.title('Elastic-Net and positive Elastic-Net')
+plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
+           loc='lower left')
+plt.axis('tight')
+plt.show()
+```

From 04509a258d9fef924788055cadbb875e7734ee23 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Feb 2018 09:10:55 +0800
Subject: [PATCH 0388/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index a045b514..228afbaf 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -2,4 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+
 #### 最小角回归（LARS）

From e04a5a65247cb6a54d195d2648e503b8a5742d61 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Feb 2018 14:12:50 +0800
Subject: [PATCH 0389/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 228afbaf..0ffde325 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 最小角回归（LARS）
+
+最小角回归(LARS)是对高维数据的回归算法， 由 Bradley Efron, Trevor Hastie, Iain Johnstone 和 Robert Tibshirani 开发完成。 LARS 和逐步回归很像。在每一步，它寻找与响应最有关联的 预测。当有很多预测有相同的关联时，它没有继续利用相同的预测，而是在这些预测中找出应该等角的方向。

From 295732dc870b095029b9196f143b4c90eaaadcf3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Feb 2018 16:13:55 +0800
Subject: [PATCH 0390/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 0ffde325..f50c60c6 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -6,3 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 最小角回归（LARS）
 
 最小角回归(LARS)是对高维数据的回归算法， 由 Bradley Efron, Trevor Hastie, Iain Johnstone 和 Robert Tibshirani 开发完成。 LARS 和逐步回归很像。在每一步，它寻找与响应最有关联的 预测。当有很多预测有相同的关联时，它没有继续利用相同的预测，而是在这些预测中找出应该等角的方向。
+
+
+
+#### 优点

From 8b95f83592a02a319c6958f03fab7485c748ab61 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:31:09 +0800
Subject: [PATCH 0391/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index f50c60c6..1e1fc4ab 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -10,3 +10,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 优点
+1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)

From b3c46fad4f80f4cad9f79db26fcbcca321729bd2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:48:29 +0800
Subject: [PATCH 0392/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 1e1fc4ab..126db629 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -11,3 +11,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 优点
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
+2.

From 383fa3868fe1d9d581cc5f715fd1d1ed9a6fbadc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:48:44 +0800
Subject: [PATCH 0393/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 126db629..dd04a39f 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -11,4 +11,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 优点
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
-2.
+2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。

From 5e4c68dcceafdc9f62ff3cdf153ecfb90043c7a0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:50:11 +0800
Subject: [PATCH 0394/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index dd04a39f..60698b3a 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -12,3 +12,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 优点
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
+3.

From 73700910dfffe50c16d83209c0cd0dbec861b361 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:50:26 +0800
Subject: [PATCH 0395/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 60698b3a..ed1d7d89 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -12,4 +12,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 优点
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
-3.
+3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。
+

From b6a28234f4173fc6272954d8711c2ee7b59cf3b8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 09:50:38 +0800
Subject: [PATCH 0396/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index ed1d7d89..9abfd8f7 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -10,6 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 优点
+
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
 3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。

From 4c9603a70da2843a5de20dbf84e84bb8391b3faa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 10:09:35 +0800
Subject: [PATCH 0397/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 9abfd8f7..6d7f813e 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
 3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。
-
+4. 如果两个变量对响应几乎有相等的联系，则它们的系数应该有相似的增长率。因此这个算法和我们直觉 上的判断一样，而且还更加稳定。

From 7a348b41b2be930fcfb1b0f4e9c0ff932a781e9b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 10:10:22 +0800
Subject: [PATCH 0398/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 6d7f813e..32add079 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -15,3 +15,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
 3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。
 4. 如果两个变量对响应几乎有相等的联系，则它们的系数应该有相似的增长率。因此这个算法和我们直觉 上的判断一样，而且还更加稳定。
+5. 它很容易修改并为其他估算器生成解，比如Least Absolute Shrinkage and Selection Operator

From 6f04b4b88c8414de7162d233aa0591e1b74fbbf3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 10:16:40 +0800
Subject: [PATCH 0399/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 32add079..190d3a87 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -15,4 +15,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
 3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。
 4. 如果两个变量对响应几乎有相等的联系，则它们的系数应该有相似的增长率。因此这个算法和我们直觉 上的判断一样，而且还更加稳定。
-5. 它很容易修改并为其他估算器生成解，比如Least Absolute Shrinkage and Selection Operator
+5. 它很容易修改并为其他估算器生成解，比如Least Absolute Shrinkage and Selection Operator。

From f0a56378ed391022a702ad5c0bdd3d6ca978f118 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 10:17:13 +0800
Subject: [PATCH 0400/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 190d3a87..938f4e52 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -9,10 +9,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 
-#### 优点
+#### 优点和缺点
+
+优点：
 
 1. 当 p >> n，该算法数值运算上非常有效。(例如当维度的数目远超点的个数)
 2. 它在计算上和前向选择一样快，和普通最小二乘法有相同的运算复杂度。
 3. 它产生了一个完整的分段线性的解决路径，在交叉验证或者其他相似的微调模型的方法上非常有用。
 4. 如果两个变量对响应几乎有相等的联系，则它们的系数应该有相似的增长率。因此这个算法和我们直觉 上的判断一样，而且还更加稳定。
 5. 它很容易修改并为其他估算器生成解，比如Least Absolute Shrinkage and Selection Operator。
+
+缺点：

From fa7757896d4ed705037b0956381a98498dec8103 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 10:24:25 +0800
Subject: [PATCH 0401/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index 938f4e52..a6ec23b1 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -20,3 +20,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 5. 它很容易修改并为其他估算器生成解，比如Least Absolute Shrinkage and Selection Operator。
 
 缺点：
+
+1. 因为 LARS 是建立在循环拟合剩余变量上的，所以它对噪声非常敏感。

From 66503ae85d080e4b364a9db3c087a9c3b7357b26 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:16:29 +0800
Subject: [PATCH 0402/1406] Update RGN.0.5.md

---
 assets/src/RGN/RGN.0.5.md | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)

diff --git a/assets/src/RGN/RGN.0.5.md b/assets/src/RGN/RGN.0.5.md
index a6ec23b1..06595fc8 100644
--- a/assets/src/RGN/RGN.0.5.md
+++ b/assets/src/RGN/RGN.0.5.md
@@ -8,6 +8,41 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 最小角回归(LARS)是对高维数据的回归算法， 由 Bradley Efron, Trevor Hastie, Iain Johnstone 和 Robert Tibshirani 开发完成。 LARS 和逐步回归很像。在每一步，它寻找与响应最有关联的 预测。当有很多预测有相同的关联时，它没有继续利用相同的预测，而是在这些预测中找出应该等角的方向。
 
 
+#### 示例应用
+```python
+print(__doc__)
+
+# Author: Fabian Pedregosa <fabian.pedregosa@inria.fr>
+#         Alexandre Gramfort <alexandre.gramfort@inria.fr>
+# License: BSD 3 clause
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from sklearn import linear_model
+from sklearn import datasets
+
+diabetes = datasets.load_diabetes()
+X = diabetes.data
+y = diabetes.target
+
+print("Computing regularization path using the LARS ...")
+alphas, _, coefs = linear_model.lars_path(X, y, method='lasso', verbose=True)
+
+xx = np.sum(np.abs(coefs.T), axis=1)
+xx /= xx[-1]
+
+plt.plot(xx, coefs.T)
+ymin, ymax = plt.ylim()
+plt.vlines(xx, ymin, ymax, linestyle='dashed')
+plt.xlabel('|coef| / max|coef|')
+plt.ylabel('Coefficients')
+plt.title('LASSO Path')
+plt.axis('tight')
+plt.show()
+```
+
+
 
 #### 优点和缺点
 

From 6418166657cfe63cee48ea85ad82e3262eceea0e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:24:43 +0800
Subject: [PATCH 0403/1406] change page

---
 README.md               | 2 +-
 assets/src/DT/DT.0.1.md | 7 +++++++
 2 files changed, 8 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/DT/DT.0.1.md

diff --git a/README.md b/README.md
index 224b36e1..30748bbe 100644
--- a/README.md
+++ b/README.md
@@ -81,7 +81,7 @@
      * [岭回归（Ridge Regression）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.2.md)
      * [LASSO（Least Absolute Shrinkage and Selection Operator）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.3.md)
      * [弹性网络(Elastic Net)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
-     * [最小角回归（LARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
+     * [最小角回归(LARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
  * [决策树算法]()
      * [分类和回归树（CART）]()
      * [ID3算法(Iterative Dichotomiser 3)]()
diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
new file mode 100644
index 00000000..91cf80c9
--- /dev/null
+++ b/assets/src/DT/DT.0.1.md
@@ -0,0 +1,7 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 决策树
+
+决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。

From 96604b50fe5234c73a0d9c141959f1deb617ec81 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:25:57 +0800
Subject: [PATCH 0404/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 30748bbe..8e73f7fd 100644
--- a/README.md
+++ b/README.md
@@ -82,7 +82,7 @@
      * [LASSO（Least Absolute Shrinkage and Selection Operator）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.3.md)
      * [弹性网络(Elastic Net)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
      * [最小角回归(LARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
- * [决策树算法]()
+ * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）]()
      * [ID3算法(Iterative Dichotomiser 3)]()
      * [CHAID（Chi-squared Automatic Interaction Detection]()

From d6ddf04d0da9388e0a8793f2fd9a23a432b70aca Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:27:52 +0800
Subject: [PATCH 0405/1406] change page of DT.0.1

---
 assets/src/DT/DT.0.1.md | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
index 91cf80c9..1cde008b 100644
--- a/assets/src/DT/DT.0.1.md
+++ b/assets/src/DT/DT.0.1.md
@@ -2,6 +2,15 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 决策树
+#### 决策树（Decision Tree）
 
 决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
+
+决策树（Decision Tree）这里的应用算法有：
+
+* 分类和回归树（CART）
+* ID3算法(Iterative Dichotomiser 3)
+* CHAID（Chi-squared Automatic Interaction Detection
+* 随机森林（Random Forest）
+* 多元自适应回归样条（MARS）
+* 梯度推进机（Gradient Boosting Machine， GBM）
\ No newline at end of file

From c625f3284f762c9a4fa59082dbb0e5e3ea70e9ea Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:28:46 +0800
Subject: [PATCH 0406/1406] change page of DT

---
 assets/src/DT/DT.0.1.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
index 1cde008b..67dd59f9 100644
--- a/assets/src/DT/DT.0.1.md
+++ b/assets/src/DT/DT.0.1.md
@@ -6,6 +6,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
 
+最早的决策树算法是由Hunt等人于1966年提出的CLS。当前最有影响的决策树算法是Quinlan于1986年提出的ID3和1993年提出的C4.5。ID3只能处理离散型描述属性，它选择信息增益最大的属性划分训练样本，其目的是进行分枝时系统的熵最小，从而提高算法的运算速度和精确度。ID3算法的主要缺陷是，用信息增益作为选择分枝属性的标准时，偏向于取值较多的属性，而在某些情况下，这类属性可能不会提供太多有价值的信息。C4.5是ID3算法的改进算法，不仅可以处理离散型描述属性，还能处理连续性描述属性。C4.5采用了信息增益比作为选择分枝属性的标准，弥补了ID3算法的不足。
+
+决策树经常在运筹学中使用，特别是在决策分析中，它帮助确定一个能最可能达到目标的策略。如果在实际中，决策不得不在没有完备知识的情况下被在线采用，一个决策树应该平行概率模型作为最佳的选择模型或在线选择模型算法。决策树的另一个使用是作为计算条件概率的描述性手段。
+
 决策树（Decision Tree）这里的应用算法有：
 
 * 分类和回归树（CART）

From 653d40b03fb9e211a7ea49d227522c15aeef5eec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 11:30:17 +0800
Subject: [PATCH 0407/1406] change page of readme

---
 README.md               | 2 +-
 assets/src/DT/DT.0.2.md | 6 ++++++
 2 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/DT/DT.0.2.md

diff --git a/README.md b/README.md
index 8e73f7fd..b19a1449 100644
--- a/README.md
+++ b/README.md
@@ -83,7 +83,7 @@
      * [弹性网络(Elastic Net)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.4.md)
      * [最小角回归(LARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
-     * [分类和回归树（CART）]()
+     * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)]()
      * [CHAID（Chi-squared Automatic Interaction Detection]()
      * [随机森林（Random Forest）]()
diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
new file mode 100644
index 00000000..347eef6a
--- /dev/null
+++ b/assets/src/DT/DT.0.2.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 分类和回归树（CART）
+

From edb1a8d6b9c51199962d85c0fac9222ed3cc566c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:33:59 +0800
Subject: [PATCH 0408/1406] Update README.md

---
 README.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b19a1449..d5ffe04d 100644
--- a/README.md
+++ b/README.md
@@ -27,7 +27,12 @@
  * [深度学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.02.md)
  * [深度学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.03.md)
  * [深度学习的应用案例]()
- * [深度学习所需要的数据]()
+
+
+#### 机器学习
+机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
+机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
+
 
 
 

From e2c8e45c9beb1dfd95c771b664f18634dca5f62a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:35:06 +0800
Subject: [PATCH 0409/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d5ffe04d..a54c3aa9 100644
--- a/README.md
+++ b/README.md
@@ -28,8 +28,8 @@
  * [深度学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.03.md)
  * [深度学习的应用案例]()
 
-
 #### 机器学习
+
 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
 

From c2a107193d467d18d340d7efb2ed51acfb9e84e2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:46:04 +0800
Subject: [PATCH 0410/1406] Update README.md

---
 README.md | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index a54c3aa9..e161ff19 100644
--- a/README.md
+++ b/README.md
@@ -19,6 +19,17 @@
 * 用学习来的算法运用在测试集上累评估算法(可能要设计到调整参数(parameter tuning) 用来验证集(validation set))
 
 
+#### 机器学习
+
+机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
+机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
+  
+ * [机器学习环境的搭建]()
+ * [机器学习的入门]()
+ * [机器学习的框架]()
+ * [机器学习的应用案例]()
+
+
 #### 深度学习
 深度学习：深度学习是基于机器学习延伸出来的一个新的领域，由以人大脑结构为启发的神经网络算法为起源加之模型结构深度的增加发展，并伴随大数据和计算能力的提高而产生的一系列新的算法。
 深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
@@ -28,13 +39,6 @@
  * [深度学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.03.md)
  * [深度学习的应用案例]()
 
-#### 机器学习
-
-机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
-机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
-
-
-
 
 #### 机器学习算法概览
 <p align="center">

From 87e602e404dbc4a3bce03a89a16ec9775b977c2a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:46:42 +0800
Subject: [PATCH 0411/1406] Update README.md

---
 README.md | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index e161ff19..f2c6ce09 100644
--- a/README.md
+++ b/README.md
@@ -20,9 +20,8 @@
 
 
 #### 机器学习
-
-机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
-机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
+* 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
+* 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
  * [机器学习环境的搭建]()
  * [机器学习的入门]()
@@ -31,8 +30,8 @@
 
 
 #### 深度学习
-深度学习：深度学习是基于机器学习延伸出来的一个新的领域，由以人大脑结构为启发的神经网络算法为起源加之模型结构深度的增加发展，并伴随大数据和计算能力的提高而产生的一系列新的算法。
-深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
+* 深度学习：深度学习是基于机器学习延伸出来的一个新的领域，由以人大脑结构为启发的神经网络算法为起源加之模型结构深度的增加发展，并伴随大数据和计算能力的提高而产生的一系列新的算法。
+* 深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
 
  * [深度神经网络](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.01.md)
  * [深度学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.02.md)

From aaf11f5157e5ee6da30bacd9e0cb865befa9594f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:49:06 +0800
Subject: [PATCH 0412/1406] Update README.md

---
 README.md | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/README.md b/README.md
index f2c6ce09..e95d22b4 100644
--- a/README.md
+++ b/README.md
@@ -175,9 +175,6 @@
 * [Artificial Intelligence](https://github.com/owainlewis/awesome-artificial-intelligence)
 * [Tensorflow新手入门](http://www.tensorfly.cn/tfdoc/tutorials/mnist_beginners.html)
 
-### 机器学习
-觉得此文章不错可以给我star！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
-
 
 ### License
 This is free software distributed under the terms of the MIT license

From 15faad93a8ffa81c33966ccafbaac645d3137aba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Feb 2018 16:49:20 +0800
Subject: [PATCH 0413/1406] Update README.md

---
 README.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/README.md b/README.md
index e95d22b4..f2c6ce09 100644
--- a/README.md
+++ b/README.md
@@ -175,6 +175,9 @@
 * [Artificial Intelligence](https://github.com/owainlewis/awesome-artificial-intelligence)
 * [Tensorflow新手入门](http://www.tensorfly.cn/tfdoc/tutorials/mnist_beginners.html)
 
+### 机器学习
+觉得此文章不错可以给我star！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
+
 
 ### License
 This is free software distributed under the terms of the MIT license

From 0daa592e99edd1eaf4d244f61300d349e287a1e6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:03:22 +0800
Subject: [PATCH 0414/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 347eef6a..d1ac7190 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -3,4 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 分类和回归树（CART）
+分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。
 
+不同于C4.5，CART本质是对特征空间进行二元划分（即CART生成的决策树是一棵二叉树），并能够对标量属性（nominal attribute）与连续属性（continuous attribute）进行分裂。

From 9d47703f160139e6baacd6c8db00a1568c98afde Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:08:35 +0800
Subject: [PATCH 0415/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index d1ac7190..e041d9f9 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -6,3 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。
 
 不同于C4.5，CART本质是对特征空间进行二元划分（即CART生成的决策树是一棵二叉树），并能够对标量属性（nominal attribute）与连续属性（continuous attribute）进行分裂。
+CART决策树是结构简洁的二叉树，采用一种二分递归分割的技术，将当前的样本集分为两个子样本集，使得生成的每个非叶子的节点都有两个分支。与普通的决策树算法一样，CART算法包括两个过程：1）决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；2）决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。

From 4f5660a4ba7e1576853973a8f50dc23caed77558 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:09:10 +0800
Subject: [PATCH 0416/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index e041d9f9..9578ace5 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -6,4 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。
 
 不同于C4.5，CART本质是对特征空间进行二元划分（即CART生成的决策树是一棵二叉树），并能够对标量属性（nominal attribute）与连续属性（continuous attribute）进行分裂。
-CART决策树是结构简洁的二叉树，采用一种二分递归分割的技术，将当前的样本集分为两个子样本集，使得生成的每个非叶子的节点都有两个分支。与普通的决策树算法一样，CART算法包括两个过程：1）决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；2）决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。
+CART决策树是结构简洁的二叉树，采用一种二分递归分割的技术，将当前的样本集分为两个子样本集，使得生成的每个非叶子的节点都有两个分支。与普通的决策树算法一样，CART算法包括两个过程： (1)决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；(2)决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。

From 6c3f1f18821f57a62b74f85c640c83b491c80174 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:14:42 +0800
Subject: [PATCH 0417/1406] Update DT.0.1.md

---
 assets/src/DT/DT.0.1.md | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
index 67dd59f9..96a0784d 100644
--- a/assets/src/DT/DT.0.1.md
+++ b/assets/src/DT/DT.0.1.md
@@ -17,4 +17,15 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * CHAID（Chi-squared Automatic Interaction Detection
 * 随机森林（Random Forest）
 * 多元自适应回归样条（MARS）
-* 梯度推进机（Gradient Boosting Machine， GBM）
\ No newline at end of file
+* 梯度推进机（Gradient Boosting Machine， GBM）
+
+#### 决策树的优点
+
+* 便于理解和解释。树的结构可以可视化出来。
+* 训练需要的数据少。其他机器学习模型通常需要数据规范化，比如构建虚拟变量和移除缺失值,不过请注意，这种模型不支持缺失值。
+* 由于训练决策树的数据点的数量导致了决策树的使用开销呈指数分布(训练树模型的时间复杂度是参与训练数据点的对数值)。
+* 能够处理数值型数据和分类数据。其他的技术通常只能用来专门分析某一种变量类型的数据集。详情请参阅算法。
+* 能够处理多路输出的问题。
+* 使用白盒模型。如果某种给定的情况在该模型中是可以观察的，那么就可以轻易的通过布尔逻辑来解释这种情况。相比之下，在黑盒模型中的结果就是很难说明清 楚地。
+* 可以通过数值统计测试来验证该模型。这对事解释验证该模型的可靠性成为可能。
+* 即使该模型假设的结果与真实模型所提供的数据有些违反，其表现依旧良好。

From 7384a307e0a8d5efca48eabbb69c2cb484558198 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:25:22 +0800
Subject: [PATCH 0418/1406] Update DT.0.1.md

---
 assets/src/DT/DT.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
index 96a0784d..4acafb87 100644
--- a/assets/src/DT/DT.0.1.md
+++ b/assets/src/DT/DT.0.1.md
@@ -29,3 +29,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 使用白盒模型。如果某种给定的情况在该模型中是可以观察的，那么就可以轻易的通过布尔逻辑来解释这种情况。相比之下，在黑盒模型中的结果就是很难说明清 楚地。
 * 可以通过数值统计测试来验证该模型。这对事解释验证该模型的可靠性成为可能。
 * 即使该模型假设的结果与真实模型所提供的数据有些违反，其表现依旧良好。
+
+#### 决策树的缺点

From 9c79490f2c69135e85d80257ed69246d4ca8a092 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:28:35 +0800
Subject: [PATCH 0419/1406] Update DT.0.1.md


From 6636e514aefd7a9e577e5cf80d0bbb8d7d2d5212 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:35:34 +0800
Subject: [PATCH 0420/1406] Update DT.0.1.md

---
 assets/src/DT/DT.0.1.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DT/DT.0.1.md b/assets/src/DT/DT.0.1.md
index 4acafb87..35229062 100644
--- a/assets/src/DT/DT.0.1.md
+++ b/assets/src/DT/DT.0.1.md
@@ -31,3 +31,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 即使该模型假设的结果与真实模型所提供的数据有些违反，其表现依旧良好。
 
 #### 决策树的缺点
+
+* 决策树模型容易产生一个过于复杂的模型,这样的模型对数据的泛化性能会很差。这就是所谓的过拟合.一些策略像剪枝、设置叶节点所需的最小样本数或设置数的最大深度是避免出现 该问题最为有效地方法。
+* 决策树可能是不稳定的，因为数据中的微小变化可能会导致完全不同的树生成。这个问题可以通过决策树的集成来得到缓解
+* 在多方面性能最优和简单化概念的要求下，学习一棵最优决策树通常是一个NP难问题。因此，实际的决策树学习算法是基于启发式算法，例如在每个节点进 行局部最优决策的贪心算法。这样的算法不能保证返回全局最优决策树。这个问题可以通过集成学习来训练多棵决策树来缓解,这多棵决策树一般通过对特征和样本有放回的随机采样来生成。
+* 有些概念很难被决策树学习到,因为决策树很难清楚的表述这些概念。例如XOR，奇偶或者复用器的问题。
+* 如果某些类在问题中占主导地位会使得创建的决策树有偏差。因此，建议在拟合前先对数据集进行平衡。

From cbb0929226d4b69adb2763393662f50eb24b011a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:48:51 +0800
Subject: [PATCH 0421/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 9578ace5..913c9701 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -6,4 +6,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。
 
 不同于C4.5，CART本质是对特征空间进行二元划分（即CART生成的决策树是一棵二叉树），并能够对标量属性（nominal attribute）与连续属性（continuous attribute）进行分裂。
-CART决策树是结构简洁的二叉树，采用一种二分递归分割的技术，将当前的样本集分为两个子样本集，使得生成的每个非叶子的节点都有两个分支。与普通的决策树算法一样，CART算法包括两个过程： (1)决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；(2)决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。
+CART决策树是结构简洁的二叉树，采用一种二分递归分割的技术，将当前的样本集分为两个子样本集，使得生成的每个非叶子的节点都有两个分支。
+
+CART算法包括两个过程： 
+1. 决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；
+2. 决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。

From d27c9faea9725b3e42bc89addd890760ac2f0f13 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Feb 2018 09:50:25 +0800
Subject: [PATCH 0422/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 913c9701..0af36544 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 分类和回归树（CART）
+
 分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。
 
 不同于C4.5，CART本质是对特征空间进行二元划分（即CART生成的决策树是一棵二叉树），并能够对标量属性（nominal attribute）与连续属性（continuous attribute）进行分裂。

From 5ac8efcfb7e191a2ed8e64dbf4a086eae305bdd0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 12:11:02 +0800
Subject: [PATCH 0423/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 0af36544..a8e404d7 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -2,6 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+
 #### 分类和回归树（CART）
 
 分类回归树(Classification And Regression Tree, CART)模型是决策树学习方法的一种，CART既可以用于分类计算，也可以用于回归。

From 7235d740e7c70784c4d92675c5b1dcb61af0055b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 21:46:06 +0800
Subject: [PATCH 0424/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index a8e404d7..cdebcf03 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -13,3 +13,5 @@ CART决策树是结构简洁的二叉树，采用一种二分递归分割的技
 CART算法包括两个过程： 
 1. 决策树的生成：基于训练数据集生成决策树，生成的决策树要尽量的大；
 2. 决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。
+
+1.决策树的生成

From b62787913b988db9dce948629cb45f7884b6df1f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 21:46:22 +0800
Subject: [PATCH 0425/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index cdebcf03..88c6ad12 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -15,3 +15,5 @@ CART算法包括两个过程：
 2. 决策树的剪枝：用验证数据集对以生成的树进行剪枝并选择最优子树，此时用损失函数最小作为剪枝的标准。
 
 1.决策树的生成
+决策树的生成就是递归的构建二叉决策树的过程。对回归树用平方误差最小化准则，对分类树用基尼指数最小化原则，进行特征选择，生成二叉树。
+主要的原理如下：(1)分类树原理：分类树采用基尼指数（Gini index, Gini）选择最优特征，同时决定该特征的最优二值切分点。基尼指数定义为：

From 8092d69009208845e6816f54bfb77de4063a522e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 21:46:43 +0800
Subject: [PATCH 0426/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 88c6ad12..70046662 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -16,4 +16,5 @@ CART算法包括两个过程：
 
 1.决策树的生成
 决策树的生成就是递归的构建二叉决策树的过程。对回归树用平方误差最小化准则，对分类树用基尼指数最小化原则，进行特征选择，生成二叉树。
+
 主要的原理如下：(1)分类树原理：分类树采用基尼指数（Gini index, Gini）选择最优特征，同时决定该特征的最优二值切分点。基尼指数定义为：

From 2d28528c9250a5a57619e40fab1049fc084ceea7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 21:47:03 +0800
Subject: [PATCH 0427/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 70046662..74a9d1b8 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -18,3 +18,6 @@ CART算法包括两个过程：
 决策树的生成就是递归的构建二叉决策树的过程。对回归树用平方误差最小化准则，对分类树用基尼指数最小化原则，进行特征选择，生成二叉树。
 
 主要的原理如下：(1)分类树原理：分类树采用基尼指数（Gini index, Gini）选择最优特征，同时决定该特征的最优二值切分点。基尼指数定义为：
+<p align="center">
+<img width="200" align="center" src="../../images/56.jpg" />
+</p>

From cb298377149c735bf3830eb60aca0d05576eb3e1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Feb 2018 21:47:48 +0800
Subject: [PATCH 0428/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 74a9d1b8..4919e414 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -21,3 +21,8 @@ CART算法包括两个过程：
 <p align="center">
 <img width="200" align="center" src="../../images/56.jpg" />
 </p>
+
+对于给定样本集合D，其基尼指数的计算为：
+<p align="center">
+<img width="200" align="center" src="../../images/57.jpg" />
+</p>

From a16768b2946c8ac553df1753c85b9714039f347e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 13 Feb 2018 09:27:22 +0800
Subject: [PATCH 0429/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 4919e414..b5c2875e 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -26,3 +26,5 @@ CART算法包括两个过程：
 <p align="center">
 <img width="200" align="center" src="../../images/57.jpg" />
 </p>
+如果样本集合D根据特征A是否取某一可能值a被分割成D1和D2两部分，即：<img width="300" align="center" src="../../images/60.jpg" />,D2=D-D1
+则在特征A的条件下，集合D的基尼指数计算公式为：

From 11bf7fb74f93f1026609189f40342bbd938f78c9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 15 Feb 2018 13:28:57 +0800
Subject: [PATCH 0430/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index b5c2875e..60ea3df3 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -28,3 +28,6 @@ CART算法包括两个过程：
 </p>
 如果样本集合D根据特征A是否取某一可能值a被分割成D1和D2两部分，即：<img width="300" align="center" src="../../images/60.jpg" />,D2=D-D1
 则在特征A的条件下，集合D的基尼指数计算公式为：
+<p align="center">
+<img width="200" align="center" src="../../images/58.jpg" />
+</p>

From db7f30b0176895a72dec5f3ba341f9c53ff817b1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 15 Feb 2018 13:29:21 +0800
Subject: [PATCH 0431/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 60ea3df3..6844d961 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -31,3 +31,4 @@ CART算法包括两个过程：
 <p align="center">
 <img width="200" align="center" src="../../images/58.jpg" />
 </p>
+基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。

From 59c8d44f46f2977987c84503a3bf4f874642909e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 15 Feb 2018 13:29:48 +0800
Subject: [PATCH 0432/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 6844d961..8cabfbbc 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -32,3 +32,4 @@ CART算法包括两个过程：
 <img width="200" align="center" src="../../images/58.jpg" />
 </p>
 基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。
+（2）回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：

From e116c3c9f7e37fb8cf82292e8470f0a84453beea Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Feb 2018 08:26:24 +0800
Subject: [PATCH 0433/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 8cabfbbc..47de3e58 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -33,3 +33,6 @@ CART算法包括两个过程：
 </p>
 基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。
 （2）回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：
+<p align="center">
+<img width="200" align="center" src="../../images/59.jpg" />
+</p>

From c673145b93ecb334f175d226601bb329575f82c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Feb 2018 08:26:42 +0800
Subject: [PATCH 0434/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 47de3e58..4a885e7b 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -33,6 +33,7 @@ CART算法包括两个过程：
 </p>
 基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。
 （2）回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：
+
 <p align="center">
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>

From b8e94d18454997f9bc3860e9b4069d33c04297a0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Feb 2018 08:27:00 +0800
Subject: [PATCH 0435/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 4a885e7b..47de3e58 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -33,7 +33,6 @@ CART算法包括两个过程：
 </p>
 基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。
 （2）回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：
-
 <p align="center">
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>

From d28b4648e186febe03aa3a5c0912ac68da009f9a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Feb 2018 08:28:06 +0800
Subject: [PATCH 0436/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 47de3e58..c0e46e36 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -36,3 +36,4 @@ CART算法包括两个过程：
 <p align="center">
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>
+其中cm表示单元Rm上的最小误差平方的最优解.

From d9dcf41cdc6bea5ead6db09150bafe97f86c4031 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 21 Feb 2018 10:49:15 +0800
Subject: [PATCH 0437/1406] Update CART.md

---
 assets/src/CART/CART.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CART/CART.md b/assets/src/CART/CART.md
index 201877e3..7c750743 100644
--- a/assets/src/CART/CART.md
+++ b/assets/src/CART/CART.md
@@ -45,6 +45,7 @@ CART算法原理:CART决策树是结构简洁的二叉树，采用一种二分
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>
 其中cm表示单元Rm上的最小误差平方的最优解.
+
 2、决策树的剪枝
 
 CART算法对于决策树剪枝方法，采用代价复杂度模型，通过交叉验证来估计对预测样本集的误分类损失，产生最小交叉验证误分类估计树。

From d95f60ed978e041bab9bf74b29dcd61003e232ee Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:17:35 +0800
Subject: [PATCH 0438/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index c0e46e36..04fee5ba 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -37,3 +37,9 @@ CART算法包括两个过程：
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>
 其中cm表示单元Rm上的最小误差平方的最优解.
+
+2、决策树的剪枝
+
+CART算法对于决策树剪枝方法，采用代价复杂度模型，通过交叉验证来估计对预测样本集的误分类损失，产生最小交叉验证误分类估计树。
+
+CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T0底端开始不断剪枝，直到T0的根节点，形成一个子树序列{T0，T1，… ，Tn}；然后通过交叉验证法在独立的验证数据集上对子树序列进行测试，从中选择最优子树。

From 1d7707e093cde256abf7c598484ef7a0216a21ba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:18:41 +0800
Subject: [PATCH 0439/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 04fee5ba..9e097183 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -43,3 +43,5 @@ CART算法包括两个过程：
 CART算法对于决策树剪枝方法，采用代价复杂度模型，通过交叉验证来估计对预测样本集的误分类损失，产生最小交叉验证误分类估计树。
 
 CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T0底端开始不断剪枝，直到T0的根节点，形成一个子树序列{T0，T1，… ，Tn}；然后通过交叉验证法在独立的验证数据集上对子树序列进行测试，从中选择最优子树。
+
+#### 相关应用

From d1c4468c8fcdd3f9be57c5272e852a1384f5b884 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:21:05 +0800
Subject: [PATCH 0440/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 9e097183..fb9f582a 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -45,3 +45,4 @@ CART算法对于决策树剪枝方法，采用代价复杂度模型，通过交
 CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T0底端开始不断剪枝，直到T0的根节点，形成一个子树序列{T0，T1，… ，Tn}；然后通过交叉验证法在独立的验证数据集上对子树序列进行测试，从中选择最优子树。
 
 #### 相关应用
+

From b5bb09f17bde3035745f4c7eee09a76683c80266 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:21:29 +0800
Subject: [PATCH 0441/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index fb9f582a..759539f4 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -46,3 +46,4 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 
 #### 相关应用
 
+分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。

From 635bf3210261e3e827c856e3c8960ea23479a5a2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:21:51 +0800
Subject: [PATCH 0442/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 759539f4..74f1a77f 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -46,4 +46,4 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 
 #### 相关应用
 
-分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。
+分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。决策树是许多商业规则归纳系统的基础。

From e8cdfb71a954b773142b8cefbf245a136a176316 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:22:49 +0800
Subject: [PATCH 0443/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 74f1a77f..d4fcb6c8 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -47,3 +47,5 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 #### 相关应用
 
 分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。决策树是许多商业规则归纳系统的基础。
+
+#### 优缺点

From 0679d803bfd2a7cfddb4dc3cde7d3b84a062d6f0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:42:11 +0800
Subject: [PATCH 0444/1406] change page of DT

---
 assets/src/DT/DT.0.3.md | 7 +++++++
 1 file changed, 7 insertions(+)
 create mode 100644 assets/src/DT/DT.0.3.md

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
new file mode 100644
index 00000000..ed7b3944
--- /dev/null
+++ b/assets/src/DT/DT.0.3.md
@@ -0,0 +1,7 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+
+#### 分类和回归树（CART）
+

From 51aa918526846666e7f65f46a3f37321b6dded2d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:43:05 +0800
Subject: [PATCH 0445/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index d4fcb6c8..616901ba 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -49,3 +49,4 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。决策树是许多商业规则归纳系统的基础。
 
 #### 优缺点
+优点：可以生成易于理解的规则；计算量相对来说不大；可处理连续和离散字段；最终结果可清晰显示字段的重要性程度。

From 426780e4b942a4d3e9ca4662e83857aa44f641fb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:43:22 +0800
Subject: [PATCH 0446/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 616901ba..7d89f3d4 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -49,4 +49,6 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 分类回归树本质上也是一种决策树算法；而决策树分类器具有很好的准确性，已被成功的应用于许多的应用领域的分类，如医学、制造和生产、金融分析、天文学与分子生物学等；具体的包括欺诈监测、针对销售、性能预测、制造和医疗整段。决策树是许多商业规则归纳系统的基础。
 
 #### 优缺点
+
 优点：可以生成易于理解的规则；计算量相对来说不大；可处理连续和离散字段；最终结果可清晰显示字段的重要性程度。
+缺点：对连续字段难以预测；处理时间序列数据，前期预处理步骤多；当类别太多，错误可能增加的较快。

From 69e5c6472d7906250a82317ab295c6abc1065eaa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:44:46 +0800
Subject: [PATCH 0447/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f2c6ce09..cc57e094 100644
--- a/README.md
+++ b/README.md
@@ -92,7 +92,7 @@
      * [最小角回归(LARS)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RGN/RGN.0.5.md)
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
-     * [ID3算法(Iterative Dichotomiser 3)]()
+     * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
      * [CHAID（Chi-squared Automatic Interaction Detection]()
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()

From 59d2a9d24a88c1fc1e2ad749303db938d5cc1556 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:48:10 +0800
Subject: [PATCH 0448/1406] Update README.md

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index cc57e094..66f2eb31 100644
--- a/README.md
+++ b/README.md
@@ -176,7 +176,8 @@
 * [Tensorflow新手入门](http://www.tensorfly.cn/tfdoc/tutorials/mnist_beginners.html)
 
 ### 机器学习
-觉得此文章不错可以给我star！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
+
+觉得此文章不错，支持我的话可以给我star ，:star: :star: :star:！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
 
 
 ### License

From c9a4f0927f95578dd1b8a46a54f2d52e29b2d850 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 24 Feb 2018 09:48:32 +0800
Subject: [PATCH 0449/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 66f2eb31..95dc1e7b 100644
--- a/README.md
+++ b/README.md
@@ -177,7 +177,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star: :star: :star:！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
 
 
 ### License

From 1c00867df43c22b3426bc6b714d5165cf59d6a4f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:41:00 +0800
Subject: [PATCH 0450/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index ed7b3944..0a83d4eb 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -3,5 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
-#### 分类和回归树（CART）
+#### ID3算法(Iterative Dichotomiser 3)
 

From cbe0b15cc78eb7f68aaa21336274eea71abf4f34 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:42:07 +0800
Subject: [PATCH 0451/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 0a83d4eb..6c5497bd 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
-
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。

From c6bc463dfdbc4900ee3b2d8083e67e1916466278 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:42:25 +0800
Subject: [PATCH 0452/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 6c5497bd..23c673a6 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,4 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
-ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法，
+
+  

From 593ed07c42eb57a999db0e674660742be8eb057e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:42:44 +0800
Subject: [PATCH 0453/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 23c673a6..ac291682 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,6 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
-ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法，
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个
 
   

From bdebee5475fec502f83ae4274839dc3800d5471d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:42:57 +0800
Subject: [PATCH 0454/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index ac291682..ea0fd763 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,6 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
-ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总
 
   

From 473c62f69981f9871086e71618c4a0b44c3bd27f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:43:17 +0800
Subject: [PATCH 0455/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index ea0fd763..bbd4235b 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,6 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
-ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
   

From dee008e0e6a1c74cbd83eda5e40f87c30f5a33cf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:43:27 +0800
Subject: [PATCH 0456/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index bbd4235b..123b82e1 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -4,6 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### ID3算法(Iterative Dichotomiser 3)
+
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
   

From 2f565673bbbc16e8f17d7f19be2b25a207d8292c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:44:27 +0800
Subject: [PATCH 0457/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 123b82e1..3326ae30 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -7,4 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
+在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息
   

From dd65152d4ca22ede46091585d3efa1836e0f7b7a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 25 Feb 2018 19:44:52 +0800
Subject: [PATCH 0458/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 3326ae30..eefb1c05 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -7,5 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
-在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息
+在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。该算法采用自顶向下的贪婪搜索遍历可能的决策空间
   

From f05a0da9d9b4050f1916ff231c809f3b51f1eece Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 26 Feb 2018 09:19:15 +0800
Subject: [PATCH 0459/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index eefb1c05..b0947408 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -7,5 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
-在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。该算法采用自顶向下的贪婪搜索遍历可能的决策空间
+在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   

From 959939b389ec19df1442b669fe76c839f5dc7e99 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 09:16:05 +0800
Subject: [PATCH 0460/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index b0947408..aeecfddc 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -7,5 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
+
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   

From bb61f7a44562ec4853166f90df2043427dc69b91 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:54:51 +0800
Subject: [PATCH 0461/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index aeecfddc..6ff4052c 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### ID3算法(Iterative Dichotomiser 3)
 
-ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser 3，迭代二叉树3代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
+ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser3，迭代二叉树三代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。

From 000cff300aac4398848dea2c73ed9dfd3f44f526 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:55:51 +0800
Subject: [PATCH 0462/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 6ff4052c..96e192c8 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -10,3 +10,4 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   
+#### 

From 58c3f4c509a078c609349ff77a44336f591a327f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:55:58 +0800
Subject: [PATCH 0463/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 96e192c8..d8865a75 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -10,4 +10,4 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   
-#### 
+#### 应用案例

From d16814b36935a80257cc50a317f9aeffc60b97d2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:56:28 +0800
Subject: [PATCH 0464/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 43 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index d8865a75..92dad417 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -11,3 +11,46 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   
 #### 应用案例
+
+```python
+# -*-coding:utf-8 -*-
+from math import log
+import operator
+
+def createDataSet():#创建一个样例数据集
+    dataSet = [[1, 1, 'yes'],
+               [1, 1, 'yes'],
+               [1, 0, 'no'],
+               [0, 1, 'no'],
+               [0, 1, 'no']]
+    labels = ['no surfacing','flippers']
+    #change to discrete values
+    return dataSet, labels
+
+def calcShannonEnt(dataSet):#香农熵计算函数
+    numEntries = len(dataSet)
+    labelCounts = {}
+    for featVec in dataSet: #the the number of unique elements and their occurance
+        currentLabel = featVec[-1]
+        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
+        labelCounts[currentLabel] += 1
+    shannonEnt = 0.0
+    for key in labelCounts:
+        prob = float(labelCounts[key])/numEntries
+        shannonEnt -= prob * log(prob,2) #log base 2
+    return shannonEnt
+    
+def splitDataSet(dataSet, axis, value):#按照给定特征划分数据集
+    retDataSet = []
+    for featVec in dataSet:
+        if featVec[axis] == value:
+            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
+            reducedFeatVec.extend(featVec[axis+1:])
+            retDataSet.append(reducedFeatVec)
+    return retDataSet
+
+作者：哈劳斯军士
+链接：https://www.jianshu.com/p/c3df8616abe6
+來源：简书
+著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
+```

From d487bc7f546a374bfa6ebec1391ae15b6d09e097 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:56:39 +0800
Subject: [PATCH 0465/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 92dad417..c53a89b0 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -49,8 +49,4 @@ def splitDataSet(dataSet, axis, value):#按照给定特征划分数据集
             retDataSet.append(reducedFeatVec)
     return retDataSet
 
-作者：哈劳斯军士
-链接：https://www.jianshu.com/p/c3df8616abe6
-來源：简书
-著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
 ```

From 7b240c29c247fa6781dcdc87fbbde1eb1b19fe24 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Feb 2018 12:57:26 +0800
Subject: [PATCH 0466/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 39 ---------------------------------------
 1 file changed, 39 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index c53a89b0..d8865a75 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -11,42 +11,3 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   
 #### 应用案例
-
-```python
-# -*-coding:utf-8 -*-
-from math import log
-import operator
-
-def createDataSet():#创建一个样例数据集
-    dataSet = [[1, 1, 'yes'],
-               [1, 1, 'yes'],
-               [1, 0, 'no'],
-               [0, 1, 'no'],
-               [0, 1, 'no']]
-    labels = ['no surfacing','flippers']
-    #change to discrete values
-    return dataSet, labels
-
-def calcShannonEnt(dataSet):#香农熵计算函数
-    numEntries = len(dataSet)
-    labelCounts = {}
-    for featVec in dataSet: #the the number of unique elements and their occurance
-        currentLabel = featVec[-1]
-        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
-        labelCounts[currentLabel] += 1
-    shannonEnt = 0.0
-    for key in labelCounts:
-        prob = float(labelCounts[key])/numEntries
-        shannonEnt -= prob * log(prob,2) #log base 2
-    return shannonEnt
-    
-def splitDataSet(dataSet, axis, value):#按照给定特征划分数据集
-    retDataSet = []
-    for featVec in dataSet:
-        if featVec[axis] == value:
-            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
-            reducedFeatVec.extend(featVec[axis+1:])
-            retDataSet.append(reducedFeatVec)
-    return retDataSet
-
-```

From 7ec5fbb8394a090fc4936631ac17cbe6cb11bfaf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 08:58:02 +0800
Subject: [PATCH 0467/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index d8865a75..82d9db7d 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -11,3 +11,5 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
   
 #### 应用案例
+
+

From 5909db0dbe4a58ce739d990eb7c0caabe0f79d7d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 08:58:18 +0800
Subject: [PATCH 0468/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 82d9db7d..115e0faa 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -12,4 +12,5 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
   
 #### 应用案例
 
-
+```python
+```

From 0018ffcd0c3b46052c9f0777b5e0fd704b8ec5d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 08:58:30 +0800
Subject: [PATCH 0469/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 325 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 325 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 115e0faa..8cd7a40a 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -13,4 +13,329 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 #### 应用案例
 
 ```python
+using namespace std;
+void ReadData() //读入数据
+{
+    ifstream fin("F:\\data.txt");
+    ;i<NUM;i++)
+    {
+      ;j<;j++)
+        {
+            fin>>DataTable[i][j];
+            cout<<DataTable[i][j]<<"\t";
+        }
+      cout<<endl;
+    }
+    fin.close();
+}
+
+double ComputLog(double &p) //计算以2为底的log
+{
+    ||p==)
+    ;
+    else
+    {
+        );
+        return result;
+    }
+}
+
+double ComputInfo(double &p) //计算信息熵
+{
+    //cout<<"The value of p is: "<<p<<endl;
+    -p;
+    /p;
+    /q;
+    return (p*ComputLog(m)+q*ComputLog(n));
+}
+
+void CountInfoNP(int begin,int end,int &CountP,int &CountN) //搜索的起始位置、终止位置、计数变量
+{
+    CountP=;
+    CountN=;
+    for(int i=begin;i<=end;i++)
+        ]=="Yes")
+            CountP++;
+        else
+            CountN++;
+}
+
+bool CompareData(string &data,int &count,string &result) //判断该属性值是否出现过
+{
+    ;k<count;k++)
+        if(data==DataValueWeight[k].AttriValueName) //如果该值出现过，则将其出现次数加一
+            {
+                DataValueWeight[k].ValueWeight+=;
+                if(result=="Yes")
+                    DataValueWeight[k].ValuePWeight+=;
+                else
+                    DataValueWeight[k].ValueNWeight+=;
+                //cout<<"Exist Here"<<endl;
+                return false;
+            }
+    return true; //如果该值没有出现过，则返回真值
+}
+
+int SearchData(const int &begin,const int &end,const int &k) //对于第k列进行检索
+{
+    //cout<<"Enter SearchData() "<<begin<<" "<<end<<" "<<k<<endl;
+    ;
+    ;i<VALUENUM;i++)
+        {
+            DataValueWeight[i].ValueWeight=;
+            DataValueWeight[i].ValueNWeight=;
+            DataValueWeight[i].ValuePWeight=;
+        }
+
+    for(int i=begin;i<=end;i++)
+        if(i==begin)
+           {
+             DataValueWeight[count].AttriValueName=DataTable[i][k];
+             DataValueWeight[count].ValueWeight+=;
+             ]=="Yes")
+                DataValueWeight[count].ValuePWeight+=;
+             else
+                DataValueWeight[count].ValueNWeight+=;
+
+             count++;
+           }
+        else
+        {
+            string data=DataTable[i][k];
+            ];
+            if(CompareData(data,count,result)) //如果该值没有出现过
+            {
+                DataValueWeight[count].AttriValueName=data;
+                DataValueWeight[count].ValueWeight+=;
+
+                ]=="Yes")
+                    DataValueWeight[count].ValuePWeight+=;
+                else
+                    DataValueWeight[count].ValueNWeight+=;
+                count++;
+            }
+        }
+
+     //for(int s=0;s<count;s++)
+     // cout<<"Hello: "<<DataValueWeight[s].AttriValueName<<"\t"<<DataValueWeight[s].ValueWeight<<
+     // "\t"<<DataValueWeight[s].ValuePWeight<<" \t"<<DataValueWeight[s].ValueNWeight<<endl;
+
+    ;i<count;i++)
+    {
+        )
+            DataValueWeight[i].ValueNWeight=DataValueWeight[i].ValueWeight/DataValueWeight[i].ValueNWeight;
+        else
+            DataValueWeight[i].ValueNWeight=;
+
+        )
+            DataValueWeight[i].ValuePWeight=DataValueWeight[i].ValueWeight/DataValueWeight[i].ValuePWeight;
+        else
+            DataValueWeight[i].ValuePWeight=;
+        //cout<<"N: "<<DataValueWeight[i].ValueNWeight<<" P: "<<DataValueWeight[i].ValuePWeight<<endl;
+    }
+    return count;
+}
+
+int PickAttri()
+{
+    ;
+    int pos;
+
+    ;i<;i++)
+    if(InfoResult[i].AttriI>max)
+    {
+        pos=i;
+        max=InfoResult[i].AttriI;
+    }
+    return pos;
+}
+int SortByAttriValue(int &begin,int &end,int &temp,int *position)
+{
+
+    for(int i=begin;i<=end;i++) //将相应的数据拷贝到另一个阵列
+        ;j<=;j++)
+        {
+            int posy=i-begin;
+            CopyDataTable[posy][j]=DataTable[i][j];
+        }
+//cout<<"have a look"<<endl;
+
+    /*cout<<"*************Show Result First****************"<<endl;
+    cout<<InfoResult[temp].AttriName<<endl;
+    for(int i=begin;i<=end;i++)
+    {
+        for(int j=0;j<=5;j++)
+            cout<<DataTable[i][j]<<"\t";
+        cout<<endl;
+    }*/
+
+    ,high=end-begin;
+    ;
+    ;
+    position[]=begin;
+    ;i<InfoResult[temp].AttriKind;i++)
+    {
+        for(int j=low;j<=high;j++)
+            if(CopyDataTable[j][temp]==DataValueWeight[i].AttriValueName)
+               {
+                    int pos=count+begin;
+
+                    ;k<;k++)
+                        DataTable[pos][k]=CopyDataTable[j][k];
+                    count++;
+               }
+        position[countpos]=count+begin;
+        countpos++;
+    }
+
+    /*cout<<"*************Show Result Second****************"<<endl;
+    cout<<InfoResult[temp].AttriName<<endl;
+    for(int i=begin;i<=end;i++)
+    {
+        for(int j=0;j<=5;j++)
+            cout<<DataTable[i][j]<<"\t";
+        cout<<endl;
+    }
+    cout<<"
+
+
+";*/
+    return countpos;
+}
+
+void BuildTree(int begin,int end,Node *parent)
+{
+    ,CountN=;
+    CountInfoNP(begin,end,CountP,CountN);
+
+    cout<<"************************The data be sorted**************************"<<endl;
+    for(int i=begin;i<=end;i++)
+    {
+        ;j<=;j++)
+            cout<<DataTable[i][j]<<"\t";
+        cout<<endl;
+    }
+    cout<<"
+
+
+";
+
+    cout<<parent->AttriName<<" have a look: "<<CountP<<endl;
+    ||CountN==) //该子集当中只包含Yes或者No时为叶子节点，返回调用处；
+    {
+        cout<<"creat leaf node"<<endl;
+        Node* t=new Node(); //建立叶子节点
+        )
+            t->AttriName="No";
+        else
+            t->AttriName="Yes";
+        parent->Children.push_back(t); //插入孩子节点
+        return;
+    }
+    else
+    {
+        double p=(double)CountP/(CountP+CountN);
+        double InfoH=ComputInfo(p); //获得信息熵
+
+        ;k<;k++) //循环计算各个属性的条件信息熵，并计算出互信息
+        {
+            int KindOfValue=SearchData(begin,end,k);
+            +end-begin;
+            ;j<KindOfValue;j++) //计算出属性的每种取值的权重的倒数
+                DataValueWeight[j].ValueWeight=DataValueWeight[j].ValueWeight/sum;
+
+            ;
+            ].ValueNWeight!=&&DataValueWeight[].ValuePWeight!=)
+                InfoGain=DataValueWeight[].ValueWeight*(ComputLog(DataValueWeight[].ValueNWeight)/DataValueWeight[].ValueNWeight+ComputLog(DataValueWeight[].ValuePWeight)/DataValueWeight[].ValuePWeight);
+
+            ;j<KindOfValue;j++) //计算条件信息
+            &&DataValueWeight[j].ValuePWeight!=)
+                InfoGain+=DataValueWeight[j].ValueWeight*(ComputLog(DataValueWeight[j].ValueNWeight)/DataValueWeight[j].ValueNWeight+ComputLog(DataValueWeight[j].ValuePWeight)/DataValueWeight[j].ValuePWeight);
+
+            InfoResult[k].AttriI=InfoH-InfoGain; //计算互信息
+            InfoResult[k].AttriKind=KindOfValue;
+        }
+        int temp=PickAttri(); //选出互信息最大的属性作为节点建树
+        Node* t=new Node();
+        t->AttriName=InfoResult[temp].AttriName;
+        SearchData(begin,end,temp);
+        ;k<InfoResult[temp].AttriKind;k++)
+        {
+            string name=DataValueWeight[k].AttriValueName;
+            t->AttriValue.push_back(name);
+        }
+        t->parent=parent;
+        parent->Children.push_back(t); //孩子节点压入vector当中
+        int position[NUMOFPOS];
+
+        cout<<"before SortByAttriValue Begin: "<<begin<<",END: "<<end<<endl;
+
+        SortByAttriValue(begin,end,temp,position); //将数据按照选定属性的取值不同进行划分
+        int times=InfoResult[temp].AttriKind;
+        ;l<=times;l++)
+            cout<<position[l]<<" ";
+        cout<<endl;
+        ;k<times;k++)
+            {
+                int head,rear;
+                head=position[k];
+                ;
+                rear=position[hire]-;
+                ;l<=times;l++)
+                cout<<position[l]<<" ";
+                cout<<endl;
+                cout<<"Head: "<<head<<" ,Rear: "<<rear<<endl;
+                BuildTree(head,rear,t);
+            }
+    }
+}
+
+void ShowTree(Node *root)
+{
+
+    if(root->AttriName=="Yes"||root->AttriName=="No")
+    {
+        cout<<root->AttriName<<endl;
+        return;
+    }
+    else
+    {
+        cout<<root->AttriName<<endl;
+        for(vector<string>::iterator itvalue=root->AttriValue.begin();itvalue!=root->AttriValue.end();itvalue++)
+        {
+            string value=*itvalue;
+            cout<<value<<" ";
+        }
+        cout<<endl;
+        for(vector<Node*>::iterator itnode=root->Children.begin();itnode!=root->Children.end();itnode++)
+        {
+            Node *t=*itnode;
+            ShowTree(t);
+        }
+    }
+}
+int main()
+{
+    InfoResult[].AttriName="天气";
+    InfoResult[].AttriName="气温";
+    InfoResult[].AttriName="湿度";
+    InfoResult[].AttriName="风";
+    ReadData();
+    Node *Root=new Node;
+    BuildTree(,NUM-,Root);
+
+    //vector<Node>::iterator it=Root.Children.begin();
+    ShowTree(Root);
+    /*Node t=*it;
+    cout<<t.AttriName<<endl;
+    for(vector<string>::iterator itvalue=t.AttriValue.begin();itvalue!=t.AttriValue.end();itvalue++)
+    cout<<*itvalue<<endl;
+    it=t.Children.begin();
+
+    t=*it;
+    cout<<t.AttriName<<endl;*/
+    //ShowTree(t);
+    //cout<<"Root: "<<t.AttriName<<" ,Value: "<<*(t.AttriValue.begin())<<endl;
+    ;
+}
 ```

From a02bcbb4bba3c14f44024ec3c98525677b56d964 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 08:59:57 +0800
Subject: [PATCH 0470/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 261 ----------------------------------------
 1 file changed, 261 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 8cd7a40a..76bf090b 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -76,266 +76,5 @@ bool CompareData(string &data,int &count,string &result) //判断该属性值是
     return true; //如果该值没有出现过，则返回真值
 }
 
-int SearchData(const int &begin,const int &end,const int &k) //对于第k列进行检索
-{
-    //cout<<"Enter SearchData() "<<begin<<" "<<end<<" "<<k<<endl;
-    ;
-    ;i<VALUENUM;i++)
-        {
-            DataValueWeight[i].ValueWeight=;
-            DataValueWeight[i].ValueNWeight=;
-            DataValueWeight[i].ValuePWeight=;
-        }
-
-    for(int i=begin;i<=end;i++)
-        if(i==begin)
-           {
-             DataValueWeight[count].AttriValueName=DataTable[i][k];
-             DataValueWeight[count].ValueWeight+=;
-             ]=="Yes")
-                DataValueWeight[count].ValuePWeight+=;
-             else
-                DataValueWeight[count].ValueNWeight+=;
-
-             count++;
-           }
-        else
-        {
-            string data=DataTable[i][k];
-            ];
-            if(CompareData(data,count,result)) //如果该值没有出现过
-            {
-                DataValueWeight[count].AttriValueName=data;
-                DataValueWeight[count].ValueWeight+=;
-
-                ]=="Yes")
-                    DataValueWeight[count].ValuePWeight+=;
-                else
-                    DataValueWeight[count].ValueNWeight+=;
-                count++;
-            }
-        }
-
-     //for(int s=0;s<count;s++)
-     // cout<<"Hello: "<<DataValueWeight[s].AttriValueName<<"\t"<<DataValueWeight[s].ValueWeight<<
-     // "\t"<<DataValueWeight[s].ValuePWeight<<" \t"<<DataValueWeight[s].ValueNWeight<<endl;
-
-    ;i<count;i++)
-    {
-        )
-            DataValueWeight[i].ValueNWeight=DataValueWeight[i].ValueWeight/DataValueWeight[i].ValueNWeight;
-        else
-            DataValueWeight[i].ValueNWeight=;
-
-        )
-            DataValueWeight[i].ValuePWeight=DataValueWeight[i].ValueWeight/DataValueWeight[i].ValuePWeight;
-        else
-            DataValueWeight[i].ValuePWeight=;
-        //cout<<"N: "<<DataValueWeight[i].ValueNWeight<<" P: "<<DataValueWeight[i].ValuePWeight<<endl;
-    }
-    return count;
-}
-
-int PickAttri()
-{
-    ;
-    int pos;
-
-    ;i<;i++)
-    if(InfoResult[i].AttriI>max)
-    {
-        pos=i;
-        max=InfoResult[i].AttriI;
-    }
-    return pos;
-}
-int SortByAttriValue(int &begin,int &end,int &temp,int *position)
-{
-
-    for(int i=begin;i<=end;i++) //将相应的数据拷贝到另一个阵列
-        ;j<=;j++)
-        {
-            int posy=i-begin;
-            CopyDataTable[posy][j]=DataTable[i][j];
-        }
-//cout<<"have a look"<<endl;
-
-    /*cout<<"*************Show Result First****************"<<endl;
-    cout<<InfoResult[temp].AttriName<<endl;
-    for(int i=begin;i<=end;i++)
-    {
-        for(int j=0;j<=5;j++)
-            cout<<DataTable[i][j]<<"\t";
-        cout<<endl;
-    }*/
-
-    ,high=end-begin;
-    ;
-    ;
-    position[]=begin;
-    ;i<InfoResult[temp].AttriKind;i++)
-    {
-        for(int j=low;j<=high;j++)
-            if(CopyDataTable[j][temp]==DataValueWeight[i].AttriValueName)
-               {
-                    int pos=count+begin;
-
-                    ;k<;k++)
-                        DataTable[pos][k]=CopyDataTable[j][k];
-                    count++;
-               }
-        position[countpos]=count+begin;
-        countpos++;
-    }
-
-    /*cout<<"*************Show Result Second****************"<<endl;
-    cout<<InfoResult[temp].AttriName<<endl;
-    for(int i=begin;i<=end;i++)
-    {
-        for(int j=0;j<=5;j++)
-            cout<<DataTable[i][j]<<"\t";
-        cout<<endl;
-    }
-    cout<<"
-
 
-";*/
-    return countpos;
-}
-
-void BuildTree(int begin,int end,Node *parent)
-{
-    ,CountN=;
-    CountInfoNP(begin,end,CountP,CountN);
-
-    cout<<"************************The data be sorted**************************"<<endl;
-    for(int i=begin;i<=end;i++)
-    {
-        ;j<=;j++)
-            cout<<DataTable[i][j]<<"\t";
-        cout<<endl;
-    }
-    cout<<"
-
-
-";
-
-    cout<<parent->AttriName<<" have a look: "<<CountP<<endl;
-    ||CountN==) //该子集当中只包含Yes或者No时为叶子节点，返回调用处；
-    {
-        cout<<"creat leaf node"<<endl;
-        Node* t=new Node(); //建立叶子节点
-        )
-            t->AttriName="No";
-        else
-            t->AttriName="Yes";
-        parent->Children.push_back(t); //插入孩子节点
-        return;
-    }
-    else
-    {
-        double p=(double)CountP/(CountP+CountN);
-        double InfoH=ComputInfo(p); //获得信息熵
-
-        ;k<;k++) //循环计算各个属性的条件信息熵，并计算出互信息
-        {
-            int KindOfValue=SearchData(begin,end,k);
-            +end-begin;
-            ;j<KindOfValue;j++) //计算出属性的每种取值的权重的倒数
-                DataValueWeight[j].ValueWeight=DataValueWeight[j].ValueWeight/sum;
-
-            ;
-            ].ValueNWeight!=&&DataValueWeight[].ValuePWeight!=)
-                InfoGain=DataValueWeight[].ValueWeight*(ComputLog(DataValueWeight[].ValueNWeight)/DataValueWeight[].ValueNWeight+ComputLog(DataValueWeight[].ValuePWeight)/DataValueWeight[].ValuePWeight);
-
-            ;j<KindOfValue;j++) //计算条件信息
-            &&DataValueWeight[j].ValuePWeight!=)
-                InfoGain+=DataValueWeight[j].ValueWeight*(ComputLog(DataValueWeight[j].ValueNWeight)/DataValueWeight[j].ValueNWeight+ComputLog(DataValueWeight[j].ValuePWeight)/DataValueWeight[j].ValuePWeight);
-
-            InfoResult[k].AttriI=InfoH-InfoGain; //计算互信息
-            InfoResult[k].AttriKind=KindOfValue;
-        }
-        int temp=PickAttri(); //选出互信息最大的属性作为节点建树
-        Node* t=new Node();
-        t->AttriName=InfoResult[temp].AttriName;
-        SearchData(begin,end,temp);
-        ;k<InfoResult[temp].AttriKind;k++)
-        {
-            string name=DataValueWeight[k].AttriValueName;
-            t->AttriValue.push_back(name);
-        }
-        t->parent=parent;
-        parent->Children.push_back(t); //孩子节点压入vector当中
-        int position[NUMOFPOS];
-
-        cout<<"before SortByAttriValue Begin: "<<begin<<",END: "<<end<<endl;
-
-        SortByAttriValue(begin,end,temp,position); //将数据按照选定属性的取值不同进行划分
-        int times=InfoResult[temp].AttriKind;
-        ;l<=times;l++)
-            cout<<position[l]<<" ";
-        cout<<endl;
-        ;k<times;k++)
-            {
-                int head,rear;
-                head=position[k];
-                ;
-                rear=position[hire]-;
-                ;l<=times;l++)
-                cout<<position[l]<<" ";
-                cout<<endl;
-                cout<<"Head: "<<head<<" ,Rear: "<<rear<<endl;
-                BuildTree(head,rear,t);
-            }
-    }
-}
-
-void ShowTree(Node *root)
-{
-
-    if(root->AttriName=="Yes"||root->AttriName=="No")
-    {
-        cout<<root->AttriName<<endl;
-        return;
-    }
-    else
-    {
-        cout<<root->AttriName<<endl;
-        for(vector<string>::iterator itvalue=root->AttriValue.begin();itvalue!=root->AttriValue.end();itvalue++)
-        {
-            string value=*itvalue;
-            cout<<value<<" ";
-        }
-        cout<<endl;
-        for(vector<Node*>::iterator itnode=root->Children.begin();itnode!=root->Children.end();itnode++)
-        {
-            Node *t=*itnode;
-            ShowTree(t);
-        }
-    }
-}
-int main()
-{
-    InfoResult[].AttriName="天气";
-    InfoResult[].AttriName="气温";
-    InfoResult[].AttriName="湿度";
-    InfoResult[].AttriName="风";
-    ReadData();
-    Node *Root=new Node;
-    BuildTree(,NUM-,Root);
-
-    //vector<Node>::iterator it=Root.Children.begin();
-    ShowTree(Root);
-    /*Node t=*it;
-    cout<<t.AttriName<<endl;
-    for(vector<string>::iterator itvalue=t.AttriValue.begin();itvalue!=t.AttriValue.end();itvalue++)
-    cout<<*itvalue<<endl;
-    it=t.Children.begin();
-
-    t=*it;
-    cout<<t.AttriName<<endl;*/
-    //ShowTree(t);
-    //cout<<"Root: "<<t.AttriName<<" ,Value: "<<*(t.AttriValue.begin())<<endl;
-    ;
-}
 ```

From b88763606daa4ffbd84c0c6f96d37c75771a58ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 09:00:19 +0800
Subject: [PATCH 0471/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 62 -----------------------------------------
 1 file changed, 62 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 76bf090b..70522c9a 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -13,68 +13,6 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 #### 应用案例
 
 ```python
-using namespace std;
-void ReadData() //读入数据
-{
-    ifstream fin("F:\\data.txt");
-    ;i<NUM;i++)
-    {
-      ;j<;j++)
-        {
-            fin>>DataTable[i][j];
-            cout<<DataTable[i][j]<<"\t";
-        }
-      cout<<endl;
-    }
-    fin.close();
-}
-
-double ComputLog(double &p) //计算以2为底的log
-{
-    ||p==)
-    ;
-    else
-    {
-        );
-        return result;
-    }
-}
-
-double ComputInfo(double &p) //计算信息熵
-{
-    //cout<<"The value of p is: "<<p<<endl;
-    -p;
-    /p;
-    /q;
-    return (p*ComputLog(m)+q*ComputLog(n));
-}
-
-void CountInfoNP(int begin,int end,int &CountP,int &CountN) //搜索的起始位置、终止位置、计数变量
-{
-    CountP=;
-    CountN=;
-    for(int i=begin;i<=end;i++)
-        ]=="Yes")
-            CountP++;
-        else
-            CountN++;
-}
-
-bool CompareData(string &data,int &count,string &result) //判断该属性值是否出现过
-{
-    ;k<count;k++)
-        if(data==DataValueWeight[k].AttriValueName) //如果该值出现过，则将其出现次数加一
-            {
-                DataValueWeight[k].ValueWeight+=;
-                if(result=="Yes")
-                    DataValueWeight[k].ValuePWeight+=;
-                else
-                    DataValueWeight[k].ValueNWeight+=;
-                //cout<<"Exist Here"<<endl;
-                return false;
-            }
-    return true; //如果该值没有出现过，则返回真值
-}
 
 
 ```

From b1c62a8a7415ee019c256b9878b1723bcc0e79a4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Feb 2018 09:01:30 +0800
Subject: [PATCH 0472/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 70522c9a..0a1e1872 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -9,6 +9,10 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
+机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,通俗说就是决策树。 一个决策树包含三种类型的节点：
+决策节点：通常用矩形框来表示
+机会节点：通常用圆圈来表示
+终结点：通常用三角形来表示,如图所示
   
 #### 应用案例
 

From e05fab9045c043aff26f19691a7ca3082be1f72d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:47:09 +0800
Subject: [PATCH 0473/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 67 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 0a1e1872..dc6eefb2 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -17,6 +17,73 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 #### 应用案例
 
 ```python
+import pandas as pd 
+from math import log 
+from anytree import Node, RenderTree
+from anytree.dotexport import RenderTreeGraph
 
+def create_decision_tree_id3(df, y_col):
+    # 计算H(C)
+    def h_value():
+        h = 0
+        for v in df.groupby(y_col).size().div(len(df)):
+            h += -v * log(v, 2)
+
+        return h
+
+    # 计算某一个属性的信息增益
+    def get_info_gain_byc(column, df, y_col):
+        # 计算p(column)
+        probs = df.groupby(column).size().div(len(df))
+        v = 0
+        for index1, v1 in probs.iteritems():
+            tmp_df = df[df[column] == index1]
+            tmp_probs = tmp_df.groupby(y_col).size().div(len(tmp_df))
+            tmp_v = 0
+            for v2 in tmp_probs:
+                # 计算H(C|X=xi)
+                tmp_v += -v2 * log(v2, 2)
+            # 计算H(y_col|column)
+            v += v1 * tmp_v
+        return v
+
+    # 获取拥有最大信息增益的属性
+    def get_max_info_gain(df, y_col):
+        d = {}
+        h = h_value()
+        for c in filter(lambda c: c != y_col, df.columns):
+            # 计算H(y_col) - H(y_col|column)
+            d[c] = h - get_info_gain_byc(c, df, y_col)
+
+        return max(d, key=d.get)
+
+    # 生成决策树
+    def train_decision_tree(node, df, y_col):
+        c = get_max_info_gain(df, y_col)
+        for v in pd.unique(df[c]):
+            gb = df[df[c] == v].groupby(y_col)
+            curr_node = Node('%s-%s' % (c, v), parent=node)
+            # 如果属性没有用完
+            if len(df.columns) > 2:
+                # 如果分区纯度是100%，则生成类别叶子节点
+                if len(gb) == 1:
+                    Node(df[df[c] == v].groupby(c)[y_col].first().iloc[0], parent=curr_node)
+                else:
+                    # 如果分区不纯则继续递归
+                    train_decision_tree(curr_node, df[df[c] == v].drop(c, axis=1), y_col)
+            # 如果属性用完，则选择数量最多的类别实例作为类别叶子结点
+            else:
+                Node(df[df[c] == v].groupby(y_col).size().idxmax(), parent=curr_node)
+
+    root_node = Node('root')
+    train_decision_tree(root_node, df, y_col)
+    return root_node
+
+df = pd.read_csv('~/allele.csv')
+root_node = create_decision_tree_id3(df, 'buys_computer')
+for pre, fill, node in RenderTree(root_node):
+    print("%s%s" % (pre, node.name))
+    
+RenderTreeGraph(root_node).to_picture("decision_tree_id3.png")
 
 ```

From 63979ab80967cc53315cdbec122bb79c880957c9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:49:58 +0800
Subject: [PATCH 0474/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index dc6eefb2..2ab835d4 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -9,10 +9,13 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
-机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,通俗说就是决策树。 一个决策树包含三种类型的节点：
-决策节点：通常用矩形框来表示
-机会节点：通常用圆圈来表示
-终结点：通常用三角形来表示,如图所示
+机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,通俗说就是决策树。 
+
+通常一个决策树会包含三种类型的节点：
+
+* 决策节点：通常用矩形框来表示
+* 机会节点：通常用圆圈来表示
+* 终结点：通常用三角形来表示,如图所示
   
 #### 应用案例
 

From c87ead7d7f80cf213138f58974d7a854314639ce Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:52:53 +0800
Subject: [PATCH 0475/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 2ab835d4..ec9a513d 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -15,7 +15,9 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 * 决策节点：通常用矩形框来表示
 * 机会节点：通常用圆圈来表示
-* 终结点：通常用三角形来表示,如图所示
+* 终结点：通常用三角形来表示
+
+
   
 #### 应用案例
 

From cf591606a29f1ea20be0727ae836afc3b062daa6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:54:29 +0800
Subject: [PATCH 0476/1406] change page

---
 assets/images/176.jpg   | Bin 0 -> 18197 bytes
 assets/images/177.jpg   | Bin 0 -> 16598 bytes
 assets/images/178.jpg   | Bin 0 -> 14683 bytes
 assets/src/DT/DT.0.3.md |   3 ++-
 4 files changed, 2 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/176.jpg
 create mode 100644 assets/images/177.jpg
 create mode 100644 assets/images/178.jpg

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diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index ec9a513d..7cbb0319 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -9,7 +9,8 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
-机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,通俗说就是决策树。 
+机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。
+决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,就是决策树。 
 
 通常一个决策树会包含三种类型的节点：
 

From f948779b010dcf5c187706e8c5db6e14f5ea9db0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:57:12 +0800
Subject: [PATCH 0477/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 7cbb0319..edb79a7f 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -9,6 +9,14 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
+信息增益是属性选择中的一个重要指标，它定义为一个属性能够为分类系统带来多少信息，带来的信息越多，该属性就越重要。而信息量，就是熵。
+熵定义为信息量的期望值。熵越大，一个变量的不确定性越大，它带来的信息量就越大。 计算信息熵的公式为：
+<p align="center">
+<img width="300" align="center" src="../../images/176.jpg" />
+</p>
+
+
+
 机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。
 决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,就是决策树。 
 

From 478cbb63a68baa0e4b21fe2f4160fbb29a883c1c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 08:57:46 +0800
Subject: [PATCH 0478/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index edb79a7f..450439c1 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -10,13 +10,13 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 
 在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
 信息增益是属性选择中的一个重要指标，它定义为一个属性能够为分类系统带来多少信息，带来的信息越多，该属性就越重要。而信息量，就是熵。
-熵定义为信息量的期望值。熵越大，一个变量的不确定性越大，它带来的信息量就越大。 计算信息熵的公式为：
+熵定义为信息量的期望值。
+
+熵越大，一个变量的不确定性越大，它带来的信息量就越大。 计算信息熵的公式为：
 <p align="center">
 <img width="300" align="center" src="../../images/176.jpg" />
 </p>
 
-
-
 机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。
 决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,就是决策树。 
 

From 3ecac3cecd9dfb8679f0f57ff68b68d7ea42d7e0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:00:05 +0800
Subject: [PATCH 0479/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 16 +++++++++++++++-
 1 file changed, 15 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 450439c1..4ce0cd27 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser3，迭代二叉树三代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
 
-在信息论中，期望信息越小，那么信息增益就越大，从而纯度就越高。ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
+ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
 信息增益是属性选择中的一个重要指标，它定义为一个属性能够为分类系统带来多少信息，带来的信息越多，该属性就越重要。而信息量，就是熵。
 熵定义为信息量的期望值。
 
@@ -17,6 +17,20 @@ ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用
 <img width="300" align="center" src="../../images/176.jpg" />
 </p>
 
+其中p为出现c分类时的概率。
+
+那么如何计算一个属性的信息增益？ 首先我们需要先根据信息熵公式计算出系统的平均熵值H(C)，然后根据某个属性计算条件熵：
+<p align="center">
+<img width="300" align="center" src="../../images/177.jpg" />
+</p>
+这是指属性X被固定时的条件熵。因为X可能的取值有n种,因此在计算条件熵时需要计算n个值，然后取均值（通过概率计算）。通过将某分类的系统熵减去某个属性的条件熵，从而得到该属性的信息增益：
+<p align="center">
+<img width="300" align="center" src="../../images/178.jpg" />
+</p>
+在信息论中一个属性的信息增益越大，表明该属性对样本的熵减少能力越强，也就是说确定这个属性会使系统越稳定有序（熵越小系统越稳定），那么该分区的纯度也就越高。
+
+
+
 机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。
 决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,就是决策树。 
 

From 25101a61eb79865a6ac063c130277bb69c285674 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:01:58 +0800
Subject: [PATCH 0480/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 4ce0cd27..d7aba301 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -7,7 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser3，迭代二叉树三代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。
 
-
 ID3算法的核心思想就是以信息增益来度量属性的选择，选择分裂后信息增益最大的属性进行分裂。
 信息增益是属性选择中的一个重要指标，它定义为一个属性能够为分类系统带来多少信息，带来的信息越多，该属性就越重要。而信息量，就是熵。
 熵定义为信息量的期望值。
@@ -23,15 +22,16 @@ ID3算法的核心思想就是以信息增益来度量属性的选择，选择
 <p align="center">
 <img width="300" align="center" src="../../images/177.jpg" />
 </p>
+
 这是指属性X被固定时的条件熵。因为X可能的取值有n种,因此在计算条件熵时需要计算n个值，然后取均值（通过概率计算）。通过将某分类的系统熵减去某个属性的条件熵，从而得到该属性的信息增益：
 <p align="center">
 <img width="300" align="center" src="../../images/178.jpg" />
 </p>
-在信息论中一个属性的信息增益越大，表明该属性对样本的熵减少能力越强，也就是说确定这个属性会使系统越稳定有序（熵越小系统越稳定），那么该分区的纯度也就越高。
-
 
+在信息论中一个属性的信息增益越大，表明该属性对样本的熵减少能力越强，也就是说确定这个属性会使系统越稳定有序（熵越小系统越稳定），那么该分区的纯度也就越高。
 
 机器学习中，决策树是一个预测模型；他代表的是对象属性与对象值之间的一种映射关系。树中每个节点表示某个对象，而每个分叉路径则代表的某个可能的属性值，而每个叶结点则对应从根节点到该叶节点所经历的路径所表示的对象的值。
+
 决策树仅有单一输出，若欲有复数输出，可以建立独立的决策树以处理不同输出。 数据挖掘中决策树是一种经常要用到的技术，可以用于分析数据，同样也可以用来作预测。 从数据产生决策树的机器学习技术叫做决策树学习,就是决策树。 
 
 通常一个决策树会包含三种类型的节点：

From e7aeef33289bec951dfb74b1c1e6076d5c0b4d13 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:02:12 +0800
Subject: [PATCH 0481/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index d7aba301..8a077e34 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -2,7 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-
 #### ID3算法(Iterative Dichotomiser 3)
 
 ID3算法是决策树的一种，它是基于奥卡姆剃刀原理的，即用尽量用较少的东西做更多的事。ID3算法,即Iterative Dichotomiser3，迭代二叉树三代，是Ross Quinlan发明的一种决策树算法，这个算法的基础就是上面提到的奥卡姆剃刀原理，越是小型的决策树越优于大的决策树，尽管如此，也不总是生成最小的树型结构，而是一个启发式算法。

From 15c8b7d0d148e465ccd3bcbda42a803b0fbac279 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:06:14 +0800
Subject: [PATCH 0482/1406] Update DT.0.3.md

---
 assets/src/DT/DT.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DT/DT.0.3.md b/assets/src/DT/DT.0.3.md
index 8a077e34..64e7dda7 100644
--- a/assets/src/DT/DT.0.3.md
+++ b/assets/src/DT/DT.0.3.md
@@ -114,3 +114,9 @@ for pre, fill, node in RenderTree(root_node):
 RenderTreeGraph(root_node).to_picture("decision_tree_id3.png")
 
 ```
+
+#### 优缺点
+
+优点：决策树ID3算法易于理解,能处理数据型的也能处理常规型的数据,还可以在相对较短的时间内能够对大型的数据集做出可行且较好的结果。
+
+缺点：决策树ID3算法比较偏向于选择属性值多的类别。

From f784537caed5d380d7e85d39c4c905201d11d0ed Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:06:30 +0800
Subject: [PATCH 0483/1406] Update DT.0.2.md

---
 assets/src/DT/DT.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.2.md b/assets/src/DT/DT.0.2.md
index 7d89f3d4..f10558ea 100644
--- a/assets/src/DT/DT.0.2.md
+++ b/assets/src/DT/DT.0.2.md
@@ -51,4 +51,5 @@ CART剪枝算法主要由两步组成：首先从生成算法产生的决策树T
 #### 优缺点
 
 优点：可以生成易于理解的规则；计算量相对来说不大；可处理连续和离散字段；最终结果可清晰显示字段的重要性程度。
+
 缺点：对连续字段难以预测；处理时间序列数据，前期预处理步骤多；当类别太多，错误可能增加的较快。

From 3277d7fb377e92ec80e0c6b93331d5f5f4e5e8d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:11:45 +0800
Subject: [PATCH 0484/1406] change page

---
 assets/src/DT/DT.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/DT/DT.0.4.md

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
new file mode 100644
index 00000000..827ab5cb
--- /dev/null
+++ b/assets/src/DT/DT.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### ID3算法(Iterative Dichotomiser 3)

From 59579c4b0709370eaedb60c68b0c25051f4b6f8d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:12:46 +0800
Subject: [PATCH 0485/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 95dc1e7b..c13ddc26 100644
--- a/README.md
+++ b/README.md
@@ -93,7 +93,7 @@
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
-     * [CHAID（Chi-squared Automatic Interaction Detection]()
+     * [CHAID（Chi-squared Automatic Interaction Detection](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()

From 2b297bfbc388c2444372cc4cb080a6188dfb0264 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:13:19 +0800
Subject: [PATCH 0486/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index c13ddc26..a149ca2c 100644
--- a/README.md
+++ b/README.md
@@ -93,7 +93,7 @@
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
-     * [CHAID（Chi-squared Automatic Interaction Detection](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
+     * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()

From b29f7fcfee75f3acdefface277f1bce45c947868 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Mar 2018 09:13:29 +0800
Subject: [PATCH 0487/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 827ab5cb..91c26c14 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### ID3算法(Iterative Dichotomiser 3)
+#### CHAID（Chi-squared Automatic Interaction Detection)

From da2178cd2985e9a1ef7f1b29ed76abc70aac4d26 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:00:09 +0800
Subject: [PATCH 0488/1406] change page

---
 README.md               | 1 -
 assets/src/DT/DT.0.4.md | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/README.md b/README.md
index a149ca2c..2d5a6fb6 100644
--- a/README.md
+++ b/README.md
@@ -93,7 +93,6 @@
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
-     * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()
diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 91c26c14..f526138f 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### CHAID（Chi-squared Automatic Interaction Detection)
+#### CHAID（Chi-squared Automatic Interaction Detection)
\ No newline at end of file

From 519e9bc79f9d99d4f6def888d738e9fed1f0cb98 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:03:35 +0800
Subject: [PATCH 0489/1406] change page

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 2d5a6fb6..e9bd8373 100644
--- a/README.md
+++ b/README.md
@@ -93,6 +93,7 @@
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
+     * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()

From 9f8ae030a8ecab92fd686024f5e5c5080ca405e9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:05:03 +0800
Subject: [PATCH 0490/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index e9bd8373..59d8585f 100644
--- a/README.md
+++ b/README.md
@@ -93,7 +93,7 @@
  * [决策树算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.1.md)
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
-     * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
+     * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）]()
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()

From 0221a5435343719a6155e78230b4a523438f1e84 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:07:36 +0800
Subject: [PATCH 0491/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index f526138f..2844007f 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### CHAID（Chi-squared Automatic Interaction Detection)
\ No newline at end of file
+#### 卡方自动交互检测 CHAID（Chi-squared Automatic Interaction Detection)

From 7259136789c5923b5f14e77355964e42f19b77df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:07:50 +0800
Subject: [PATCH 0492/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 2844007f..a1334f8c 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 卡方自动交互检测 CHAID（Chi-squared Automatic Interaction Detection)
+#### 卡方自动交互检测算法 CHAID（Chi-squared Automatic Interaction Detection)

From 76e0daa435636140405698747791556142b415b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:09:37 +0800
Subject: [PATCH 0493/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index a1334f8c..1c3f4198 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 卡方自动交互检测算法 CHAID（Chi-squared Automatic Interaction Detection)
+卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具。CHAID可用于预测（类似回归分析，CHAID最初被称为XAID）以及分类，并用于检测变量之间的相互作用。

From 5e17011b24479b8ec74556f2bca2dbad65c6ca62 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:40:03 +0800
Subject: [PATCH 0494/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 1c3f4198..aede2c43 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 卡方自动交互检测算法 CHAID（Chi-squared Automatic Interaction Detection)
-卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具。CHAID可用于预测（类似回归分析，CHAID最初被称为XAID）以及分类，并用于检测变量之间的相互作用。
+卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具，是一种基于调整后的显着性检验（邦费罗尼检验）决策树技术。其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。

From 9284e59a25d911e6b7ea70c892de7db48f323a32 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Mar 2018 09:41:01 +0800
Subject: [PATCH 0495/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index aede2c43..a565f68b 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -3,4 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 卡方自动交互检测算法 CHAID（Chi-squared Automatic Interaction Detection)
-卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具，是一种基于调整后的显着性检验（邦费罗尼检验）决策树技术。其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。
+卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具，是一种基于调整后的显着性检验（邦费罗尼检验）决策树技术。
+
+其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。

From f422c0e4089bc2fb8fededfa708be3f63b647582 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Mar 2018 08:44:48 +0800
Subject: [PATCH 0496/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index a565f68b..f3b17099 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -6,3 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具，是一种基于调整后的显着性检验（邦费罗尼检验）决策树技术。
 
 其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。
+

From 4e3481684b73d2d3cdd16db8e9288a0079cade06 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Mar 2018 08:57:22 +0800
Subject: [PATCH 0497/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index f3b17099..9cb5918b 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -7,3 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。
 
+在实践中，CHAID经常使用在直销的背景下，选择消费者群体，并预测他们的反应，一些变量如何影响其他变量，而其他早期应用是在医学和精神病学的研究领域。

From 1aa3712d1f4409178b4cbe860ff7cf891e88c845 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Mar 2018 08:58:26 +0800
Subject: [PATCH 0498/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 9cb5918b..88b224c3 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -8,3 +8,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。
 
 在实践中，CHAID经常使用在直销的背景下，选择消费者群体，并预测他们的反应，一些变量如何影响其他变量，而其他早期应用是在医学和精神病学的研究领域。
+
+
+CHAID分析构建了一个预测模型，或树，以帮助确定给定因变量，变量如何最好地合来解释结果。CHAID分析，名义，有序和连续数据可以使用，在连续预测类别被分成大致相等的若干观测。CHAID对每个分类预测创建了交叉表，直到达到最好的结果，无法继续分类为止。在CHAID技术中，我们可以直观地看到在树的分割变量和相关因子之间的关系。决策树或分类树的展开，始于确定作为根节点的目标变量或因变量。 CHAID分析将目标变量分割成两个或两个以上的类被称为根节点，或者父节点，然后使用统计算法将节点分为子节点。不同于回归分析，CHAID技术并不要求数据是正态分布.
+
+CHAID的优势是它的结果是非常直观的易于理解的。由于默认情况下CHAID采用多路分割，需要相当大的样本量，来有效地开展工作，而小样本组受访者可以迅速分为太小了的组，而无法可靠的分析。

From 9da1f0f8880cc471a7729b08192e8c139d849712 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Mar 2018 08:59:15 +0800
Subject: [PATCH 0499/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 88b224c3..b0a2733d 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -13,3 +13,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 CHAID分析构建了一个预测模型，或树，以帮助确定给定因变量，变量如何最好地合来解释结果。CHAID分析，名义，有序和连续数据可以使用，在连续预测类别被分成大致相等的若干观测。CHAID对每个分类预测创建了交叉表，直到达到最好的结果，无法继续分类为止。在CHAID技术中，我们可以直观地看到在树的分割变量和相关因子之间的关系。决策树或分类树的展开，始于确定作为根节点的目标变量或因变量。 CHAID分析将目标变量分割成两个或两个以上的类被称为根节点，或者父节点，然后使用统计算法将节点分为子节点。不同于回归分析，CHAID技术并不要求数据是正态分布.
 
 CHAID的优势是它的结果是非常直观的易于理解的。由于默认情况下CHAID采用多路分割，需要相当大的样本量，来有效地开展工作，而小样本组受访者可以迅速分为太小了的组，而无法可靠的分析。
+
+CHAID决策树的构成包括：
+* 根节点：根节点包含因变量或目标变量。例如，CHAID使用于，银行根据年龄，收入，信用卡等，来预测信用卡风险。在这个例子中，信用卡风险是目标变量，其余变量是预测变量。
+* 父节点：该算法将目标变量分割成两个或多个分类。这些分类被称为父节点或者初始节点。在银行的例子中，父节点是高，中，低三个分类。

From bd7d5e3220e9b6a3f3e89f16022949ee79ff7fbc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Mar 2018 09:06:48 +0800
Subject: [PATCH 0500/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index b0a2733d..aed875f2 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -17,3 +17,8 @@ CHAID的优势是它的结果是非常直观的易于理解的。由于默认情
 CHAID决策树的构成包括：
 * 根节点：根节点包含因变量或目标变量。例如，CHAID使用于，银行根据年龄，收入，信用卡等，来预测信用卡风险。在这个例子中，信用卡风险是目标变量，其余变量是预测变量。
 * 父节点：该算法将目标变量分割成两个或多个分类。这些分类被称为父节点或者初始节点。在银行的例子中，父节点是高，中，低三个分类。
+* 子节点：CHAID分析树中独立变量分类低于父节点的分类被称为子节点。
+* 终端节点：CHAID分析树最后一个分类被称为终端节点。 CHAID分析树中，主要的影响变量排在前面，次要的排在后面。因此，它被称为终端节点。
+
+#### CHAID的应用
+

From 800b63cf4bde0263d58f0a4bf15b187f3dbdcfdf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Mar 2018 09:04:10 +0800
Subject: [PATCH 0501/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index aed875f2..7adbfb08 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -20,5 +20,6 @@ CHAID决策树的构成包括：
 * 子节点：CHAID分析树中独立变量分类低于父节点的分类被称为子节点。
 * 终端节点：CHAID分析树最后一个分类被称为终端节点。 CHAID分析树中，主要的影响变量排在前面，次要的排在后面。因此，它被称为终端节点。
 
+
 #### CHAID的应用
 

From de4b62e7781f32ef1927f6b78a39d4dfe03c28c2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Mar 2018 09:07:36 +0800
Subject: [PATCH 0502/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 7adbfb08..2283af9e 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -14,6 +14,7 @@ CHAID分析构建了一个预测模型，或树，以帮助确定给定因变量
 
 CHAID的优势是它的结果是非常直观的易于理解的。由于默认情况下CHAID采用多路分割，需要相当大的样本量，来有效地开展工作，而小样本组受访者可以迅速分为太小了的组，而无法可靠的分析。
 
+
 CHAID决策树的构成包括：
 * 根节点：根节点包含因变量或目标变量。例如，CHAID使用于，银行根据年龄，收入，信用卡等，来预测信用卡风险。在这个例子中，信用卡风险是目标变量，其余变量是预测变量。
 * 父节点：该算法将目标变量分割成两个或多个分类。这些分类被称为父节点或者初始节点。在银行的例子中，父节点是高，中，低三个分类。

From cd55d052c7690f2e95d9efa5aa19875dcde2bba6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 6 Mar 2018 18:08:51 +0800
Subject: [PATCH 0503/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 2283af9e..a9f84799 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 卡方自动交互检测算法 CHAID（Chi-squared Automatic Interaction Detection)
+
 卡方自动交互检测法（chi-squared automatic interaction detector, CHAID）最早由Kass于1980年提出，是一个用来发现变量之间关系的工具，是一种基于调整后的显着性检验（邦费罗尼检验）决策树技术。
 
 其核心思想是：根据给定的反应变量和解释变量对样本进行最优分割，按照卡方检验的显著性进行多元列联表的自动判断分组。利用卡方自动交互检测法可以快速、有效地挖掘出主要的影响因素，它不仅可以处理非线性和高度相关的数据，而且可以将缺失值考虑在内，能克服传统的参数检验方法在这些方面的限制。

From 475e94e5e92e95c2e33093e138a69d945c484f4d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 6 Mar 2018 22:39:17 +0800
Subject: [PATCH 0504/1406] change page

---
 README.md                |   4 ++++
 assets/images/global.png | Bin 0 -> 216379 bytes
 2 files changed, 4 insertions(+)
 create mode 100644 assets/images/global.png

diff --git a/README.md b/README.md
index 59d8585f..503f0750 100644
--- a/README.md
+++ b/README.md
@@ -2,6 +2,10 @@
 最近以来一直在学习机器学习和算法，然后自己就在不断总结和写笔记，记录下自己的学习AI与算法历程。
 机器学习(Machine Learning, ML)是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。专门研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。
 
+<p align="center">
+<img width="100%" align="center" src="assets/images/global.png" />
+</p>
+
 * 机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。
 * 机器学习：多领域交叉学科，涉及概率论统计学，逼近论，凸分析，算法复杂度理论等多门学科。
 * 机器学习的应用：语音识别，自动驾驶，语言翻译，计算机视觉，推荐系统，无人机，识别垃圾邮件，人脸识别，电商推荐系统。
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HcmV?d00001


From 34c57818ee3b5a2bbeaae24c08f45acbb73badea Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:46:45 +0800
Subject: [PATCH 0505/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index a9f84799..15a5d6f0 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -23,5 +23,5 @@ CHAID决策树的构成包括：
 * 终端节点：CHAID分析树最后一个分类被称为终端节点。 CHAID分析树中，主要的影响变量排在前面，次要的排在后面。因此，它被称为终端节点。
 
 
-#### CHAID的应用
+#### CHAID的优点
 

From 9a9d62ef5389f34819c3267613651f0c6773a15f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:47:28 +0800
Subject: [PATCH 0506/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index 15a5d6f0..d2ee96d5 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -24,4 +24,7 @@ CHAID决策树的构成包括：
 
 
 #### CHAID的优点
-
+1. 可产生多分枝的决策树
+2. 目标变量可以定距或定类
+3. 从统计显著性角度确定分支变量和分割值，进而优化树的分枝过程
+4. 建立在因果关系探讨中，依据目标变量实现对输入变量众多水平划分

From f0a4f10e3f10f9f1001d21f5dfd5f1c850862ce8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:50:25 +0800
Subject: [PATCH 0507/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 503f0750..5221546f 100644
--- a/README.md
+++ b/README.md
@@ -98,7 +98,7 @@
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
-     * [随机森林（Random Forest）]()
+     * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()
  * [贝叶斯算法]()

From fd303a5165ddb83ab05b087301b691ca7ed4c2bb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:51:23 +0800
Subject: [PATCH 0508/1406] change DT

---
 assets/src/DT/DT.0.5.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/DT/DT.0.5.md

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
new file mode 100644
index 00000000..7972c74e
--- /dev/null
+++ b/assets/src/DT/DT.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 随机森林（Random Forest）

From f5ae61f1e4a27781ddd5f7be65dae78ab446a60e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:51:48 +0800
Subject: [PATCH 0509/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 5221546f..6885ebf7 100644
--- a/README.md
+++ b/README.md
@@ -98,7 +98,7 @@
      * [分类和回归树（CART）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.2.md)
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
-     * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
+     * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
      * [多元自适应回归样条（MARS）]()
      * [梯度推进机（Gradient Boosting Machine， GBM）]()
  * [贝叶斯算法]()

From 097b66d4b0c6868ae29e82b48b11a26f82741a8e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:54:49 +0800
Subject: [PATCH 0510/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 7972c74e..7b07704b 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 随机森林（Random Forest）
+
+随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。

From d09de1d3a1c7f1fe99bdd496189948efa9575bec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:55:02 +0800
Subject: [PATCH 0511/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 7b07704b..43812c92 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -2,6 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+
 #### 随机森林（Random Forest）
 
 随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。

From c41d328a592c57d038d018e2c55613f98fb992ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 7 Mar 2018 08:55:44 +0800
Subject: [PATCH 0512/1406] Update DT.0.4.md

---
 assets/src/DT/DT.0.4.md | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/assets/src/DT/DT.0.4.md b/assets/src/DT/DT.0.4.md
index d2ee96d5..3b8fc66e 100644
--- a/assets/src/DT/DT.0.4.md
+++ b/assets/src/DT/DT.0.4.md
@@ -10,19 +10,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在实践中，CHAID经常使用在直销的背景下，选择消费者群体，并预测他们的反应，一些变量如何影响其他变量，而其他早期应用是在医学和精神病学的研究领域。
 
-
 CHAID分析构建了一个预测模型，或树，以帮助确定给定因变量，变量如何最好地合来解释结果。CHAID分析，名义，有序和连续数据可以使用，在连续预测类别被分成大致相等的若干观测。CHAID对每个分类预测创建了交叉表，直到达到最好的结果，无法继续分类为止。在CHAID技术中，我们可以直观地看到在树的分割变量和相关因子之间的关系。决策树或分类树的展开，始于确定作为根节点的目标变量或因变量。 CHAID分析将目标变量分割成两个或两个以上的类被称为根节点，或者父节点，然后使用统计算法将节点分为子节点。不同于回归分析，CHAID技术并不要求数据是正态分布.
 
 CHAID的优势是它的结果是非常直观的易于理解的。由于默认情况下CHAID采用多路分割，需要相当大的样本量，来有效地开展工作，而小样本组受访者可以迅速分为太小了的组，而无法可靠的分析。
 
-
 CHAID决策树的构成包括：
 * 根节点：根节点包含因变量或目标变量。例如，CHAID使用于，银行根据年龄，收入，信用卡等，来预测信用卡风险。在这个例子中，信用卡风险是目标变量，其余变量是预测变量。
 * 父节点：该算法将目标变量分割成两个或多个分类。这些分类被称为父节点或者初始节点。在银行的例子中，父节点是高，中，低三个分类。
 * 子节点：CHAID分析树中独立变量分类低于父节点的分类被称为子节点。
 * 终端节点：CHAID分析树最后一个分类被称为终端节点。 CHAID分析树中，主要的影响变量排在前面，次要的排在后面。因此，它被称为终端节点。
 
-
 #### CHAID的优点
 1. 可产生多分枝的决策树
 2. 目标变量可以定距或定类

From c5821ae8951e77b95739aab7c5c8efb6df83521b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 9 Mar 2018 08:56:29 +0800
Subject: [PATCH 0513/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 43812c92..50ad9b02 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -5,4 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 随机森林（Random Forest）
 
+
 随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。

From 99a423261f06f8d9ea0530ef5569e1d731f2003c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 11:52:01 +0800
Subject: [PATCH 0514/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 50ad9b02..c5233e04 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -7,3 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。
+
+随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。

From e7956f697a4847757e323821c234b611cc4a81f0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 11:52:22 +0800
Subject: [PATCH 0515/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index c5233e04..2883b7df 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -8,4 +8,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。
 
-随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。
+随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。其实从直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。

From 72093d20d90d08ede0b96bb277b9f48c567e4bee Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 10 Mar 2018 11:56:17 +0800
Subject: [PATCH 0516/1406] chaneg page

---
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 assets/src/DT/DT.0.5.md |   3 +++
 2 files changed, 3 insertions(+)
 create mode 100644 assets/images/179.jpg

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diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 2883b7df..08dcfb78 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -9,3 +9,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。
 
 随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。其实从直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。
+<p align="center">
+<img width="500" align="center" src="../../images/179.jpg" />
+</p>

From 1819b0655ad55fc7e8e8c3a3d29d1410897e571e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 11:57:31 +0800
Subject: [PATCH 0517/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 08dcfb78..968ba8f3 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -10,5 +10,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。其实从直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。
 <p align="center">
-<img width="500" align="center" src="../../images/179.jpg" />
+<img width="700" align="center" src="../../images/179.jpg" />
 </p>

From e39518aef77c8456eeae9634c9a77072cbec7b3a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 11:59:17 +0800
Subject: [PATCH 0518/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 109 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 968ba8f3..a2ebb4f2 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -12,3 +12,112 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="700" align="center" src="../../images/179.jpg" />
 </p>
+
+
+#### 应用案例
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.colors import ListedColormap
+from sklearn.cross_validation import train_test_split
+from sklearn.preprocessing import StandardScaler
+from sklearn.datasets import make_moons, make_circles, make_classification
+from sklearn.neighbors import KNeighborsClassifier
+from sklearn.svm import SVC
+from sklearn.tree import DecisionTreeClassifier
+from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
+from sklearn.naive_bayes import GaussianNB
+from sklearn.lda import LDA
+from sklearn.qda import QDA
+
+h = .02  # step size in the mesh
+
+names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Decision Tree",
+         "Random Forest", "AdaBoost", "Naive Bayes", "LDA", "QDA"]
+classifiers = [
+    KNeighborsClassifier(3),
+    SVC(kernel="linear", C=0.025),
+    SVC(gamma=2, C=1),
+    DecisionTreeClassifier(max_depth=5),
+    RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),
+    AdaBoostClassifier(),
+    GaussianNB(),
+    LDA(),
+    QDA()]
+
+X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
+                           random_state=1, n_clusters_per_class=1)
+rng = np.random.RandomState(2)
+X += 2 * rng.uniform(size=X.shape)
+linearly_separable = (X, y)
+
+datasets = [make_moons(noise=0.3, random_state=0),
+            make_circles(noise=0.2, factor=0.5, random_state=1),
+            linearly_separable
+            ]
+
+figure = plt.figure(figsize=(27, 9))
+i = 1
+# iterate over datasets
+for ds in datasets:
+    # preprocess dataset, split into training and test part
+    X, y = ds
+    X = StandardScaler().fit_transform(X)
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)
+
+    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
+    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
+                         np.arange(y_min, y_max, h))
+
+    # just plot the dataset first
+    cm = plt.cm.RdBu
+    cm_bright = ListedColormap(['#FF0000', '#0000FF'])
+    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
+    # Plot the training points
+    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
+    # and testing points
+    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
+    ax.set_xlim(xx.min(), xx.max())
+    ax.set_ylim(yy.min(), yy.max())
+    ax.set_xticks(())
+    ax.set_yticks(())
+    i += 1
+
+    # iterate over classifiers
+    for name, clf in zip(names, classifiers):
+        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
+        clf.fit(X_train, y_train)
+        score = clf.score(X_test, y_test)
+
+        # Plot the decision boundary. For that, we will assign a color to each
+        # point in the mesh [x_min, m_max]x[y_min, y_max].
+        if hasattr(clf, "decision_function"):
+            Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
+        else:
+            Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
+
+        # Put the result into a color plot
+        Z = Z.reshape(xx.shape)
+        ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)
+
+        # Plot also the training points
+        ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
+        # and testing points
+        ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
+                   alpha=0.6)
+
+        ax.set_xlim(xx.min(), xx.max())
+        ax.set_ylim(yy.min(), yy.max())
+        ax.set_xticks(())
+        ax.set_yticks(())
+        ax.set_title(name)
+        ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
+                size=15, horizontalalignment='right')
+        i += 1
+
+figure.subplots_adjust(left=.02, right=.98)
+plt.show()
+
+```

From 1542983da5382eab302267b6fbec6dc339aa6a7b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 12:01:14 +0800
Subject: [PATCH 0519/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index a2ebb4f2..3f4d38d7 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -14,6 +14,15 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
+随机森林是一种很灵活实用的方法，它有如下几个特点:
+* 在当前所有算法中，具有极好的准确率;
+* 能够有效地运行在大数据集上;
+* 能够处理具有高维特征的输入样本，而且不需要降维;
+* 能够评估各个特征在分类问题上的重要性;
+* 在生成过程中，能够获取到内部生成误差的一种无偏估计;
+* 对于缺省值问题也能够获得很好得结果;
+
+
 #### 应用案例
 
 ```python

From af11a65f1512c309ab8e4a7be976fbd0e4521219 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 10 Mar 2018 12:07:31 +0800
Subject: [PATCH 0520/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 6885ebf7..3a49b6dc 100644
--- a/README.md
+++ b/README.md
@@ -27,7 +27,7 @@
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
- * [机器学习环境的搭建]()
+ * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)
  * [机器学习的入门]()
  * [机器学习的框架]()
  * [机器学习的应用案例]()

From a5da73e79f9c52a84a9b7387f4074b1ef1ef5bd0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Mar 2018 08:55:20 +0800
Subject: [PATCH 0521/1406] change page

---
 assets/src/DT/DT.0.6.md | 132 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 132 insertions(+)
 create mode 100644 assets/src/DT/DT.0.6.md

diff --git a/assets/src/DT/DT.0.6.md b/assets/src/DT/DT.0.6.md
new file mode 100644
index 00000000..3f4d38d7
--- /dev/null
+++ b/assets/src/DT/DT.0.6.md
@@ -0,0 +1,132 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+
+#### 随机森林（Random Forest）
+
+
+随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。
+
+随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。其实从直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。
+<p align="center">
+<img width="700" align="center" src="../../images/179.jpg" />
+</p>
+
+
+随机森林是一种很灵活实用的方法，它有如下几个特点:
+* 在当前所有算法中，具有极好的准确率;
+* 能够有效地运行在大数据集上;
+* 能够处理具有高维特征的输入样本，而且不需要降维;
+* 能够评估各个特征在分类问题上的重要性;
+* 在生成过程中，能够获取到内部生成误差的一种无偏估计;
+* 对于缺省值问题也能够获得很好得结果;
+
+
+#### 应用案例
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.colors import ListedColormap
+from sklearn.cross_validation import train_test_split
+from sklearn.preprocessing import StandardScaler
+from sklearn.datasets import make_moons, make_circles, make_classification
+from sklearn.neighbors import KNeighborsClassifier
+from sklearn.svm import SVC
+from sklearn.tree import DecisionTreeClassifier
+from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
+from sklearn.naive_bayes import GaussianNB
+from sklearn.lda import LDA
+from sklearn.qda import QDA
+
+h = .02  # step size in the mesh
+
+names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Decision Tree",
+         "Random Forest", "AdaBoost", "Naive Bayes", "LDA", "QDA"]
+classifiers = [
+    KNeighborsClassifier(3),
+    SVC(kernel="linear", C=0.025),
+    SVC(gamma=2, C=1),
+    DecisionTreeClassifier(max_depth=5),
+    RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),
+    AdaBoostClassifier(),
+    GaussianNB(),
+    LDA(),
+    QDA()]
+
+X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
+                           random_state=1, n_clusters_per_class=1)
+rng = np.random.RandomState(2)
+X += 2 * rng.uniform(size=X.shape)
+linearly_separable = (X, y)
+
+datasets = [make_moons(noise=0.3, random_state=0),
+            make_circles(noise=0.2, factor=0.5, random_state=1),
+            linearly_separable
+            ]
+
+figure = plt.figure(figsize=(27, 9))
+i = 1
+# iterate over datasets
+for ds in datasets:
+    # preprocess dataset, split into training and test part
+    X, y = ds
+    X = StandardScaler().fit_transform(X)
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)
+
+    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
+    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
+                         np.arange(y_min, y_max, h))
+
+    # just plot the dataset first
+    cm = plt.cm.RdBu
+    cm_bright = ListedColormap(['#FF0000', '#0000FF'])
+    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
+    # Plot the training points
+    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
+    # and testing points
+    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
+    ax.set_xlim(xx.min(), xx.max())
+    ax.set_ylim(yy.min(), yy.max())
+    ax.set_xticks(())
+    ax.set_yticks(())
+    i += 1
+
+    # iterate over classifiers
+    for name, clf in zip(names, classifiers):
+        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
+        clf.fit(X_train, y_train)
+        score = clf.score(X_test, y_test)
+
+        # Plot the decision boundary. For that, we will assign a color to each
+        # point in the mesh [x_min, m_max]x[y_min, y_max].
+        if hasattr(clf, "decision_function"):
+            Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
+        else:
+            Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
+
+        # Put the result into a color plot
+        Z = Z.reshape(xx.shape)
+        ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)
+
+        # Plot also the training points
+        ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
+        # and testing points
+        ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
+                   alpha=0.6)
+
+        ax.set_xlim(xx.min(), xx.max())
+        ax.set_ylim(yy.min(), yy.max())
+        ax.set_xticks(())
+        ax.set_yticks(())
+        ax.set_title(name)
+        ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
+                size=15, horizontalalignment='right')
+        i += 1
+
+figure.subplots_adjust(left=.02, right=.98)
+plt.show()
+
+```

From 97f87607ff89a90e9f2ce7260561bee7fc0359fe Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Mar 2018 08:57:01 +0800
Subject: [PATCH 0522/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3a49b6dc..6a2056ab 100644
--- a/README.md
+++ b/README.md
@@ -99,7 +99,7 @@
      * [ID3算法(Iterative Dichotomiser 3)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.3.md)
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
-     * [多元自适应回归样条（MARS）]()
+     * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
      * [梯度推进机（Gradient Boosting Machine， GBM）]()
  * [贝叶斯算法]()
      * [朴素贝叶斯]()

From a4f1cd81f0b1842de00aaae5ce61e6f957e503d3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Mar 2018 08:57:44 +0800
Subject: [PATCH 0523/1406] Update DT.0.6.md

---
 assets/src/DT/DT.0.6.md | 127 +---------------------------------------
 1 file changed, 1 insertion(+), 126 deletions(-)

diff --git a/assets/src/DT/DT.0.6.md b/assets/src/DT/DT.0.6.md
index 3f4d38d7..25640b36 100644
--- a/assets/src/DT/DT.0.6.md
+++ b/assets/src/DT/DT.0.6.md
@@ -3,130 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
-#### 随机森林（Random Forest）
+#### 多元自适应回归样条（MARS）
 
-
-随机森林是一个包含多个决策树的分类器，并且其输出的类别是由个别树输出的类别的众数而定。 Leo Breiman和Adele Cutler发展出推论出随机森林的算法。而"Random Forests"是他们的商标。这个术语是1995年由贝尔实验室的Tin Kam Ho所提出的随机决策森林（random decision forests）而来的。这个方法则是结合Breimans的"Bootstrap aggregating"想法和Ho的"random subspace method" 以建造决策树的集合。
-
-随机森林通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。随机森林的名称中有两个关键词，一个是“随机”，一个就是"森林"。"森林"我们很好理解，一棵叫做树，那么成百上千棵就可以叫做森林了，这样的比喻还是很贴切的，其实这也是随机森林的主要思想--集成思想的体现。其实从直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。
-<p align="center">
-<img width="700" align="center" src="../../images/179.jpg" />
-</p>
-
-
-随机森林是一种很灵活实用的方法，它有如下几个特点:
-* 在当前所有算法中，具有极好的准确率;
-* 能够有效地运行在大数据集上;
-* 能够处理具有高维特征的输入样本，而且不需要降维;
-* 能够评估各个特征在分类问题上的重要性;
-* 在生成过程中，能够获取到内部生成误差的一种无偏估计;
-* 对于缺省值问题也能够获得很好得结果;
-
-
-#### 应用案例
-
-```python
-import numpy as np
-import matplotlib.pyplot as plt
-from matplotlib.colors import ListedColormap
-from sklearn.cross_validation import train_test_split
-from sklearn.preprocessing import StandardScaler
-from sklearn.datasets import make_moons, make_circles, make_classification
-from sklearn.neighbors import KNeighborsClassifier
-from sklearn.svm import SVC
-from sklearn.tree import DecisionTreeClassifier
-from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
-from sklearn.naive_bayes import GaussianNB
-from sklearn.lda import LDA
-from sklearn.qda import QDA
-
-h = .02  # step size in the mesh
-
-names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Decision Tree",
-         "Random Forest", "AdaBoost", "Naive Bayes", "LDA", "QDA"]
-classifiers = [
-    KNeighborsClassifier(3),
-    SVC(kernel="linear", C=0.025),
-    SVC(gamma=2, C=1),
-    DecisionTreeClassifier(max_depth=5),
-    RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),
-    AdaBoostClassifier(),
-    GaussianNB(),
-    LDA(),
-    QDA()]
-
-X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
-                           random_state=1, n_clusters_per_class=1)
-rng = np.random.RandomState(2)
-X += 2 * rng.uniform(size=X.shape)
-linearly_separable = (X, y)
-
-datasets = [make_moons(noise=0.3, random_state=0),
-            make_circles(noise=0.2, factor=0.5, random_state=1),
-            linearly_separable
-            ]
-
-figure = plt.figure(figsize=(27, 9))
-i = 1
-# iterate over datasets
-for ds in datasets:
-    # preprocess dataset, split into training and test part
-    X, y = ds
-    X = StandardScaler().fit_transform(X)
-    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)
-
-    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
-    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
-    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
-                         np.arange(y_min, y_max, h))
-
-    # just plot the dataset first
-    cm = plt.cm.RdBu
-    cm_bright = ListedColormap(['#FF0000', '#0000FF'])
-    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
-    # Plot the training points
-    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
-    # and testing points
-    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
-    ax.set_xlim(xx.min(), xx.max())
-    ax.set_ylim(yy.min(), yy.max())
-    ax.set_xticks(())
-    ax.set_yticks(())
-    i += 1
-
-    # iterate over classifiers
-    for name, clf in zip(names, classifiers):
-        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
-        clf.fit(X_train, y_train)
-        score = clf.score(X_test, y_test)
-
-        # Plot the decision boundary. For that, we will assign a color to each
-        # point in the mesh [x_min, m_max]x[y_min, y_max].
-        if hasattr(clf, "decision_function"):
-            Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
-        else:
-            Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
-
-        # Put the result into a color plot
-        Z = Z.reshape(xx.shape)
-        ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)
-
-        # Plot also the training points
-        ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
-        # and testing points
-        ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
-                   alpha=0.6)
-
-        ax.set_xlim(xx.min(), xx.max())
-        ax.set_ylim(yy.min(), yy.max())
-        ax.set_xticks(())
-        ax.set_yticks(())
-        ax.set_title(name)
-        ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
-                size=15, horizontalalignment='right')
-        i += 1
-
-figure.subplots_adjust(left=.02, right=.98)
-plt.show()
-
-```

From 9abd1a065a73839ff1ea131d66899b3a923c7c42 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Mar 2018 08:59:49 +0800
Subject: [PATCH 0524/1406] Update DT.0.5.md

---
 assets/src/DT/DT.0.5.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/assets/src/DT/DT.0.5.md b/assets/src/DT/DT.0.5.md
index 3f4d38d7..f94d0a38 100644
--- a/assets/src/DT/DT.0.5.md
+++ b/assets/src/DT/DT.0.5.md
@@ -130,3 +130,15 @@ figure.subplots_adjust(left=.02, right=.98)
 plt.show()
 
 ```
+
+#### 优点
+* 随机森林对于很多种数据，它可以产生高准确度的分类器。
+* 随机森林可以处理大量的输入变量。
+* 随机森林可以在决定类别时，评估变量的重要性。
+* 在建造森林时，它可以在内部对于一般化后的误差产生不偏差的估计。
+* 随机森林包含一个好方法可以估计丢失的数据，并且，如果有很大一部分的数据丢失，仍可以维持准确度。
+* 它提供一个实验方法，可以去侦测variable interactions。
+* 对于不平衡的分类数据集来说，它可以平衡误差。
+* 它计算各例中的亲近度，对于数据挖掘、侦测离群点（outlier）和将数据可视化非常有用。
+* 它可被延伸应用在未标记的数据上，这类数据通常是使用非监督式聚类。也可侦测偏离者和观看数据。
+* 学习过程是很快速的。

From 614c891b3f59307bb78c406b4e89ac106497b8da Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Mar 2018 09:06:20 +0800
Subject: [PATCH 0525/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 6a2056ab..1bc282dd 100644
--- a/README.md
+++ b/README.md
@@ -181,7 +181,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,可以一起交流算法和机器学习！
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,加入我们的交流群一起交流算法和机器学习！
 
 
 ### License

From ff0f655e07f32da5c7bed398edf97acb577c9646 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 13 Mar 2018 08:34:57 +0800
Subject: [PATCH 0526/1406] Update DT.0.6.md

---
 assets/src/DT/DT.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.6.md b/assets/src/DT/DT.0.6.md
index 25640b36..1ae8767f 100644
--- a/assets/src/DT/DT.0.6.md
+++ b/assets/src/DT/DT.0.6.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 多元自适应回归样条（MARS）
-
+多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优点在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。

From c47f29f2be7acf7f5f8bf6f99dec779edfa83fc5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 08:58:28 +0800
Subject: [PATCH 0527/1406] Update DT.0.6.md

---
 assets/src/DT/DT.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.6.md b/assets/src/DT/DT.0.6.md
index 1ae8767f..d7197c2d 100644
--- a/assets/src/DT/DT.0.6.md
+++ b/assets/src/DT/DT.0.6.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多元自适应回归样条（MARS）
 多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优点在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
+
+在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符; 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。 论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。

From 9ca7d56d5c2f5e5ff2bd6af459143607bad05eab Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 08:58:39 +0800
Subject: [PATCH 0528/1406] Update DT.0.6.md

---
 assets/src/DT/DT.0.6.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DT/DT.0.6.md b/assets/src/DT/DT.0.6.md
index d7197c2d..1f814a27 100644
--- a/assets/src/DT/DT.0.6.md
+++ b/assets/src/DT/DT.0.6.md
@@ -7,3 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优点在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
 
 在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符; 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。 论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
+
+
+MARS是回归的自适应过程，非常适合高维问题（比如，存在大量的输入）。可以从两个角度来理解它，首先，它可以看成是逐步线性回归的推广，其次，也可以看成是为了提高CART在回归中的效果而进行的改进。我们从第一种观点引入MARS，接着与CART联系起来。

From 79c9b4d05229d68e92864ee3381ad37956c8ffc8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:00:03 +0800
Subject: [PATCH 0529/1406] change page

---
 assets/src/DT/DT.0.7.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 assets/src/DT/DT.0.7.md

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
new file mode 100644
index 00000000..1f814a27
--- /dev/null
+++ b/assets/src/DT/DT.0.7.md
@@ -0,0 +1,12 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+
+#### 多元自适应回归样条（MARS）
+多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优点在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
+
+在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符; 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。 论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
+
+
+MARS是回归的自适应过程，非常适合高维问题（比如，存在大量的输入）。可以从两个角度来理解它，首先，它可以看成是逐步线性回归的推广，其次，也可以看成是为了提高CART在回归中的效果而进行的改进。我们从第一种观点引入MARS，接着与CART联系起来。

From dccac7351962bbe29cae187b58df1a406de54303 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:01:06 +0800
Subject: [PATCH 0530/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1bc282dd..c01e91a1 100644
--- a/README.md
+++ b/README.md
@@ -100,7 +100,7 @@
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
-     * [梯度推进机（Gradient Boosting Machine， GBM）]()
+     * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
  * [贝叶斯算法]()
      * [朴素贝叶斯]()
      * [高斯朴素贝叶斯]()

From 108254ab65e02425410948bed84e162672c039c3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:02:07 +0800
Subject: [PATCH 0531/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index c01e91a1..0d95c61d 100644
--- a/README.md
+++ b/README.md
@@ -100,7 +100,7 @@
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
-     * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
+     * [梯度推进机（Gradient Boosting Machine,GBM）]()
  * [贝叶斯算法]()
      * [朴素贝叶斯]()
      * [高斯朴素贝叶斯]()

From 2fccba8f88f5af13889acbae6fa9cf80a21ff497 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:03:02 +0800
Subject: [PATCH 0532/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0d95c61d..c01e91a1 100644
--- a/README.md
+++ b/README.md
@@ -100,7 +100,7 @@
      * [CHAID（Chi-squared Automatic Interaction Detection)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.4.md)
      * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
-     * [梯度推进机（Gradient Boosting Machine,GBM）]()
+     * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
  * [贝叶斯算法]()
      * [朴素贝叶斯]()
      * [高斯朴素贝叶斯]()

From 080e637084f38d6d63cbe6fcdbf153ff7e1c8dfe Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:03:20 +0800
Subject: [PATCH 0533/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 1f814a27..d85d928a 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -4,9 +4,3 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 多元自适应回归样条（MARS）
-多元自适应回归样条(Multivariate Adaptive Regression Splines,MARS)是由美国的统计学家Jerome Friedman于1991年提出的一种数据分析方法。 该方法以样条函数的张量积作为基函数,分为前向过程、后向剪枝过程与模型选取三个步骤。其优点在于能够处理数据量大、维度高的数据,而且计算快捷、模型精确。在一般回归分析理论和样条理论的基础上,系统地研究了MARS的建模过程,提出引入Bernstein基函数建模的思想,并针对冶金工业领域一类数据分析其成分优化问题,应用该方法进行建模和预测。
-
-在前向过程中,通过自适应的选取节点对数据进行分割,每选取一个节点就生成两个新的基函数,前向过程结束后生成一个过拟合的模型。后向剪枝过程中在保证模型准确度的前提下,删除过拟合模型中对模型贡献度小的基函数,最后选取一个最优的模型作为回归模型。 研究过程中对采集的原始数据进行了消除负差、剔除异常数据、数据标准化等预处理工作,选取精华样本,分别建立了线性模型、非线性模型、神经网络模型等,并与MARS方法做比较。得到如下结论:由于模型的限制,线性回归模型精度较低,与实际经验不符; 神经网络对部分元素的描述优于线性回归模型,但不能得出相应的显式表达式,同时线性回归与神经网络都未能考虑变量间的交互作用;MARS模型对问题的描述比较符合实际经验,同时能够反映元素间的交互作用,能够对两个变量做可视化处理,并能够给出显式表达式。 论文以数据科学为背景,属于问题驱动的应用数学研究,不仅对多元自适应回归方法进行了理论探索,也为工业领域的数据分析与优化提供了理论依据。
-
-
-MARS是回归的自适应过程，非常适合高维问题（比如，存在大量的输入）。可以从两个角度来理解它，首先，它可以看成是逐步线性回归的推广，其次，也可以看成是为了提高CART在回归中的效果而进行的改进。我们从第一种观点引入MARS，接着与CART联系起来。

From bfe0ab4b76e1aaa2cbba13e63a631e211e9352af Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Mar 2018 09:03:49 +0800
Subject: [PATCH 0534/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index d85d928a..b41db12a 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
-#### 多元自适应回归样条（MARS）
+#### 梯度推进机（Gradient Boosting Machine,GBM）

From b3afdc383e4e3c8403d327b3461afcba51c7a62c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 15 Mar 2018 08:58:57 +0800
Subject: [PATCH 0535/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index b41db12a..13da0c60 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 梯度推进机（Gradient Boosting Machine,GBM）
+
+梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。

From ad4d5a92ed2fdb4ce2c87d272249bcd106c0e2af Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 08:46:54 +0800
Subject: [PATCH 0536/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 13da0c60..82413992 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -6,3 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 梯度推进机（Gradient Boosting Machine,GBM）
 
 梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。
+

From 29a994213f1c97aff48ba048d7758afb87205bda Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 14:15:07 +0000
Subject: [PATCH 0537/1406] Update DT.0.7.md

change page
---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 82413992..611a42ee 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -5,5 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 梯度推进机（Gradient Boosting Machine,GBM）
 
-梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。
+梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度提升是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 

From faadba9e256b0c697010cb08a2aaca12a36e9b22 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 14:15:39 +0000
Subject: [PATCH 0538/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 611a42ee..d8706776 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -5,5 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 梯度推进机（Gradient Boosting Machine,GBM）
 
-梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度提升是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
+梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度推进是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 

From 694db16a22264c2311fe910ec43ea87de7c7cf6d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 14:20:25 +0000
Subject: [PATCH 0539/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index d8706776..45176201 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -7,3 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度推进是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 
+梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。

From 227cd4622d48876c4e95621ba4b6cf351f082e3f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:24:08 +0800
Subject: [PATCH 0540/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 45176201..078a6b60 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -7,4 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度推进是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 
-梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
+度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。

From 72b92621e25c612ada9a9a4dfea6f57d7378c923 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:24:32 +0800
Subject: [PATCH 0541/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 078a6b60..45176201 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -7,4 +7,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度推进是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 
-度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
+梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。

From eaa6a9e982f7be00f8b3bbd0b70f46165684dfb5 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 16 Mar 2018 22:44:17 +0800
Subject: [PATCH 0542/1406] change page

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From 4b548adc93054639e6f3aa3c17f7308c26e1cb55 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:53:03 +0800
Subject: [PATCH 0543/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 45176201..bab6792c 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -8,3 +8,17 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 梯度推进理论核心是梯度推移理论。它认为，不同国家或不同地区间存在着产业梯度和经济梯度，存在梯度地区技术经济势差，就存在着技术经济推移的动力，就会形成生产力的空间推移。梯度推进是一种用于回归和分类问题的机器学习技术，该技术以弱预测模型（通常为决策树）的集合的形式产生预测模型。它像其他增强方法那样以阶段式方式构建模型，并且通过允许优化任意可微损失函数来推广它们。
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
+
+梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="150" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="150" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
+
+在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="150" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="150" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="150" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+<p align="center">
+<img width="150" align="center" src="../../images/185.jpg" />
+</p>
+
+或者等同地，
+<p align="center">
+<img width="150" align="center" src="../../images/186.jpg" />
+</p>
+
+因此，梯度升压将适合h到残余<img width="150" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="150" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="150" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="150" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于<img width="150" align="center" src="../../images/188.jpg" />)<img width="150" align="center" src="../../images/189.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From 3f6429926fb3254bbb0d12940e31cb31f8e299ff Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:57:10 +0800
Subject: [PATCH 0544/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index bab6792c..ef56b98b 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -9,16 +9,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="150" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="150" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
+梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
-在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="150" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="150" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="150" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="60" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="60" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
-<img width="150" align="center" src="../../images/185.jpg" />
+<img width="500" align="center" src="../../images/185.jpg" />
 </p>
 
 或者等同地，
 <p align="center">
-<img width="150" align="center" src="../../images/186.jpg" />
+<img width="500" align="center" src="../../images/186.jpg" />
 </p>
 
 因此，梯度升压将适合h到残余<img width="150" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="150" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="150" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="150" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于<img width="150" align="center" src="../../images/188.jpg" />)<img width="150" align="center" src="../../images/189.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From 59b9bc4ac889d96243cc260a14f88a43147c8479 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:57:36 +0800
Subject: [PATCH 0545/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index ef56b98b..69207acc 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -18,7 +18,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 或者等同地，
 <p align="center">
-<img width="500" align="center" src="../../images/186.jpg" />
+<img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
 因此，梯度升压将适合h到残余<img width="150" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="150" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="150" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="150" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于<img width="150" align="center" src="../../images/188.jpg" />)<img width="150" align="center" src="../../images/189.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From a2202f1f74f184c88b02dc735e720d34780b6421 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 22:59:20 +0800
Subject: [PATCH 0546/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 69207acc..c0ca8fe6 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="150" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="150" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="150" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="150" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于<img width="150" align="center" src="../../images/188.jpg" />)<img width="150" align="center" src="../../images/189.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="70" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="7" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="70" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="70" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From f3248cfa086e456152b477769beb889d80691cc2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:01:52 +0800
Subject: [PATCH 0547/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index c0ca8fe6..0ab07e1f 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="70" align="center" src="../../images/187.jpg" />.就像其他增强型变体一样，<img width="7" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="70" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="70" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="100" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="100" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="70" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From 2e78088e71b36a3934e60fa77aa67aea55e7d49f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:03:09 +0800
Subject: [PATCH 0548/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 0ab07e1f..b3832d59 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
-在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="60" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="60" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="50" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="50" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
 <img width="500" align="center" src="../../images/185.jpg" />
 </p>
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="100" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="100" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="70" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="100" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="50" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From fe526c45ca675fe506fcb019f734f19964dcf921 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:04:48 +0800
Subject: [PATCH 0549/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index b3832d59..8fa1df05 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="100" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="50" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="130" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From 58ae549d9fa3e2c6ac8c4290236a4147565dca70 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:07:39 +0800
Subject: [PATCH 0550/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 8fa1df05..a7491a71 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="130" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From d2252a83318f007d9dcf9e2a30876d150db23238 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 16 Mar 2018 23:10:13 +0800
Subject: [PATCH 0551/1406] chaneg page

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 assets/src/DT/DT.0.7.md |   2 +-
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diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index a7491a71..22c93025 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/191.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From a95cdde7a92abb51d7318ecb181057e60ad13d28 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:14:43 +0800
Subject: [PATCH 0552/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 22c93025..03e56875 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -22,3 +22,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+
+
+#### 梯度提升
+
+梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
+

From 23b7ec011dc3489445460e59f22292de67715966 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:35:49 +0800
Subject: [PATCH 0553/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 03e56875..7f3fe947 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -28,3 +28,20 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
+第m步中的通用梯度提升将适合决策树<img width="70" align="center" src="../../images/191.jpg" />伪残差。让<img width="70" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="70" align="center" src="../../images/192.jpg" />不相交的地区<img width="70" align="center" src="../../images/193.jpg" />，...，<img width="70" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="70" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
+<p align="center">
+<img width="300" align="center" src="../../images/195.jpg" />
+</p>
+
+哪里<img width="70" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="70" align="center" src="../../images/197.jpg" />。
+
+然后是系数<img width="70" align="center" src="../../images/196.jpg" />乘以某个值<img width="70" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
+<p align="center">
+<img width="300" align="center" src="../../images/199.jpg" />
+</p>
+
+弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="100" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
+<img width="100" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="70" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
+<p align="center">
+<img width="300" align="center" src="../../images/200.jpg" />
+</p>

From ea5652a7c905983c669ee38e78c43f3f7b30cbd8 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 16 Mar 2018 23:46:46 +0800
Subject: [PATCH 0554/1406] change page

---
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 assets/images/192.jpg | Bin 0 -> 1177 bytes
 assets/images/193.jpg | Bin 0 -> 1427 bytes
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 assets/images/197.jpg | Bin 0 -> 1536 bytes
 assets/images/198.jpg | Bin 0 -> 1131 bytes
 assets/images/199.jpg | Bin 0 -> 15594 bytes
 assets/images/200.jpg | Bin 0 -> 17534 bytes
 assets/images/201.jpg | Bin 0 -> 1563 bytes
 11 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/191.jpg
 create mode 100644 assets/images/192.jpg
 create mode 100644 assets/images/193.jpg
 create mode 100644 assets/images/194.jpg
 create mode 100644 assets/images/195.jpg
 create mode 100644 assets/images/196.jpg
 create mode 100644 assets/images/197.jpg
 create mode 100644 assets/images/198.jpg
 create mode 100644 assets/images/199.jpg
 create mode 100644 assets/images/200.jpg
 create mode 100644 assets/images/201.jpg

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From b0b969f108318b39547eda6544620d98a7c6fbb1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 16 Mar 2018 23:48:41 +0800
Subject: [PATCH 0555/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 7f3fe947..eec41737 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -37,11 +37,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 然后是系数<img width="70" align="center" src="../../images/196.jpg" />乘以某个值<img width="70" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
 <p align="center">
-<img width="300" align="center" src="../../images/199.jpg" />
+<img width="600" align="center" src="../../images/199.jpg" />
 </p>
 
 弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="100" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
 <img width="100" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="70" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
 <p align="center">
-<img width="300" align="center" src="../../images/200.jpg" />
+<img width="600" align="center" src="../../images/200.jpg" />
 </p>

From 82471fe7f20001eff72eb86f938e86fbbc413916 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:51:15 +0800
Subject: [PATCH 0556/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index eec41737..45da3308 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
-在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="50" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="50" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
 <img width="500" align="center" src="../../images/185.jpg" />
 </p>
@@ -21,14 +21,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="50" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
 
 
 #### 梯度提升
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-第m步中的通用梯度提升将适合决策树<img width="70" align="center" src="../../images/191.jpg" />伪残差。让<img width="70" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="70" align="center" src="../../images/192.jpg" />不相交的地区<img width="70" align="center" src="../../images/193.jpg" />，...，<img width="70" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="70" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
+第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="70" align="center" src="../../images/192.jpg" />不相交的地区<img width="70" align="center" src="../../images/193.jpg" />，...，<img width="70" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="70" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
 <p align="center">
 <img width="300" align="center" src="../../images/195.jpg" />
 </p>

From 0c66296518342776451e0d50f12c2d4e7d14e95a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:51:50 +0800
Subject: [PATCH 0557/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 45da3308..a83b8ff1 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -13,12 +13,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
-<img width="500" align="center" src="../../images/185.jpg" />
+<img width="400" align="center" src="../../images/185.jpg" />
 </p>
 
 或者等同地，
 <p align="center">
-<img width="300" align="center" src="../../images/186.jpg" />
+<img width="200" align="center" src="../../images/186.jpg" />
 </p>
 
 因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。

From 563dc7aa3e4a69c8533cb81809fa01359ede8661 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:52:41 +0800
Subject: [PATCH 0558/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index a83b8ff1..2dc2c039 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -28,7 +28,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="70" align="center" src="../../images/192.jpg" />不相交的地区<img width="70" align="center" src="../../images/193.jpg" />，...，<img width="70" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="70" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
+第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="30" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="30" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
 <p align="center">
 <img width="300" align="center" src="../../images/195.jpg" />
 </p>

From 05b1a61a9911add8d2db10d90b1dea6384f480ba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:53:25 +0800
Subject: [PATCH 0559/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 2dc2c039..ae157e02 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -33,9 +33,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/195.jpg" />
 </p>
 
-哪里<img width="70" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="70" align="center" src="../../images/197.jpg" />。
+哪里<img width="30" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="30" align="center" src="../../images/197.jpg" />。
 
-然后是系数<img width="70" align="center" src="../../images/196.jpg" />乘以某个值<img width="70" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
+然后是系数<img width="30" align="center" src="../../images/196.jpg" />乘以某个值<img width="30" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
 <p align="center">
 <img width="600" align="center" src="../../images/199.jpg" />
 </p>

From 26cc7c991525f8d619074a01b59c511fcbf04381 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:54:13 +0800
Subject: [PATCH 0560/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index ae157e02..514baec3 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -28,12 +28,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="30" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="30" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
+第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="40" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="40" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
 <p align="center">
 <img width="300" align="center" src="../../images/195.jpg" />
 </p>
 
-哪里<img width="30" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="30" align="center" src="../../images/197.jpg" />。
+哪里<img width="40" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="40" align="center" src="../../images/197.jpg" />。
 
 然后是系数<img width="30" align="center" src="../../images/196.jpg" />乘以某个值<img width="30" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
 <p align="center">

From 7bddf7e656cae5f9efbb670d118cfca06f9759b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:55:09 +0800
Subject: [PATCH 0561/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 514baec3..1e4de40e 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -28,7 +28,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-第m步中的通用梯度提升将适合决策树<img width="30" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="40" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="40" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
+第m步中的通用梯度提升将适合决策树<img width="40" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="40" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="40" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
 <p align="center">
 <img width="300" align="center" src="../../images/195.jpg" />
 </p>

From d1da643d5ff005f63b3f17c78836031f951633aa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:56:05 +0800
Subject: [PATCH 0562/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 1e4de40e..2c95819b 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -40,8 +40,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="600" align="center" src="../../images/199.jpg" />
 </p>
 
-弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="100" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
-<img width="100" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="70" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
+弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="40" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
+<img width="40" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="40" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
 <p align="center">
 <img width="600" align="center" src="../../images/200.jpg" />
 </p>

From 970beaffab8fed8eeb32675095193fab520561b3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:57:01 +0800
Subject: [PATCH 0563/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 2c95819b..ecbf6bc9 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
-在每个阶段 m，<img width="150" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+在每个阶段 m，<img width="80" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
 <img width="400" align="center" src="../../images/185.jpg" />
 </p>

From d575afec524f2e0f6cb3887ea13d3ce4b585db0e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 08:58:03 +0800
Subject: [PATCH 0564/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index ecbf6bc9..97523916 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
-在每个阶段 m，<img width="80" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
+在每个阶段 m，<img width="100" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">
 <img width="400" align="center" src="../../images/185.jpg" />
 </p>
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x))<img width="150" align="center" src="../../images/190.jpg" />.所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x)) <img width="100" align="center" src="../../images/190.jpg" /> 。所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
 
 
 #### 梯度提升

From 521242962f2ce3bff69c67b862e933c77c705b69 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 09:01:29 +0800
Subject: [PATCH 0565/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 97523916..7c46e3f3 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -30,18 +30,18 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 第m步中的通用梯度提升将适合决策树<img width="40" align="center" src="../../images/191.jpg" />伪残差。让<img width="30" align="center" src="../../images/192.jpg" />是它的叶子的数量。树将输入空间分成<img width="30" align="center" src="../../images/192.jpg" />不相交的地区<img width="30" align="center" src="../../images/193.jpg" />，...，<img width="40" align="center" src="../../images/194.jpg" />并预测每个地区的恒定值。使用指标符号，输出<img width="40" align="center" src="../../images/191.jpg" />对于输入x可以写成总和：
 <p align="center">
-<img width="300" align="center" src="../../images/195.jpg" />
+<img width="200" align="center" src="../../images/195.jpg" />
 </p>
 
 哪里<img width="40" align="center" src="../../images/196.jpg" />是该地区预测的价值<img width="40" align="center" src="../../images/197.jpg" />。
 
 然后是系数<img width="30" align="center" src="../../images/196.jpg" />乘以某个值<img width="30" align="center" src="../../images/198.jpg" />，使用线搜索选择以便最小化损失函数，并且模型更新如下：
 <p align="center">
-<img width="600" align="center" src="../../images/199.jpg" />
+<img width="650" align="center" src="../../images/199.jpg" />
 </p>
 
 弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="40" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
 <img width="40" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="40" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
 <p align="center">
-<img width="600" align="center" src="../../images/200.jpg" />
+<img width="650" align="center" src="../../images/200.jpg" />
 </p>

From df5f4ca78807ee4f2767c4eb8b03f84183439c66 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 09:04:31 +0800
Subject: [PATCH 0566/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index b2858aa5..cd31cea0 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络
 
-贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNs，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
+贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
 
 从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
 

From d40f13a240a04cad9723db53fab6e9d604b6aac8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 09:24:04 +0800
Subject: [PATCH 0567/1406] chaneg page

---
 README.md                 |  6 +++---
 assets/src/BNS/BNS.0.1.md | 39 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 42 insertions(+), 3 deletions(-)
 create mode 100644 assets/src/BNS/BNS.0.1.md

diff --git a/README.md b/README.md
index c01e91a1..266d8cc7 100644
--- a/README.md
+++ b/README.md
@@ -102,9 +102,9 @@
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
      * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
  * [贝叶斯算法]()
-     * [朴素贝叶斯]()
-     * [高斯朴素贝叶斯]()
-     * [多项式朴素贝叶斯]()
+     * [朴素贝叶斯(Naive Bayes)]()
+     * [高斯朴素贝叶斯(Gaussian Naive Bayes)]()
+     * [多项式朴素贝叶斯(Multinomial Naive Bayes)]()
      * [AODE（Averaged One-Dependence Estimators）]()
      * [贝叶斯网络（Bayesian Belief Network）]()
  * [基于核的算法]()   
diff --git a/assets/src/BNS/BNS.0.1.md b/assets/src/BNS/BNS.0.1.md
new file mode 100644
index 00000000..445e0af4
--- /dev/null
+++ b/assets/src/BNS/BNS.0.1.md
@@ -0,0 +1,39 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 贝叶斯网络
+
+决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
+
+最早的决策树算法是由Hunt等人于1966年提出的CLS。当前最有影响的决策树算法是Quinlan于1986年提出的ID3和1993年提出的C4.5。ID3只能处理离散型描述属性，它选择信息增益最大的属性划分训练样本，其目的是进行分枝时系统的熵最小，从而提高算法的运算速度和精确度。ID3算法的主要缺陷是，用信息增益作为选择分枝属性的标准时，偏向于取值较多的属性，而在某些情况下，这类属性可能不会提供太多有价值的信息。C4.5是ID3算法的改进算法，不仅可以处理离散型描述属性，还能处理连续性描述属性。C4.5采用了信息增益比作为选择分枝属性的标准，弥补了ID3算法的不足。
+
+决策树经常在运筹学中使用，特别是在决策分析中，它帮助确定一个能最可能达到目标的策略。如果在实际中，决策不得不在没有完备知识的情况下被在线采用，一个决策树应该平行概率模型作为最佳的选择模型或在线选择模型算法。决策树的另一个使用是作为计算条件概率的描述性手段。
+
+决策树（Decision Tree）这里的应用算法有：
+
+* 分类和回归树（CART）
+* ID3算法(Iterative Dichotomiser 3)
+* CHAID（Chi-squared Automatic Interaction Detection
+* 随机森林（Random Forest）
+* 多元自适应回归样条（MARS）
+* 梯度推进机（Gradient Boosting Machine， GBM）
+
+#### 决策树的优点
+
+* 便于理解和解释。树的结构可以可视化出来。
+* 训练需要的数据少。其他机器学习模型通常需要数据规范化，比如构建虚拟变量和移除缺失值,不过请注意，这种模型不支持缺失值。
+* 由于训练决策树的数据点的数量导致了决策树的使用开销呈指数分布(训练树模型的时间复杂度是参与训练数据点的对数值)。
+* 能够处理数值型数据和分类数据。其他的技术通常只能用来专门分析某一种变量类型的数据集。详情请参阅算法。
+* 能够处理多路输出的问题。
+* 使用白盒模型。如果某种给定的情况在该模型中是可以观察的，那么就可以轻易的通过布尔逻辑来解释这种情况。相比之下，在黑盒模型中的结果就是很难说明清 楚地。
+* 可以通过数值统计测试来验证该模型。这对事解释验证该模型的可靠性成为可能。
+* 即使该模型假设的结果与真实模型所提供的数据有些违反，其表现依旧良好。
+
+#### 决策树的缺点
+
+* 决策树模型容易产生一个过于复杂的模型,这样的模型对数据的泛化性能会很差。这就是所谓的过拟合.一些策略像剪枝、设置叶节点所需的最小样本数或设置数的最大深度是避免出现 该问题最为有效地方法。
+* 决策树可能是不稳定的，因为数据中的微小变化可能会导致完全不同的树生成。这个问题可以通过决策树的集成来得到缓解
+* 在多方面性能最优和简单化概念的要求下，学习一棵最优决策树通常是一个NP难问题。因此，实际的决策树学习算法是基于启发式算法，例如在每个节点进 行局部最优决策的贪心算法。这样的算法不能保证返回全局最优决策树。这个问题可以通过集成学习来训练多棵决策树来缓解,这多棵决策树一般通过对特征和样本有放回的随机采样来生成。
+* 有些概念很难被决策树学习到,因为决策树很难清楚的表述这些概念。例如XOR，奇偶或者复用器的问题。
+* 如果某些类在问题中占主导地位会使得创建的决策树有偏差。因此，建议在拟合前先对数据集进行平衡。

From db4aeb8b13ea8c17eb8254e84d1c2c4db0142e97 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 17 Mar 2018 09:32:11 +0800
Subject: [PATCH 0568/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 266d8cc7..1e2d8f52 100644
--- a/README.md
+++ b/README.md
@@ -101,7 +101,7 @@
      * [随机森林（Random Forest）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.5.md)
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
      * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
- * [贝叶斯算法]()
+ * [贝叶斯算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.1.md)
      * [朴素贝叶斯(Naive Bayes)]()
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)]()
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)]()

From 6a1b1590e0af9c53aeab8da29a3ecac91a7412bc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 18 Mar 2018 11:04:01 +0800
Subject: [PATCH 0569/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 7c46e3f3..bbc0f22c 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -40,8 +40,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="650" align="center" src="../../images/199.jpg" />
 </p>
 
+
 弗里德曼提出修改这个算法，以便它选择一个单独的最优值<img width="40" align="center" src="../../images/201.jpg" />对于每个树的区域，而不是一个
 <img width="40" align="center" src="../../images/198.jpg" />为整棵树。他称修改后的算法为“TreeBoost”。系数<img width="40" align="center" src="../../images/196.jpg" />从树形拟合过程可以简单地被丢弃并且模型更新规则变为：
 <p align="center">
 <img width="650" align="center" src="../../images/200.jpg" />
 </p>
+

From 520823ac5ee119ae385869872d3967d28b55a71a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 18 Mar 2018 11:04:36 +0800
Subject: [PATCH 0570/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index bbc0f22c..7ab88530 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -9,7 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 梯度提升通常用于作为基础学习者的固定大小的决策树（特别是CART树）。对于这种特殊情况，弗里德曼提出了对梯度提升方法的修改，该方法可以提高每个基础学习者的适应质量。
 
-梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="100" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
+梯度推进理论梯度提升将弱“学习者”以迭代的方式组合成一个强大的学习者。在最小二乘回归设置中解释最容易，其目标是“教”一个模型F预测表单的值<img width="70" align="center" src="../../images/180.jpg" />通过最小化均方误差<img width="70" align="center" src="../../images/181.jpg" />，在输出变量的一些实际值的训练集上进行平均y。
 
 在每个阶段 m，<img width="100" align="center" src="../../images/182.jpg" />，梯度提升，可以假定存在一些不完善的模型<img width="30" align="center" src="../../images/183.jpg" />（首先，可以使用一个非常弱的模型，它可以预测训练集中的平均值y).梯度提升算法进一步改进<img width="30" align="center" src="../../images/183.jpg" />通过构建一个新的模型来增加一个估计器h来提供一个更好的模型：<img width="200" align="center" src="../../images/184.jpg" />.寻找h梯度增强解决方案从观察到完美的h意味着开始
 <p align="center">

From de5ac9026f2385ea2c917a0a33e18920ee010682 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 18 Mar 2018 11:06:15 +0800
Subject: [PATCH 0571/1406] Update DT.0.7.md

---
 assets/src/DT/DT.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DT/DT.0.7.md b/assets/src/DT/DT.0.7.md
index 7ab88530..bf60c464 100644
--- a/assets/src/DT/DT.0.7.md
+++ b/assets/src/DT/DT.0.7.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/186.jpg" />
 </p>
 
-因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="70" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x)) <img width="100" align="center" src="../../images/190.jpg" /> 。所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
+因此，梯度升压将适合h到残余<img width="100" align="center" src="../../images/187.jpg" />。就像其他增强型变体一样，<img width="60" align="center" src="../../images/188.jpg" />学会纠正其前任 <img width="30" align="center" src="../../images/183.jpg" />.把这个想法推广到除了平方误差之外的损失函数 - 以及分类和排序问题 - 从观察残差开始<img width="100" align="center" src="../../images/187.jpg" />对于给定的模型是平方误差损失函数的负梯度(相对于F(x)) <img width="100" align="center" src="../../images/190.jpg" /> 。所以，梯度增强是一种梯度下降算法; 并推广它需要“插入”不同的损失及其梯度。
 
 
 #### 梯度提升

From 24d08728e41ceac9caf331fae4b82fb065103d0e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 19 Mar 2018 08:54:53 +0800
Subject: [PATCH 0572/1406] Update BNS.0.1.md

---
 assets/src/BNS/BNS.0.1.md | 34 ----------------------------------
 1 file changed, 34 deletions(-)

diff --git a/assets/src/BNS/BNS.0.1.md b/assets/src/BNS/BNS.0.1.md
index 445e0af4..a92e03f2 100644
--- a/assets/src/BNS/BNS.0.1.md
+++ b/assets/src/BNS/BNS.0.1.md
@@ -3,37 +3,3 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络
-
-决策树（Decision Tree）是应用于分类的一种树结构。其中的每个内部节点（internal node）代表对某个属性的一次测试判别，一个分枝代表一个测试结果，叶子（leaf）代表某个类（class）或者类的分布（class distribution）。最顶层的节点是根结点。可以将决策树理解为一个if-then规则的集合，由决策树的根节点到叶节点的每一条路径构建一条规则。
-
-最早的决策树算法是由Hunt等人于1966年提出的CLS。当前最有影响的决策树算法是Quinlan于1986年提出的ID3和1993年提出的C4.5。ID3只能处理离散型描述属性，它选择信息增益最大的属性划分训练样本，其目的是进行分枝时系统的熵最小，从而提高算法的运算速度和精确度。ID3算法的主要缺陷是，用信息增益作为选择分枝属性的标准时，偏向于取值较多的属性，而在某些情况下，这类属性可能不会提供太多有价值的信息。C4.5是ID3算法的改进算法，不仅可以处理离散型描述属性，还能处理连续性描述属性。C4.5采用了信息增益比作为选择分枝属性的标准，弥补了ID3算法的不足。
-
-决策树经常在运筹学中使用，特别是在决策分析中，它帮助确定一个能最可能达到目标的策略。如果在实际中，决策不得不在没有完备知识的情况下被在线采用，一个决策树应该平行概率模型作为最佳的选择模型或在线选择模型算法。决策树的另一个使用是作为计算条件概率的描述性手段。
-
-决策树（Decision Tree）这里的应用算法有：
-
-* 分类和回归树（CART）
-* ID3算法(Iterative Dichotomiser 3)
-* CHAID（Chi-squared Automatic Interaction Detection
-* 随机森林（Random Forest）
-* 多元自适应回归样条（MARS）
-* 梯度推进机（Gradient Boosting Machine， GBM）
-
-#### 决策树的优点
-
-* 便于理解和解释。树的结构可以可视化出来。
-* 训练需要的数据少。其他机器学习模型通常需要数据规范化，比如构建虚拟变量和移除缺失值,不过请注意，这种模型不支持缺失值。
-* 由于训练决策树的数据点的数量导致了决策树的使用开销呈指数分布(训练树模型的时间复杂度是参与训练数据点的对数值)。
-* 能够处理数值型数据和分类数据。其他的技术通常只能用来专门分析某一种变量类型的数据集。详情请参阅算法。
-* 能够处理多路输出的问题。
-* 使用白盒模型。如果某种给定的情况在该模型中是可以观察的，那么就可以轻易的通过布尔逻辑来解释这种情况。相比之下，在黑盒模型中的结果就是很难说明清 楚地。
-* 可以通过数值统计测试来验证该模型。这对事解释验证该模型的可靠性成为可能。
-* 即使该模型假设的结果与真实模型所提供的数据有些违反，其表现依旧良好。
-
-#### 决策树的缺点
-
-* 决策树模型容易产生一个过于复杂的模型,这样的模型对数据的泛化性能会很差。这就是所谓的过拟合.一些策略像剪枝、设置叶节点所需的最小样本数或设置数的最大深度是避免出现 该问题最为有效地方法。
-* 决策树可能是不稳定的，因为数据中的微小变化可能会导致完全不同的树生成。这个问题可以通过决策树的集成来得到缓解
-* 在多方面性能最优和简单化概念的要求下，学习一棵最优决策树通常是一个NP难问题。因此，实际的决策树学习算法是基于启发式算法，例如在每个节点进 行局部最优决策的贪心算法。这样的算法不能保证返回全局最优决策树。这个问题可以通过集成学习来训练多棵决策树来缓解,这多棵决策树一般通过对特征和样本有放回的随机采样来生成。
-* 有些概念很难被决策树学习到,因为决策树很难清楚的表述这些概念。例如XOR，奇偶或者复用器的问题。
-* 如果某些类在问题中占主导地位会使得创建的决策树有偏差。因此，建议在拟合前先对数据集进行平衡。

From 1bffb8eba6add3a1e9044ff73baaac99eac887eb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 19 Mar 2018 09:01:08 +0800
Subject: [PATCH 0573/1406] Update BNS.0.1.md

---
 assets/src/BNS/BNS.0.1.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/BNS/BNS.0.1.md b/assets/src/BNS/BNS.0.1.md
index a92e03f2..89798558 100644
--- a/assets/src/BNS/BNS.0.1.md
+++ b/assets/src/BNS/BNS.0.1.md
@@ -3,3 +3,12 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络
+
+贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
+
+从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
+
+在贝叶斯网络中，每个节点代表一个有限状态数的离散随机变量，节点之间的单向箭头代表其间的因果关系。如果某个节点不具有父节点（即没有箭头指向它），那么这个节点就具有一个边缘概率表，其中记录了该节点取不同状态值的概率分布；反之，若某节点有父节点（即存在一条或多条有向箭头指向它），则它就拥有一个条件概率表。条件概率表中的每个元素对应该节点在其父节点处于某种状态组合下，其本身状态值的概率分布规律。
+
+贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
+

From 624b8ece45d20f771bad371891445fb599da0df9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 19 Mar 2018 09:03:56 +0800
Subject: [PATCH 0574/1406] Update BNS.0.1.md

---
 assets/src/BNS/BNS.0.1.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.1.md b/assets/src/BNS/BNS.0.1.md
index 89798558..1cb4e79e 100644
--- a/assets/src/BNS/BNS.0.1.md
+++ b/assets/src/BNS/BNS.0.1.md
@@ -2,7 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 贝叶斯网络
+#### 贝叶斯算法
 
 贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
 
@@ -12,3 +12,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
 
+贝叶斯网络（Bayesian networks or Bayesnets）这里的应用算法有：
+
+* 朴素贝叶斯(Naive Bayes)
+* 高斯朴素贝叶斯(Gaussian Naive Bayes)
+* 多项式朴素贝叶斯(Multinomial Naive Bayes)
+* AODE（Averaged One-Dependence Estimators）
+* 多元自适应回归样条（MARS）
+* 贝叶斯网络（Bayesian Belief Network）

From f20ddf1ad101eac04dbcc5710914c26db62dc47e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 19 Mar 2018 22:07:22 +0800
Subject: [PATCH 0575/1406] change page

---
 assets/src/BNS/BNS.0.2.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 assets/src/BNS/BNS.0.2.md

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
new file mode 100644
index 00000000..1cb4e79e
--- /dev/null
+++ b/assets/src/BNS/BNS.0.2.md
@@ -0,0 +1,22 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 贝叶斯算法
+
+贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
+
+从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
+
+在贝叶斯网络中，每个节点代表一个有限状态数的离散随机变量，节点之间的单向箭头代表其间的因果关系。如果某个节点不具有父节点（即没有箭头指向它），那么这个节点就具有一个边缘概率表，其中记录了该节点取不同状态值的概率分布；反之，若某节点有父节点（即存在一条或多条有向箭头指向它），则它就拥有一个条件概率表。条件概率表中的每个元素对应该节点在其父节点处于某种状态组合下，其本身状态值的概率分布规律。
+
+贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
+
+贝叶斯网络（Bayesian networks or Bayesnets）这里的应用算法有：
+
+* 朴素贝叶斯(Naive Bayes)
+* 高斯朴素贝叶斯(Gaussian Naive Bayes)
+* 多项式朴素贝叶斯(Multinomial Naive Bayes)
+* AODE（Averaged One-Dependence Estimators）
+* 多元自适应回归样条（MARS）
+* 贝叶斯网络（Bayesian Belief Network）

From 4ee89380b5c74cb7c97ecd5d9482921304466fe3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 19 Mar 2018 22:08:13 +0800
Subject: [PATCH 0576/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1e2d8f52..e490146c 100644
--- a/README.md
+++ b/README.md
@@ -102,7 +102,7 @@
      * [多元自适应回归样条（MARS）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.6.md)
      * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
  * [贝叶斯算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.1.md)
-     * [朴素贝叶斯(Naive Bayes)]()
+     * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)]()
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)]()
      * [AODE（Averaged One-Dependence Estimators）]()

From e451439bde085ca15963879574ff035d3e8842e8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 19 Mar 2018 22:08:41 +0800
Subject: [PATCH 0577/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 19 +------------------
 1 file changed, 1 insertion(+), 18 deletions(-)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 1cb4e79e..47247269 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -2,21 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 贝叶斯算法
-
-贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
-
-从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
-
-在贝叶斯网络中，每个节点代表一个有限状态数的离散随机变量，节点之间的单向箭头代表其间的因果关系。如果某个节点不具有父节点（即没有箭头指向它），那么这个节点就具有一个边缘概率表，其中记录了该节点取不同状态值的概率分布；反之，若某节点有父节点（即存在一条或多条有向箭头指向它），则它就拥有一个条件概率表。条件概率表中的每个元素对应该节点在其父节点处于某种状态组合下，其本身状态值的概率分布规律。
-
-贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
-
-贝叶斯网络（Bayesian networks or Bayesnets）这里的应用算法有：
-
-* 朴素贝叶斯(Naive Bayes)
-* 高斯朴素贝叶斯(Gaussian Naive Bayes)
-* 多项式朴素贝叶斯(Multinomial Naive Bayes)
-* AODE（Averaged One-Dependence Estimators）
-* 多元自适应回归样条（MARS）
-* 贝叶斯网络（Bayesian Belief Network）
+#### 朴素贝叶斯(Naive Bayes)

From ce874113f883ff8ebd4e2b102e978d03f5366511 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 20 Mar 2018 08:43:22 +0800
Subject: [PATCH 0578/1406] change page

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1e2d8f52..7c9778ee 100644
--- a/README.md
+++ b/README.md
@@ -28,7 +28,7 @@
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)
- * [机器学习的入门]()
+ * [机器学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.02.md)
  * [机器学习的框架]()
  * [机器学习的应用案例]()
 

From 08f917f9c6c3eb164ed648fbaa80daa968630ccd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 20 Mar 2018 10:31:20 +0800
Subject: [PATCH 0579/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index e490146c..3cd66ac1 100644
--- a/README.md
+++ b/README.md
@@ -28,7 +28,7 @@
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)
- * [机器学习的入门]()
+ * [机器学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.02.md)
  * [机器学习的框架]()
  * [机器学习的应用案例]()
 

From 2e3b31f6ef7b33b4f032660729db8e596814c2c7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 20 Mar 2018 11:42:44 +0800
Subject: [PATCH 0580/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3cd66ac1..0c0cef77 100644
--- a/README.md
+++ b/README.md
@@ -181,7 +181,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,加入我们的交流群一起交流算法和机器学习！
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,加入我们的交流群一起交流学习！
 
 
 ### License

From cc79c42fdb194e3a0376a4ffd716d9eb8bd8384f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 21 Mar 2018 08:36:05 +0800
Subject: [PATCH 0581/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 47247269..b2ce076a 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 朴素贝叶斯(Naive Bayes)
+机器学习中，朴素贝叶斯分类器是一系列以假设特征之间强（朴素）独立下运用贝叶斯定理为基础的简单概率分类器。

From 6961e632584382bd96de6f48aba9b196d28ba59d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 21 Mar 2018 08:38:22 +0800
Subject: [PATCH 0582/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index b2ce076a..31cd0535 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -4,3 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 朴素贝叶斯(Naive Bayes)
 机器学习中，朴素贝叶斯分类器是一系列以假设特征之间强（朴素）独立下运用贝叶斯定理为基础的简单概率分类器。
+朴素贝叶斯是一种构建分类器的简单方法。该分类器模型会给问题实例分配用特征值表示的类标签，类标签取自有限集合。它不是训练这种分类器的单一算法，而是一系列基于相同原理的算法：所有朴素贝叶斯分类器都假定样本每个特征与其他特征都不相关。举个例子，如果一种水果其具有红，圆，直径大概3英寸等特征，该水果可以被判定为是苹果。尽管这些特征相互依赖或者有些特征由其他特征决定，然而朴素贝叶斯分类器认为这些属性在判定该水果是否为苹果的概率分布上独立的。
+对于某些类型的概率模型，在监督式学习的样本集中能获取得非常好的分类效果。在许多实际应用中，朴素贝叶斯模型参数估计使用最大似然估计方法；换而言之，在不用到贝叶斯概率或者任何贝叶斯模型的情况下，朴素贝叶斯模型也能奏效。
+
+尽管是带着这些朴素思想和过于简单化的假设，但朴素贝叶斯分类器在很多复杂的现实情形中仍能够获取相当好的效果。2004年，一篇分析贝叶斯分类器问题的文章揭示了朴素贝叶斯分类器获取看上去不可思议的分类效果的若干理论上的原因。尽管如此，2006年有一篇文章详细比较了各种分类方法，发现更新的方法（如决策树和随机森林）的性能超过了贝叶斯分类器。
+
+朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。

From 7adf87b89dee6edd4e62ce04fe388bb6d75845c0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 22 Mar 2018 08:33:39 +0800
Subject: [PATCH 0583/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 31cd0535..a1dfed70 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -5,6 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 朴素贝叶斯(Naive Bayes)
 机器学习中，朴素贝叶斯分类器是一系列以假设特征之间强（朴素）独立下运用贝叶斯定理为基础的简单概率分类器。
 朴素贝叶斯是一种构建分类器的简单方法。该分类器模型会给问题实例分配用特征值表示的类标签，类标签取自有限集合。它不是训练这种分类器的单一算法，而是一系列基于相同原理的算法：所有朴素贝叶斯分类器都假定样本每个特征与其他特征都不相关。举个例子，如果一种水果其具有红，圆，直径大概3英寸等特征，该水果可以被判定为是苹果。尽管这些特征相互依赖或者有些特征由其他特征决定，然而朴素贝叶斯分类器认为这些属性在判定该水果是否为苹果的概率分布上独立的。
+
 对于某些类型的概率模型，在监督式学习的样本集中能获取得非常好的分类效果。在许多实际应用中，朴素贝叶斯模型参数估计使用最大似然估计方法；换而言之，在不用到贝叶斯概率或者任何贝叶斯模型的情况下，朴素贝叶斯模型也能奏效。
 
 尽管是带着这些朴素思想和过于简单化的假设，但朴素贝叶斯分类器在很多复杂的现实情形中仍能够获取相当好的效果。2004年，一篇分析贝叶斯分类器问题的文章揭示了朴素贝叶斯分类器获取看上去不可思议的分类效果的若干理论上的原因。尽管如此，2006年有一篇文章详细比较了各种分类方法，发现更新的方法（如决策树和随机森林）的性能超过了贝叶斯分类器。

From dc27bade646ac0b5106215df98340aac91d7c5ab Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 22 Mar 2018 08:38:03 +0800
Subject: [PATCH 0584/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index a1dfed70..502822b2 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -11,3 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 尽管是带着这些朴素思想和过于简单化的假设，但朴素贝叶斯分类器在很多复杂的现实情形中仍能够获取相当好的效果。2004年，一篇分析贝叶斯分类器问题的文章揭示了朴素贝叶斯分类器获取看上去不可思议的分类效果的若干理论上的原因。尽管如此，2006年有一篇文章详细比较了各种分类方法，发现更新的方法（如决策树和随机森林）的性能超过了贝叶斯分类器。
 
 朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
+
+
+
+#### 应用案例

From cfb3f33d03ba2cdfeafbaa20da330638698e096c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 22 Mar 2018 08:38:59 +0800
Subject: [PATCH 0585/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 502822b2..4ddcaea8 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -12,6 +12,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
 
-
-
 #### 应用案例

From cb16cebd888b89fc5ef20e6648bdb9eff7ea4fef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 23 Mar 2018 08:43:55 +0800
Subject: [PATCH 0586/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 4ddcaea8..06c8b8ab 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -10,6 +10,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 尽管是带着这些朴素思想和过于简单化的假设，但朴素贝叶斯分类器在很多复杂的现实情形中仍能够获取相当好的效果。2004年，一篇分析贝叶斯分类器问题的文章揭示了朴素贝叶斯分类器获取看上去不可思议的分类效果的若干理论上的原因。尽管如此，2006年有一篇文章详细比较了各种分类方法，发现更新的方法（如决策树和随机森林）的性能超过了贝叶斯分类器。
 
-朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
+朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据就可以估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
 
 #### 应用案例

From 72e859784225b84d24bf4c80313071c580264766 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 26 Mar 2018 08:44:30 +0800
Subject: [PATCH 0587/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 06c8b8ab..8f61c27d 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -13,3 +13,23 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据就可以估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
 
 #### 应用案例
+```python
+import org.apache.spark.mllib.classification.{NaiveBayes, NaiveBayesModel}
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.regression.LabeledPoint
+//读取并处理数据
+val data = sc.textFile("data/mllib/sample_naive_bayes_data.txt")
+val parsedData = data.map { line =>
+  val parts = line.split(',')
+  LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))
+}
+// 切分数据为训练数据和测试数据
+val splits = parsedData.randomSplit(Array(0.6, 0.4), seed = 11L)
+val training = splits(0)
+val test = splits(1)
+//训练模型
+val model = NaiveBayes.train(training, lambda = 1.0, modelType = "multinomial")
+//测试数据
+val predictionAndLabel = test.map(p => (model.predict(p.features), p.label))
+val accuracy = 1.0 * predictionAndLabel.filter(x => x._1 == x._2).count() / test.count()
+```

From 8a14ecc80954727192ee8cb6849d247c98a0bbc3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 26 Mar 2018 08:45:01 +0800
Subject: [PATCH 0588/1406] Update BNS.0.2.md

---
 assets/src/BNS/BNS.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 8f61c27d..38626443 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -33,3 +33,8 @@ val model = NaiveBayes.train(training, lambda = 1.0, modelType = "multinomial")
 val predictionAndLabel = test.map(p => (model.predict(p.features), p.label))
 val accuracy = 1.0 * predictionAndLabel.filter(x => x._1 == x._2).count() / test.count()
 ```
+#### 优缺点
+
+优点：学习和预测的效率高，且易于实现；在数据较少的情况下仍然有效，可以处理多分类问题。
+
+缺点：分类效果不一定很高，特征独立性假设会是朴素贝叶斯变得简单，但是会牺牲一定的分类准确率。

From adb39383ce5d260eff663d945234678b082d0adb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 26 Mar 2018 08:56:17 +0800
Subject: [PATCH 0589/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0c0cef77..932e51e7 100644
--- a/README.md
+++ b/README.md
@@ -103,7 +103,7 @@
      * [梯度推进机（Gradient Boosting Machine,GBM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DT/DT.0.7.md)
  * [贝叶斯算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.1.md)
      * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
-     * [高斯朴素贝叶斯(Gaussian Naive Bayes)]()
+     * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)]()
      * [AODE（Averaged One-Dependence Estimators）]()
      * [贝叶斯网络（Bayesian Belief Network）]()

From bd7d06ada0bc5269cbf82bf8622b2786b1ab334c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 26 Mar 2018 08:56:59 +0800
Subject: [PATCH 0590/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 37 +------------------------------------
 1 file changed, 1 insertion(+), 36 deletions(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 38626443..6ad42f23 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -2,39 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 朴素贝叶斯(Naive Bayes)
-机器学习中，朴素贝叶斯分类器是一系列以假设特征之间强（朴素）独立下运用贝叶斯定理为基础的简单概率分类器。
-朴素贝叶斯是一种构建分类器的简单方法。该分类器模型会给问题实例分配用特征值表示的类标签，类标签取自有限集合。它不是训练这种分类器的单一算法，而是一系列基于相同原理的算法：所有朴素贝叶斯分类器都假定样本每个特征与其他特征都不相关。举个例子，如果一种水果其具有红，圆，直径大概3英寸等特征，该水果可以被判定为是苹果。尽管这些特征相互依赖或者有些特征由其他特征决定，然而朴素贝叶斯分类器认为这些属性在判定该水果是否为苹果的概率分布上独立的。
-
-对于某些类型的概率模型，在监督式学习的样本集中能获取得非常好的分类效果。在许多实际应用中，朴素贝叶斯模型参数估计使用最大似然估计方法；换而言之，在不用到贝叶斯概率或者任何贝叶斯模型的情况下，朴素贝叶斯模型也能奏效。
-
-尽管是带着这些朴素思想和过于简单化的假设，但朴素贝叶斯分类器在很多复杂的现实情形中仍能够获取相当好的效果。2004年，一篇分析贝叶斯分类器问题的文章揭示了朴素贝叶斯分类器获取看上去不可思议的分类效果的若干理论上的原因。尽管如此，2006年有一篇文章详细比较了各种分类方法，发现更新的方法（如决策树和随机森林）的性能超过了贝叶斯分类器。
-
-朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据就可以估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
-
-#### 应用案例
-```python
-import org.apache.spark.mllib.classification.{NaiveBayes, NaiveBayesModel}
-import org.apache.spark.mllib.linalg.Vectors
-import org.apache.spark.mllib.regression.LabeledPoint
-//读取并处理数据
-val data = sc.textFile("data/mllib/sample_naive_bayes_data.txt")
-val parsedData = data.map { line =>
-  val parts = line.split(',')
-  LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))
-}
-// 切分数据为训练数据和测试数据
-val splits = parsedData.randomSplit(Array(0.6, 0.4), seed = 11L)
-val training = splits(0)
-val test = splits(1)
-//训练模型
-val model = NaiveBayes.train(training, lambda = 1.0, modelType = "multinomial")
-//测试数据
-val predictionAndLabel = test.map(p => (model.predict(p.features), p.label))
-val accuracy = 1.0 * predictionAndLabel.filter(x => x._1 == x._2).count() / test.count()
-```
-#### 优缺点
-
-优点：学习和预测的效率高，且易于实现；在数据较少的情况下仍然有效，可以处理多分类问题。
-
-缺点：分类效果不一定很高，特征独立性假设会是朴素贝叶斯变得简单，但是会牺牲一定的分类准确率。
+#### 高斯朴素贝叶斯(Gaussian Naive Bayes)

From eac8638dcd2f79809f24f5855e07620b6ac2c1dd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 08:47:48 +0800
Subject: [PATCH 0591/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 6ad42f23..18f09da7 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
+
+贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。

From 8f39144b8f1863bdd4f034777bb4af453ca6ce05 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 08:49:15 +0800
Subject: [PATCH 0592/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 18f09da7..22de7e84 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
 
-贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。
+贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。而高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。

From 95c0c5bbdebc1d4c7a59f8673abe88554a7f7614 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 08:51:40 +0800
Subject: [PATCH 0593/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 22de7e84..ebcad045 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -4,4 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
 
-贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。而高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。
+贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。而高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：
+其中分别为均值和方差。对于维向量，多变量的高斯分布形式为：
+其中为维均值向量，为的协方差矩阵。是的行列式。
+高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。

From bce637716505cebbd47245ccdfa73fba1c928577 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 09:00:15 +0800
Subject: [PATCH 0594/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index ebcad045..207603d2 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -3,8 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
-
-贝叶斯定理是基于条件概率。条件概率可以帮助我们通过已经发生的事情来计算将要发生的事情。而高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：
+高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：
 其中分别为均值和方差。对于维向量，多变量的高斯分布形式为：
 其中为维均值向量，为的协方差矩阵。是的行列式。
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。

From 3636557f8030f50744df2cb864bfe4df8926b5b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 09:02:10 +0800
Subject: [PATCH 0595/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 207603d2..30c7424b 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
-高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：
-其中分别为均值和方差。对于维向量，多变量的高斯分布形式为：
-其中为维均值向量，为的协方差矩阵。是的行列式。
-高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
+高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
+
+对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。

From 4412348e9237da9992b91c6dfba63ba1fd122d10 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 27 Mar 2018 09:04:01 +0800
Subject: [PATCH 0596/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 30c7424b..2130856a 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
+
 高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
 
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。

From 39c6683f2e4f22b7c4108dcccbdd6499c0200462 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 08:51:16 +0800
Subject: [PATCH 0597/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 2130856a..30c7424b 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
-
 高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
 
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。

From 4a1c26edfd8ba10a664bb35fbacccc2c8bee5d7e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:21:13 +0800
Subject: [PATCH 0598/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 30c7424b..7ac66bd7 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -6,3 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
 
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
+
+高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
+另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布（Walker, 1969）。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
+

From b1919ddf3e7381cbf3aeb5ee58adb7f79598c72e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 21:24:31 +0800
Subject: [PATCH 0599/1406] change page

---
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 assets/images/203.jpg     | Bin 0 -> 41951 bytes
 assets/images/204.jpg     | Bin 0 -> 46769 bytes
 assets/src/BNS/BNS.0.3.md |   4 +++-
 4 files changed, 3 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/202.jpg
 create mode 100644 assets/images/203.jpg
 create mode 100644 assets/images/204.jpg

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diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 7ac66bd7..7db6ace2 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -9,4 +9,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布（Walker, 1969）。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
-
+<p align="center">
+<img width="400" align="center" src="../../images/202.jpg" />
+</p>

From befff94ebd96dffe13e86d4c0f104d1da86ecd73 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:26:40 +0800
Subject: [PATCH 0600/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 7db6ace2..5e4915c9 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -10,5 +10,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布（Walker, 1969）。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
 <p align="center">
-<img width="400" align="center" src="../../images/202.jpg" />
+<img width="600" align="center" src="../../images/202.jpg" />
 </p>

From 7798c84ee181408777f5d3b166a7756e072978d0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:27:15 +0800
Subject: [PATCH 0601/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 5e4915c9..833dca05 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
-另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布（Walker, 1969）。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
+另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
 <p align="center">
 <img width="600" align="center" src="../../images/202.jpg" />
 </p>

From e3220de2a68f8af2492649b5105624f81b4e8dc1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:32:06 +0800
Subject: [PATCH 0602/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 833dca05..55c176fd 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -12,3 +12,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="600" align="center" src="../../images/202.jpg" />
 </p>
+在实际应用中，随着N的增加，分布会很快的收敛于高斯分布。因而二元随机变量在次观测中出现次的二项分布将会在时趋向于高斯分布。在考虑高斯分布的几何形式。高斯通过出现在指数位置上的。
+这个二次型依赖于。被称为到的马氏距离（ Mahalanobis distance），当是单位矩阵时，退化成欧式距离。当这个二次型在空间中是常数的时候，高斯分布的曲面也是常数。
+首先，我们注意到矩阵可以不失一般性的取为对称矩阵，因为任何非对称项都会从指数中消失。现在考虑，协方差矩阵的特征向量方程因为是实对称矩阵，所以它的特征值也是实数，特征向量可以从正交集中选择，得到的单位矩阵的元素，满足协方差矩阵可以表示成特征向量的展开的形式。
+二次型和高斯密度在曲面上为常数。如果所有特征值都是正的，那么这些曲面是中心位于，轴方向为，轴方向的缩放比例为的椭球面。
+<p align="center">
+<img width="600" align="center" src="../../images/203.jpg" />
+</p>

From 6ac2928ccf28e4f78de0b767ab0297ceb972482f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:35:42 +0800
Subject: [PATCH 0603/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 55c176fd..6386fb5f 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -19,3 +19,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="600" align="center" src="../../images/203.jpg" />
 </p>
+为了很好的定义高斯分布，需要协方差矩阵的特征值严格为正，不然分布就不能标准化。每一个特征值都严格为正的矩阵被称为正定的（positive definite）。
+
+尽管，高斯分布被当作密度模型广泛使用，但是它有着一些巨大的局限性。考虑分布中自由参数的数量。一个通用的对称协方差矩阵有个独立参数，和其中的另外的独立参数。对于大的，参数的总数以平方的方式增长，且大矩阵的计算和求逆会相当困难。为了解决这个问题的其中一种方式是使用限制形式的协方差矩阵。如果考虑对角化的协方差矩阵，即，那么密度模型中总共有个独立参数。对应的常数密度的轮廓线由轴对齐的椭球给出。可以进一步地限制协方差矩阵为单位矩阵的倍数，即（这被称为同性协方差），那么模型总共有个独立参数，且得到恒定密度的球面。下图分别展示了通用的、对角的以及同性的协方差矩阵的概率。
+<p align="center">
+<img width="600" align="center" src="../../images/204.jpg" />
+</p>

From 1d58e7ad24acf29e2e83d72366aa5f1c29d6799f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:36:57 +0800
Subject: [PATCH 0604/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 6386fb5f..20ed91cc 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -25,3 +25,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="600" align="center" src="../../images/204.jpg" />
 </p>
+二维高斯分布的固定概率密度等高线。其中，(a)图对应的协方差矩阵为一般形式，(b)图对应的协方差矩阵为对角矩阵，图中椭圆的等高线与坐标轴对齐，(c)图对应的协方差矩阵正比于单位矩阵，图中的等高线是同心圆。尽管这样的方法限制了概率分布的的自由度的数量，使得求协方差矩阵的逆可以很快地完成，但也极大地束缚了概率密度的形式，且限制了它获取数据中有趣的相关性的能力。
+
+高斯分布的另一个局限是它本质上是单峰的（即只有一个最大值），因此不能够很好地近似多峰分布。因此高斯分布一方面相当灵活，因为它有很多参数。另一方面，它又有很大的局限性，因为它不能够描述很多概率分布。

From 4743dd127f4ea18785dd99700b67df17a21cdb8f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 21:42:29 +0800
Subject: [PATCH 0605/1406] change page

---
 assets/images/205.jpg     | Bin 0 -> 1583 bytes
 assets/src/BNS/BNS.0.3.md |   6 +++++-
 2 files changed, 5 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/205.jpg

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diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 20ed91cc..a32196ad 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -4,14 +4,18 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
 高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
+<p align="center">
+<img width="600" align="center" src="../../images/205.jpg" />
+</p>
 
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
 <p align="center">
-<img width="600" align="center" src="../../images/202.jpg" />
+<img width="600" align="center" src="../../images/205.jpg" />
 </p>
+
 在实际应用中，随着N的增加，分布会很快的收敛于高斯分布。因而二元随机变量在次观测中出现次的二项分布将会在时趋向于高斯分布。在考虑高斯分布的几何形式。高斯通过出现在指数位置上的。
 这个二次型依赖于。被称为到的马氏距离（ Mahalanobis distance），当是单位矩阵时，退化成欧式距离。当这个二次型在空间中是常数的时候，高斯分布的曲面也是常数。
 首先，我们注意到矩阵可以不失一般性的取为对称矩阵，因为任何非对称项都会从指数中消失。现在考虑，协方差矩阵的特征向量方程因为是实对称矩阵，所以它的特征值也是实数，特征向量可以从正交集中选择，得到的单位矩阵的元素，满足协方差矩阵可以表示成特征向量的展开的形式。

From 2c600a57445a97c43c08f9c8c0f5f1eb150fa485 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:43:17 +0800
Subject: [PATCH 0606/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index a32196ad..7629e8da 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 高斯朴素贝叶斯(Gaussian Naive Bayes)
 高斯朴素贝叶斯算法是一种特殊类型的NB算法，它特别用于当特征具有连续值时。同时假定所有特征都遵循高斯分布，即正态分布。高斯也称为正态分布，是连续变量分布上广泛使用的一种模型。对于单变量，高斯分布可以写成：均值和方差。
 <p align="center">
-<img width="600" align="center" src="../../images/205.jpg" />
+<img width="400" align="center" src="../../images/205.jpg" />
 </p>
 
 对于维向量，多变量的高斯分布形式为：其中为维均值向量，协方差矩阵行列式。高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
@@ -13,7 +13,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 高斯分布会出现在许多不同的问题中，可以从多个不同的角度来理解。例如，我们已经证明，对于单个实值变量，使熵最大的是高斯分布。这个性质同样适用于多变量高斯。
 另一种情况是，多个随机变量之和也会产生高斯分布。中心极限定理（由拉普拉斯提出）告诉我们，温和的一组随机变量的和的概率分布随着项的增加，趋向于高斯分布。为了阐述这个，考虑个区间[0, 1]上的均匀分布的随机变量，确定它们的均值的分布。如下图所展示的，对于大的，趋向于高斯分布。
 <p align="center">
-<img width="600" align="center" src="../../images/205.jpg" />
+<img width="600" align="center" src="../../images/202.jpg" />
 </p>
 
 在实际应用中，随着N的增加，分布会很快的收敛于高斯分布。因而二元随机变量在次观测中出现次的二项分布将会在时趋向于高斯分布。在考虑高斯分布的几何形式。高斯通过出现在指数位置上的。

From 71f601609c28c00171b4ee816dfc235d1bf46685 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:46:27 +0800
Subject: [PATCH 0607/1406] Update BNS.0.3.md

---
 assets/src/BNS/BNS.0.3.md | 103 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 103 insertions(+)

diff --git a/assets/src/BNS/BNS.0.3.md b/assets/src/BNS/BNS.0.3.md
index 7629e8da..7eb40daf 100644
--- a/assets/src/BNS/BNS.0.3.md
+++ b/assets/src/BNS/BNS.0.3.md
@@ -32,3 +32,106 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 二维高斯分布的固定概率密度等高线。其中，(a)图对应的协方差矩阵为一般形式，(b)图对应的协方差矩阵为对角矩阵，图中椭圆的等高线与坐标轴对齐，(c)图对应的协方差矩阵正比于单位矩阵，图中的等高线是同心圆。尽管这样的方法限制了概率分布的的自由度的数量，使得求协方差矩阵的逆可以很快地完成，但也极大地束缚了概率密度的形式，且限制了它获取数据中有趣的相关性的能力。
 
 高斯分布的另一个局限是它本质上是单峰的（即只有一个最大值），因此不能够很好地近似多峰分布。因此高斯分布一方面相当灵活，因为它有很多参数。另一方面，它又有很大的局限性，因为它不能够描述很多概率分布。
+
+
+#### 应用实例
+```python
+import numpy as np  
+from sklearn.utils import array2d  
+from sklearn.utils.extmath import logsumexp  
+import random  
+import matplotlib.pylab as plt  
+class GaussianBayes:  
+    def __init__(self):  
+        pass  
+    def train(self, x, y):  
+        n_samples, n_features = x.shape  
+        if(n_samples != y.shape[0]):  
+            raise ValueError('x and y have incompatible shapes.')  
+        self._classes = unique_y = np.unique(y)  
+        n_classes = unique_y.shape[0]  
+        self._theta = np.zeros((n_classes, n_features))  
+        self._sigma = np.zeros((n_classes, n_features))  
+        self._class_prior = np.zeros(n_classes)  
+        epsilon = 1e-9  
+        for i, y_i in enumerate(unique_y):  
+            self._theta[i, :] = np.mean(x[y == y_i, :], axis = 0)  
+            self._sigma[i, :] = np.var(x[y == y_i, :]) + epsilon  
+            self._class_prior[i] = np.float(np.sum(y == y_i)) / n_samples  
+        return self  
+    def predict(self, x):  
+        prob = self.predict_proba(x)  
+        indexs = []  
+        scores = []  
+        for ele in prob:  
+            index = np.argmax(ele)  
+            score = ele[index]  
+            indexs.append(index)  
+            scores.append(score)  
+        return [indexs, scores]  
+    def predict_log_prob(self, x):  
+        joint = self.joint_log_likelihood(x)  
+        #log_like_x = np.log(np.sum(np.exp(joint)))  
+        log_like_x = logsumexp(joint, axis = 1)  
+        return joint - np.atleast_2d(log_like_x).T  
+    def predict_proba(self, x):  
+        return np.exp(self.predict_log_prob(x))  
+    def joint_log_likelihood(self, x):  
+        x = array2d(x)  
+        joint_log_likelihood = []  
+        for i in xrange(np.size(self._classes)):  
+            jointi = np.log(self._class_prior[i])  
+            n_ij = - 0.5 * np.sum(np.log(np.pi * self._sigma[i, :]))  
+            n_ij -= 0.5 * np.sum(((x - self._theta[i, :]) ** 2) /  
+                                 (self._sigma[i, :]), 1)  
+            joint_log_likelihood.append(jointi + n_ij)  
+  
+        joint_log_likelihood = np.array(joint_log_likelihood).T  
+        return joint_log_likelihood  
+          
+def samples(n_samples, n_features = 10, classes = 5, rat = 0.2):  
+    x = np.zeros((n_samples, n_features))  
+    y = np.zeros((n_samples, 1))  
+    num = int(n_samples / classes)  
+    for i in range(0, classes):  
+        x[i*num:i*num + num] = np.random.random((num,n_features)) + i  
+  
+    for i in range(0, x.shape[0]):  
+        y[i, 0] = int(i / num)  
+    index = np.arange(0, x.shape[0])  
+    random.shuffle(index)  
+    train_index = index[0: int((1-rat) * x.shape[0])]  
+    test_index = index[int((1-rat) * x.shape[0]):-1]  
+    train_x = x[train_index, :]  
+    train_y = y[train_index]  
+    test_x = x[test_index, :]  
+    test_y = y[test_index]  
+    return [train_x, train_y, test_x, test_y]           
+def plotRes(pre, real, test_x):    
+    s = set(pre)    
+    col = ['r','b','g','y','m']    
+    fig = plt.figure()    
+    pre = np.array(pre)  
+    ax = fig.add_subplot(111)    
+    for i in range(0, len(s)):    
+        index1 = pre == i    
+        index2 = real == i    
+        x1 = test_x[index1, :]    
+        x2 = test_x[index2, :]    
+        ax.scatter(x1[:,0],x1[:,1],color=col[i],marker='v',linewidths=0.5)    
+        ax.scatter(x2[:,0],x2[:,1],color=col[i],marker='.',linewidths=12)    
+    plt.title('The prediction of the Gaussian Bayes')    
+    plt.legend(('c1:predict','c1:true',    
+                'c2:predict','c2:true',    
+                'c3:predict','c3:true',    
+                'c4:predict','c4:true',    
+                'c5:predict','c5:true'), shadow = True, loc = (0.01, 0.4))    
+    plt.show()          
+if __name__ == '__main__':  
+    [train_x, train_y, test_x, test_y] = samples(2000, 30, 5)  
+    gb = GaussianBayes()  
+    gb.train(train_x, train_y)  
+      
+    pred_y = gb.predict(test_x)  
+    plotRes(pred_y[0], test_y.ravel(), test_x)  
+```

From 3279cbc50180f000a38b78fffbb79c3fd5dc8011 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 21:48:00 +0800
Subject: [PATCH 0608/1406] change page

---
 assets/src/BNS/BNS.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/BNS/BNS.0.4.md

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
new file mode 100644
index 00000000..47247269
--- /dev/null
+++ b/assets/src/BNS/BNS.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 朴素贝叶斯(Naive Bayes)

From d455ab28c065f33be793785e03abe93d469da7f1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:49:43 +0800
Subject: [PATCH 0609/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 932e51e7..7d86b785 100644
--- a/README.md
+++ b/README.md
@@ -104,7 +104,7 @@
  * [贝叶斯算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.1.md)
      * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
-     * [多项式朴素贝叶斯(Multinomial Naive Bayes)]()
+     * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
      * [AODE（Averaged One-Dependence Estimators）]()
      * [贝叶斯网络（Bayesian Belief Network）]()
  * [基于核的算法]()   

From 7f69229fe3eff145a44b120882ed40feb0862b68 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 21:50:10 +0800
Subject: [PATCH 0610/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 47247269..9d3e8644 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 朴素贝叶斯(Naive Bayes)
+#### 多项式朴素贝叶斯(Multinomial Naive Bayes)

From ba4617630fbbbbaae2d352c014a01da993152dae Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 22:04:20 +0800
Subject: [PATCH 0611/1406] add BNS

---
 assets/src/BNS/BNS.0.2.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/BNS/BNS.0.2.md b/assets/src/BNS/BNS.0.2.md
index 38626443..de939a1f 100644
--- a/assets/src/BNS/BNS.0.2.md
+++ b/assets/src/BNS/BNS.0.2.md
@@ -12,6 +12,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 朴素贝叶斯分类器的一个优势在于只需要根据少量的训练数据就可以估计出必要的参数（变量的均值和方差）。由于变量独立假设，只需要估计各个变量的方法，而不需要确定整个协方差矩阵。
 
+ 朴素贝叶斯的应用过程：
+ * 收集数据：可以使用任何方法。
+ * 准备数据：需要数值型或者布尔型数据。
+ * 分析数据：有大量特征时，绘制特征作用不大，此时使用直方图效果更好。
+ * 训练算法：计算不同的独立特征的条件概率。
+ * 测试算法：计算错误率。
+ * 使用算法：一个常见的朴素贝叶斯应用是文档分类。可以在任意的分类场景中使用朴素贝叶斯分类器，不一定非要是文本。
+ 
 #### 应用案例
 ```python
 import org.apache.spark.mllib.classification.{NaiveBayes, NaiveBayesModel}

From 907602227c7e808eab469e625870b4c97d9f5e70 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:18:49 +0800
Subject: [PATCH 0612/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 9d3e8644..be7ccb61 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
+
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。

From 818d2616dcf98e62533dcc98e0258d23b2ca850d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 22:20:55 +0800
Subject: [PATCH 0613/1406] add BNS

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From 21737657ffb36d747ef875bfa2d8e0021cf7d3e1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:22:56 +0800
Subject: [PATCH 0614/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index be7ccb61..9ad6c1cb 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width=60" align="center" src="../../images/206.jpg" />的<img width=60" align="center" src="../../images/207.jpg" />

From 335669bba95508439451efb723a19b529402795f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:24:13 +0800
Subject: [PATCH 0615/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 9ad6c1cb..481dc732 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width=60" align="center" src="../../images/206.jpg" />的<img width=60" align="center" src="../../images/207.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类

From 5c50949bdc8dfecac102a53a9a4419dedfb548a1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:24:42 +0800
Subject: [PATCH 0616/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 481dc732..0d7340d5 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="60" align="center" src="../../images/206.jpg" />

From 93b1959dc95d9ddee703d999c32b1b493fc5b6a8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:25:53 +0800
Subject: [PATCH 0617/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 0d7340d5..03fb87de 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="60" align="center" src="../../images/206.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="30" align="center" src="../../images/206.jpg" />的<img width="30" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="60" align="center" src="../../images/208.jpg" />

From 6442372561cc26e6366caed1cd2a5ea8e622d43e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:26:44 +0800
Subject: [PATCH 0618/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 03fb87de..c098e416 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="30" align="center" src="../../images/206.jpg" />的<img width="30" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="60" align="center" src="../../images/208.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="30" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="10" align="center" src="../../images/208.jpg" />

From 3aca25119b38b36239a276b3a932b06f01df5d5d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:27:33 +0800
Subject: [PATCH 0619/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index c098e416..3797f2fe 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="30" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="10" align="center" src="../../images/208.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="100" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="50" align="center" src="../../images/208.jpg" />

From 004de0458f34d7b0ee3096230227e645030f8539 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:27:58 +0800
Subject: [PATCH 0620/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 3797f2fe..24fd10d0 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="100" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="50" align="center" src="../../images/208.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />

From 8178481701d0c55eb91f5f2ff5ab7c3012af496e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:28:56 +0800
Subject: [PATCH 0621/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 24fd10d0..79619d05 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="70" align="center" src="../../images/209.jpg" /> 。

From aad071430a32b97b959b8150c9416d71f9cdae24 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:29:47 +0800
Subject: [PATCH 0622/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 79619d05..1e1906e5 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="70" align="center" src="../../images/209.jpg" /> 。
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="100" align="center" src="../../images/209.jpg" /> 。

From a55d53fcc2c3449d25aca162d019e9d576899149 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:30:17 +0800
Subject: [PATCH 0623/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 1e1906e5..19a40eb4 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="100" align="center" src="../../images/209.jpg" /> 。
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="90" align="center" src="../../images/209.jpg" /> 。

From 783878afed695187e4332b28b79b5031f2de6f41 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:32:16 +0800
Subject: [PATCH 0624/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 19a40eb4..19f24d42 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -4,4 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多项式朴素贝叶斯(Multinomial Naive Bayes)
 
- 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="90" align="center" src="../../images/209.jpg" /> 。
+ 多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="80" align="center" src="../../images/209.jpg" /> 。
+ 
+参数 <img width="80" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
+<p align="center">
+<img width="300" align="center" src="../../images/210.jpg" />
+</p>

From ee217fc1b8c42283e69864688e07288d78f9009e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:33:32 +0800
Subject: [PATCH 0625/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 19f24d42..c4b89a18 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -6,7 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
  多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="80" align="center" src="../../images/209.jpg" /> 。
  
-参数 <img width="80" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
+参数 <img width="30" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
 <p align="center">
-<img width="300" align="center" src="../../images/210.jpg" />
+<img width="300" align="center" src="../../images/211.jpg" />
 </p>

From ab751259bb1ac00010279e302c1d3ceca82b933e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:33:53 +0800
Subject: [PATCH 0626/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index c4b89a18..b608e409 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -8,5 +8,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
  
 参数 <img width="30" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
 <p align="center">
-<img width="300" align="center" src="../../images/211.jpg" />
+<img width="200" align="center" src="../../images/211.jpg" />
 </p>

From da1fc7bd32995169a574f5299df11f98c5fa5f08 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:34:21 +0800
Subject: [PATCH 0627/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index b608e409..cc9188eb 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -8,5 +8,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
  
 参数 <img width="30" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
 <p align="center">
-<img width="200" align="center" src="../../images/211.jpg" />
+<img width="190" align="center" src="../../images/211.jpg" />
 </p>

From 055b61142d97446c952a3abf85fe4e929d44e7bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:36:02 +0800
Subject: [PATCH 0628/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index cc9188eb..9f7d4779 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -6,7 +6,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
  多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="80" align="center" src="../../images/209.jpg" /> 。
  
-参数 <img width="30" align="center" src="../../images/210.jpg" /> 。 使用平滑过的最大似然估计法来估计，即相对频率计数:
+参数 <img width="30" align="center" src="../../images/210.jpg" />使用平滑过的最大似然估计法来估计，即相对频率计数:
 <p align="center">
 <img width="190" align="center" src="../../images/211.jpg" />
 </p>
+式中<img width="30" align="center" src="../../images/212.jpg" /> 是训练集T中特征 i 在类 y 中出现的次数，<img width="30" align="center" src="../../images/213.jpg" /> 是类 y 中出现所有特征的计数总和。

From 187967eb5e04fbf9f1406f8f72c56dcb0c3064ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:37:05 +0800
Subject: [PATCH 0629/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 9f7d4779..21f97eab 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -10,4 +10,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="190" align="center" src="../../images/211.jpg" />
 </p>
-式中<img width="30" align="center" src="../../images/212.jpg" /> 是训练集T中特征 i 在类 y 中出现的次数，<img width="30" align="center" src="../../images/213.jpg" /> 是类 y 中出现所有特征的计数总和。
+式中<img width="70" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="70" align="center" src="../../images/213.jpg" />是类 y 中出现所有特征的计数总和。

From 4863306518afebf3457429b720c33160099c1ce0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:37:36 +0800
Subject: [PATCH 0630/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 21f97eab..f2b61a99 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -7,7 +7,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
  多项式朴素贝叶斯(Multinomial Naive Bayes)算法，用于文本分类(这个领域中数据往往以词向量表示，尽管在实践中 tf-idf向量在预测时表现良好)的两大经典朴素贝叶斯算法之一。分布参数由每类<img width="10" align="center" src="../../images/206.jpg" />的<img width="160" align="center" src="../../images/207.jpg" />向量决定， 式中 n 是特征的数量(对于文本分类，是词汇量的大小)<img width="30" align="center" src="../../images/208.jpg" />是样本中属于类 y 中特征i概率<img width="80" align="center" src="../../images/209.jpg" /> 。
  
 参数 <img width="30" align="center" src="../../images/210.jpg" />使用平滑过的最大似然估计法来估计，即相对频率计数:
+
 <p align="center">
 <img width="190" align="center" src="../../images/211.jpg" />
 </p>
-式中<img width="70" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="70" align="center" src="../../images/213.jpg" />是类 y 中出现所有特征的计数总和。
+
+式中<img width="70" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="70" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。

From 756778b830127d7df849494f5b0d1a0b5532369a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:37:58 +0800
Subject: [PATCH 0631/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index f2b61a99..c363c2fb 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -12,4 +12,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="190" align="center" src="../../images/211.jpg" />
 </p>
 
-式中<img width="70" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="70" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
+式中<img width="170" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="170" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。

From 38ede43cd3f7ac6cee6b4ae051839bf7b5614591 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:38:18 +0800
Subject: [PATCH 0632/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index c363c2fb..aaf61f66 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -12,4 +12,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="190" align="center" src="../../images/211.jpg" />
 </p>
 
-式中<img width="170" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="170" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
+式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。

From 750c1439be94f301b8b893d4947ab3d33bcef411 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:39:32 +0800
Subject: [PATCH 0633/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index aaf61f66..25a77b06 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -13,3 +13,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
+
+先验平滑因子<img width="130" align="center" src="../../images/213.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/214.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而 <img width="130" align="center" src="../../images/215.jpg" />被称为利德斯通(Lidstone smoothing)。

From 5fe0650e6ede0a3d0c6520b7743e945ff2d3dd03 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:40:22 +0800
Subject: [PATCH 0634/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 25a77b06..50ba3635 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
 
-先验平滑因子<img width="130" align="center" src="../../images/213.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/214.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而 <img width="130" align="center" src="../../images/215.jpg" />被称为利德斯通(Lidstone smoothing)。
+先验平滑因子<img width="130" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/215.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而 <img width="130" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。

From cc0080d7219123fc230308b305183d55f8a7790b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:41:29 +0800
Subject: [PATCH 0635/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 50ba3635..a8ccd62f 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
 
-先验平滑因子<img width="130" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/215.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而 <img width="130" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。
+先验平滑因子<img width="130" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/215.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="130" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。

From c291162ce21c353d460dfcd25eca4b098fefd5ae Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:42:47 +0800
Subject: [PATCH 0636/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index a8ccd62f..93098d15 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
 
-先验平滑因子<img width="130" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="130" align="center" src="../../images/215.jpg" />被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="130" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。
+先验平滑因子<img width="70" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="70" align="center" src="../../images/215.jpg" /> 被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="70" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。

From c6b6c12b48e521607ceb571bb6e1620a54e56d82 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 22:43:43 +0800
Subject: [PATCH 0637/1406] change page

---
 assets/images/{215jpg.png => 215.jpg} | Bin
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename assets/images/{215jpg.png => 215.jpg} (100%)

diff --git a/assets/images/215jpg.png b/assets/images/215.jpg
similarity index 100%
rename from assets/images/215jpg.png
rename to assets/images/215.jpg

From cafd61a0a5955a96a34580bc6b22f443ec2e85ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:56:02 +0800
Subject: [PATCH 0638/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 93098d15..783f28a5 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -9,9 +9,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 参数 <img width="30" align="center" src="../../images/210.jpg" />使用平滑过的最大似然估计法来估计，即相对频率计数:
 
 <p align="center">
-<img width="190" align="center" src="../../images/211.jpg" />
+<img width="150" align="center" src="../../images/211.jpg" />
 </p>
 
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
 
-先验平滑因子<img width="70" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="70" align="center" src="../../images/215.jpg" /> 被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="70" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。
+先验平滑因子<img width="50" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="50" align="center" src="../../images/215.jpg" /> 被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="50" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。

From 141a9aa980019c271b1ce245aac0e8844a5b0b22 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 28 Mar 2018 22:59:32 +0800
Subject: [PATCH 0639/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 783f28a5..18cbb543 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -15,3 +15,33 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 式中<img width="160" align="center" src="../../images/212.jpg" />是训练集T中特征 i 在类 y 中出现的次数，<img width="160" align="center" src="../../images/213.jpg" />是类y中出现所有特征的计数总和。
 
 先验平滑因子<img width="50" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="50" align="center" src="../../images/215.jpg" /> 被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="50" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。
+
+
+#### 应用实例
+```python
+#GaussianNB differ from MultinomialNB in these two method:
+# _calculate_feature_prob, _get_xj_prob
+class GaussianNB(MultinomialNB):
+        """
+        GaussianNB inherit from MultinomialNB,so it has self.alpha
+        and self.fit() use alpha to calculate class_prior
+        However,GaussianNB should calculate class_prior without alpha.
+        Anyway,it make no big different
+
+        """
+        #calculate mean(mu) and standard deviation(sigma) of the given feature
+        def _calculate_feature_prob(self,feature):
+                mu = np.mean(feature)
+                sigma = np.std(feature)
+                return (mu,sigma)
+
+        #the probability density for the Gaussian distribution 
+        def _prob_gaussian(self,mu,sigma,x):
+                return ( 1.0/(sigma * np.sqrt(2 * np.pi)) *
+                        np.exp( - (x - mu)**2 / (2 * sigma**2)) )
+
+        #given mu and sigma , return Gaussian distribution probability for target_value
+        def _get_xj_prob(self,mu_sigma,target_value):
+                return self._prob_gaussian(mu_sigma[0],mu_sigma[1],target_value)
+
+```

From 93d4d8c53fafa86bf7701dc4f5b3faed66affbd6 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 23:02:17 +0800
Subject: [PATCH 0640/1406] change page

---
 README.md                 | 2 +-
 assets/src/BNS/BNS.0.5.md | 6 ++++++
 2 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/BNS/BNS.0.5.md

diff --git a/README.md b/README.md
index 7d86b785..0d574f53 100644
--- a/README.md
+++ b/README.md
@@ -105,7 +105,7 @@
      * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
-     * [AODE（Averaged One-Dependence Estimators）]()
+     * [AODE（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
      * [贝叶斯网络（Bayesian Belief Network）]()
  * [基于核的算法]()   
      * [支持向量机（SVM）]()
diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
new file mode 100644
index 00000000..7071d604
--- /dev/null
+++ b/assets/src/BNS/BNS.0.5.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### AODE（Averaged One-Dependence Estimators）
+

From 148f529386289f2e4b725f8dafed18439b5f6b25 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 28 Mar 2018 23:10:43 +0800
Subject: [PATCH 0641/1406] change page of BNS

---
 assets/src/BNS/BNS.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 7071d604..22bbe35b 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### AODE（Averaged One-Dependence Estimators）
-
+平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。

From 0d727eff0f5a20292e1c6637a7bbd7437772b871 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 29 Mar 2018 08:46:48 +0800
Subject: [PATCH 0642/1406] Update BNS.0.4.md

---
 assets/src/BNS/BNS.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.4.md b/assets/src/BNS/BNS.0.4.md
index 18cbb543..e2f0e368 100644
--- a/assets/src/BNS/BNS.0.4.md
+++ b/assets/src/BNS/BNS.0.4.md
@@ -17,6 +17,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 先验平滑因子<img width="50" align="center" src="../../images/214.jpg" />应用于在学习样本中没有出现的特征，以防在将来的计算中出现0概率输出。 把  <img width="50" align="center" src="../../images/215.jpg" /> 被称为拉普拉斯平滑(Lapalce smoothing)，而<img width="50" align="center" src="../../images/216.jpg" />被称为利德斯通(Lidstone smoothing)。
 
 
+
 #### 应用实例
 ```python
 #GaussianNB differ from MultinomialNB in these two method:

From 0d5b71e92be5a77e74dd3f71ba735547e784c286 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 29 Mar 2018 08:49:03 +0800
Subject: [PATCH 0643/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 22bbe35b..7ccb4c36 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -4,3 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### AODE（Averaged One-Dependence Estimators）
 平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
+像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。

From fa63f8ea1b76af470b3626a5010b0d50f94364b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 29 Mar 2018 08:50:52 +0800
Subject: [PATCH 0644/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 7ccb4c36..2b092325 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### AODE（Averaged One-Dependence Estimators）
 平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。
+
+AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。

From dcca22796fec986588421d97a935cf973b4e0295 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 29 Mar 2018 08:51:06 +0800
Subject: [PATCH 0645/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 2b092325..dc2f7a1e 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -6,4 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。
 
-AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
+AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。

From 738806f11ca41551eabed7777c6045dae70d6af5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 30 Mar 2018 08:56:50 +0800
Subject: [PATCH 0646/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index dc2f7a1e..ba35af5b 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### AODE（Averaged One-Dependence Estimators）
+
 平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。
 

From 5653fa56fe600cfe650848b1e9cf82386fc808a2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 30 Mar 2018 21:39:10 +0800
Subject: [PATCH 0647/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0d574f53..b579f14c 100644
--- a/README.md
+++ b/README.md
@@ -105,7 +105,7 @@
      * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
-     * [AODE（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
+     * [平均依赖性评估（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
      * [贝叶斯网络（Bayesian Belief Network）]()
  * [基于核的算法]()   
      * [支持向量机（SVM）]()

From ce8eb21b829e860331e4efef8131d4454678b327 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 30 Mar 2018 21:40:17 +0800
Subject: [PATCH 0648/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b579f14c..afaf24a2 100644
--- a/README.md
+++ b/README.md
@@ -105,7 +105,7 @@
      * [朴素贝叶斯(Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.2.md)
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
-     * [平均依赖性评估（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
+     * [平均单依赖估计量（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
      * [贝叶斯网络（Bayesian Belief Network）]()
  * [基于核的算法]()   
      * [支持向量机（SVM）]()

From 8146b284042457cceef5249d02e3d6265bf59dd9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 30 Mar 2018 21:40:55 +0800
Subject: [PATCH 0649/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index ba35af5b..1a5e4704 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -2,7 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### AODE（Averaged One-Dependence Estimators）
+#### 平均单依赖估计量（Averaged One-Dependence Estimators）
 
 平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。

From fd8c21bc2e99b4d7c8357cc34db6cfa33dceb0fd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 08:50:43 +0800
Subject: [PATCH 0650/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 1a5e4704..9d76c5ca 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 平均单依赖估计量（Averaged One-Dependence Estimators）
 
-平均单依赖估计量（AODE）是一种概率分类学习技术。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
+平均单依赖估计量是一种半朴素贝叶斯学习方法。它通过聚合多个单依赖分类器的预测来执行分类，其中所有属性依赖于相同的单独父属性以及类。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。
 
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。

From 447c5289f008092b88e11fecdf98928581f16d14 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 08:56:08 +0800
Subject: [PATCH 0651/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 9d76c5ca..57710338 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -5,6 +5,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 平均单依赖估计量（Averaged One-Dependence Estimators）
 
 平均单依赖估计量是一种半朴素贝叶斯学习方法。它通过聚合多个单依赖分类器的预测来执行分类，其中所有属性依赖于相同的单独父属性以及类。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
-像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。
+像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。为了保持效率，可以期望利用单依赖分类器，诸如树扩展型朴素贝叶斯分类器,Tree Augmented Naive Bayes(TAN)，其中每个属性取决于类和至多一个其他属性。然而，大多数单依赖分类器学习的方法执行模型选择，这个过程通常会带来相当大的计算开销并且相对于朴素贝叶斯大大增加了方差。 
+
+AODE通过对多个单依赖分类器的预测进行平均来避免模型选择。在每个单依赖分类器中，选择一个属性作为所有其他属性的父属性。该属性称为SuperParent，这种单依赖性分类器称为SuperParent单依赖性估计器（SPODE）。
 
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
+
+。

From 2d992ac11dc5e890ff39c04868eceb2574448dc6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:00:33 +0800
Subject: [PATCH 0652/1406] change page of BNS

---
 assets/src/BNS/BNS.0.5.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 57710338..e21ce2f4 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -11,4 +11,3 @@ AODE通过对多个单依赖分类器的预测进行平均来避免模型选择
 
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
 
-。

From e6c5e4a27111ce47fccb93cea8f28150f5a25118 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:05:03 +0800
Subject: [PATCH 0653/1406] change page

---
 assets/images/217.jpg     | Bin 0 -> 7541 bytes
 assets/src/BNS/BNS.0.5.md |   8 +++++++-
 2 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/217.jpg

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diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index e21ce2f4..c3d8d204 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -4,10 +4,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 平均单依赖估计量（Averaged One-Dependence Estimators）
 
-平均单依赖估计量是一种半朴素贝叶斯学习方法。它通过聚合多个单依赖分类器的预测来执行分类，其中所有属性依赖于相同的单独父属性以及类。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
+平均单依赖估计量（Averaged One-Dependence Estimators）是一种半朴素贝叶斯学习方法。它通过聚合多个单依赖分类器的预测来执行分类，其中所有属性依赖于相同的单独父属性以及类。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
 像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。为了保持效率，可以期望利用单依赖分类器，诸如树扩展型朴素贝叶斯分类器,Tree Augmented Naive Bayes(TAN)，其中每个属性取决于类和至多一个其他属性。然而，大多数单依赖分类器学习的方法执行模型选择，这个过程通常会带来相当大的计算开销并且相对于朴素贝叶斯大大增加了方差。 
 
 AODE通过对多个单依赖分类器的预测进行平均来避免模型选择。在每个单依赖分类器中，选择一个属性作为所有其他属性的父属性。该属性称为SuperParent，这种单依赖性分类器称为SuperParent单依赖性估计器（SPODE）。
 
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
 
+<p align="center">
+<img width="150" align="center" src="../../images/216.jpg" />
+</p>
+
+由于AODE在避免模型选择的同时，比朴素贝叶斯更弱的属性条件独立性假设，它的偏差大大降低，方差增加很小。
+当一个新实例可用时，如朴素贝叶斯，AODE只需要更新概率估计值。因此，它也适合增量学习。
\ No newline at end of file

From c5649ebae583178f6c1720d37d2c281c53a19fa5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:05:45 +0800
Subject: [PATCH 0654/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index c3d8d204..7f431a0b 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -5,15 +5,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 平均单依赖估计量（Averaged One-Dependence Estimators）
 
 平均单依赖估计量（Averaged One-Dependence Estimators）是一种半朴素贝叶斯学习方法。它通过聚合多个单依赖分类器的预测来执行分类，其中所有属性依赖于相同的单独父属性以及类。它的开发旨在解决流行的朴素贝叶斯分类器的属性独立性问题。它常常以计算量适度增加为代价，比朴素贝叶斯开发出更准确的分类器。
-像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。为了保持效率，可以期望利用单依赖分类器，诸如树扩展型朴素贝叶斯分类器,Tree Augmented Naive Bayes(TAN)，其中每个属性取决于类和至多一个其他属性。然而，大多数单依赖分类器学习的方法执行模型选择，这个过程通常会带来相当大的计算开销并且相对于朴素贝叶斯大大增加了方差。 
+像朴素贝叶斯一样，AODE不执行模型选择，也不使用可调参数。因此，它具有较低的方差。
+
+它支持增量学习，通过这些学习，分类器可以通过新示例提供的信息进行有效更新。它预测类别概率，而不是简单地预测单个类别，从而允许用户确定每个分类的可信度。其概率模型可以直接处理某些数据丢失的情况。为了保持效率，可以期望利用单依赖分类器，诸如树扩展型朴素贝叶斯分类器,Tree Augmented Naive Bayes(TAN)，其中每个属性取决于类和至多一个其他属性。然而，大多数单依赖分类器学习的方法执行模型选择，这个过程通常会带来相当大的计算开销并且相对于朴素贝叶斯大大增加了方差。 
 
 AODE通过对多个单依赖分类器的预测进行平均来避免模型选择。在每个单依赖分类器中，选择一个属性作为所有其他属性的父属性。该属性称为SuperParent，这种单依赖性分类器称为SuperParent单依赖性估计器（SPODE）。
 
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
 
 <p align="center">
-<img width="150" align="center" src="../../images/216.jpg" />
+<img width="150" align="center" src="../../images/217.jpg" />
 </p>
 
 由于AODE在避免模型选择的同时，比朴素贝叶斯更弱的属性条件独立性假设，它的偏差大大降低，方差增加很小。
-当一个新实例可用时，如朴素贝叶斯，AODE只需要更新概率估计值。因此，它也适合增量学习。
\ No newline at end of file

From 63e95a75edc009f101351fcd3797233b2466b81f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:06:02 +0800
Subject: [PATCH 0655/1406] Update BNS.0.5.md

---
 assets/src/BNS/BNS.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.5.md b/assets/src/BNS/BNS.0.5.md
index 7f431a0b..ea35a35a 100644
--- a/assets/src/BNS/BNS.0.5.md
+++ b/assets/src/BNS/BNS.0.5.md
@@ -14,7 +14,7 @@ AODE通过对多个单依赖分类器的预测进行平均来避免模型选择
 AODE具有计算复杂性 O（ln ^2）在训练时间和 O（kn^2)在分类时刻，其中n是特征的数量，l是训练样本的数量，k是类别的数量。这使得应用于高维数据是不可行的。然而，在这个限制内，它与训练样例的数量成线性关系，因此可以有效地处理大量的训练样例。
 
 <p align="center">
-<img width="150" align="center" src="../../images/217.jpg" />
+<img width="500" align="center" src="../../images/217.jpg" />
 </p>
 
 由于AODE在避免模型选择的同时，比朴素贝叶斯更弱的属性条件独立性假设，它的偏差大大降低，方差增加很小。

From 7946f74b2f4148ee5429ead3f0113597078781ee Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:11:25 +0800
Subject: [PATCH 0656/1406] change page of BNS

---
 assets/src/BNS/BNS.0.6.md | 6 ++++++
 1 file changed, 6 insertions(+)
 create mode 100644 assets/src/BNS/BNS.0.6.md

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
new file mode 100644
index 00000000..8e76d8bf
--- /dev/null
+++ b/assets/src/BNS/BNS.0.6.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 贝叶斯网络（Bayesian Belief Network）
+

From 52a3757ade083d9f23da69d1c971d0d8b7b378ba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:12:01 +0800
Subject: [PATCH 0657/1406] change page of BNS

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index afaf24a2..213d2118 100644
--- a/README.md
+++ b/README.md
@@ -106,7 +106,7 @@
      * [高斯朴素贝叶斯(Gaussian Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.3.md)
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
      * [平均单依赖估计量（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
-     * [贝叶斯网络（Bayesian Belief Network）]()
+     * [贝叶斯网络（Bayesian Belief Network）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.6.md)
  * [基于核的算法]()   
      * [支持向量机（SVM）]()
      * [径向基函数（Radial Basis Function ，RBF)]()

From f563112dc1b97f1d003c919e291973c90d98e41e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:16:08 +0800
Subject: [PATCH 0658/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index 8e76d8bf..d1d531a0 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -4,3 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络（Bayesian Belief Network）
 
+贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出。它是一种模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。
+
+贝叶斯网络的有向无环图中的节点表示随机变量，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。

From 93c0aa5d5a6df0a31a69059de3f7d7efcd4defdf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:17:10 +0800
Subject: [PATCH 0659/1406] add page BNS

---
 assets/images/218.jpg     | Bin 0 -> 586 bytes
 assets/src/BNS/BNS.0.6.md |   2 +-
 2 files changed, 1 insertion(+), 1 deletion(-)
 create mode 100644 assets/images/218.jpg

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z=%-nb2zwEK?BYdfZ1))CGPbs=U(dG4oNZ-#&f&>5y|Z5gHK$LU_j#7YuT@5-ea(*!
zy!gfIetiD_f&htWm0ww87dqu|tIfJmenO^1aHW~x&bJB|yR4Hfbv2sJ<-aBuNglr{
zcyz&(m%hPkw)TcNeG+};@-}yt&C4hLwL4?>eZO}zU%dFB(6x+|><$lI4b{RU_s?}+
v_}EvjG1>HrxzbkCjrZc657kTl^Zv`galg2iJ^yqUC^>k#`njxgN@xNA3VHJ2

literal 0
HcmV?d00001

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index d1d531a0..ea87bf39 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -6,4 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出。它是一种模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。
 
-贝叶斯网络的有向无环图中的节点表示随机变量，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。
+贝叶斯网络的有向无环图中的节点表示随机变量<img width="70" align="center" src="../../images/218.jpg" />，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。

From 4af66ceb7c1ef3c16f7774e339bd291d12f9918d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:17:39 +0800
Subject: [PATCH 0660/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index ea87bf39..b81d932d 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -6,4 +6,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出。它是一种模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。
 
-贝叶斯网络的有向无环图中的节点表示随机变量<img width="70" align="center" src="../../images/218.jpg" />，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。
+贝叶斯网络的有向无环图中的节点表示随机变量<img width="120" align="center" src="../../images/218.jpg" />，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。

From 7b6aa1f9c0ef7d122903433fde8152387b37d30f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:22:42 +0800
Subject: [PATCH 0661/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index b81d932d..37055db4 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -4,6 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络（Bayesian Belief Network）
 
-贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出。它是一种模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。
+贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出，它是基于概率推理的图形化网络，可以模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。而贝叶斯公式则是这个概率网络的基础。贝叶斯网络是基于概率推理的数学模型，所谓概率推理就是通过一些变量的信息来获取其他的概率信息的过程，基于概率推理的贝叶斯网络(Bayesian network)是为了解决不定性和不完整性问题而提出的，它对于解决复杂设备不确定性和关联性引起的故障有很大的优势，在多个领域中获得广泛应用。
 
 贝叶斯网络的有向无环图中的节点表示随机变量<img width="120" align="center" src="../../images/218.jpg" />，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。

From 14e857d8640055ed0cfabb90736748ec52c6e54c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 31 Mar 2018 09:27:09 +0800
Subject: [PATCH 0662/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index 37055db4..57712ec6 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -6,4 +6,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出，它是基于概率推理的图形化网络，可以模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。而贝叶斯公式则是这个概率网络的基础。贝叶斯网络是基于概率推理的数学模型，所谓概率推理就是通过一些变量的信息来获取其他的概率信息的过程，基于概率推理的贝叶斯网络(Bayesian network)是为了解决不定性和不完整性问题而提出的，它对于解决复杂设备不确定性和关联性引起的故障有很大的优势，在多个领域中获得广泛应用。
 
-贝叶斯网络的有向无环图中的节点表示随机变量<img width="120" align="center" src="../../images/218.jpg" />，它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。
+贝叶斯网络的有向无环图(Directed Acyclic Graph,DAG)中的节点表示随机变量<img width="120" align="center" src="../../images/218.jpg" />，,由代表变量节点及连接这些节点有向边构成。它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。节点代表随机变量，节点间的有向边代表了节点间的互相关系(由父节点指向其子节点)，用条件概率进行表达关系强度，没有父节点的用先验概率进行信息表达。节点变量可以是任何问题的抽象，如：测试值，观测现象，意见征询等。适用于表达和分析不确定性和概率性的事件，应用于有条件地依赖多种控制因素的决策，可以从不完全、不精确或不确定的知识或信息中做出推理。
+
+使用贝叶斯网络必须知道各个状态之间相关的概率。得到这些参数的过程叫做训练。和训练马尔可夫模型一样，训练贝叶斯网络要用一些已知的数据。比如在训练上面的网络，需要知道一些心血管疾病和吸烟、家族病史等有关的情况。相比马尔可夫链，贝叶斯网络的训练比较复杂，从理论上讲，它是一个 NP-complete问题，也就是说，现阶段没有可以在多项式时间内完成的算法。但是，对于某些应用，这个训练过程可以简化，并在计算上高效实现。
+
+贝叶斯理论是处理不确定性信息的重要工具。作为一种基于概率的不确定性推理方法，贝叶斯网络在处理不确定信息的智能化系统中已得到了重要的应用，已成功地用于医疗诊断、统计决策、专家系统、学习预测等领域。这些成功的应用，充分体现了贝叶斯网络技术是一种强有力的不确定性推理方法。

From 8a3ee29c0fd77b9a2c80570edcd4f18a8ca9f522 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 1 Apr 2018 22:22:19 +0800
Subject: [PATCH 0663/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 43 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index 57712ec6..6ba7cfb4 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -11,3 +11,46 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 使用贝叶斯网络必须知道各个状态之间相关的概率。得到这些参数的过程叫做训练。和训练马尔可夫模型一样，训练贝叶斯网络要用一些已知的数据。比如在训练上面的网络，需要知道一些心血管疾病和吸烟、家族病史等有关的情况。相比马尔可夫链，贝叶斯网络的训练比较复杂，从理论上讲，它是一个 NP-complete问题，也就是说，现阶段没有可以在多项式时间内完成的算法。但是，对于某些应用，这个训练过程可以简化，并在计算上高效实现。
 
 贝叶斯理论是处理不确定性信息的重要工具。作为一种基于概率的不确定性推理方法，贝叶斯网络在处理不确定信息的智能化系统中已得到了重要的应用，已成功地用于医疗诊断、统计决策、专家系统、学习预测等领域。这些成功的应用，充分体现了贝叶斯网络技术是一种强有力的不确定性推理方法。
+
+#### 应用示例
+
+```python
+from bayesian.bbn import build_bbn
+
+def f_prize_door(prize_door):
+    return 0.33333333
+def f_guest_door(guest_door):
+    return 0.33333333
+def f_monty_door(prize_door, guest_door, monty_door):
+    if prize_door == guest_door:  # 参赛者猜对了
+        if prize_door == monty_door:
+            return 0     # Monty不会打开有车的那扇门，不可能发生
+        else:
+            return 0.5   # Monty会打开其它两扇门，二选一
+    elif prize_door == monty_door:
+        return 0         #  Monty不会打开有车的那扇门，不可能发生
+    elif guest_door == monty_door:
+        return 0         # 门已经由参赛者选定，不可能发生
+    else:
+        return 1    # Monty打开另一扇有羊的门
+
+if __name__ == '__main__':
+    g = build_bbn(
+        f_prize_door,
+        f_guest_door,
+        f_monty_door,
+        domains=dict(
+            prize_door=['A', 'B', 'C'],
+            guest_door=['A', 'B', 'C'],
+            monty_door=['A', 'B', 'C']))
+
+    g.q()
+    g.q(guest_door='A')
+g.q(guest_door='A', monty_door='B')
+
+作者：xieyan0811
+链接：https://www.jianshu.com/p/83288566f834
+來源：简书
+著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
+
+```

From f22ad7b3c4939df9abd0a6eca659736576c89382 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 1 Apr 2018 22:23:19 +0800
Subject: [PATCH 0664/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index 6ba7cfb4..cf8a77f3 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -48,9 +48,4 @@ if __name__ == '__main__':
     g.q(guest_door='A')
 g.q(guest_door='A', monty_door='B')
 
-作者：xieyan0811
-链接：https://www.jianshu.com/p/83288566f834
-來源：简书
-著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
-
 ```

From 9842ac7101411a83388e97c0245d374cbd51225b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 1 Apr 2018 22:23:39 +0800
Subject: [PATCH 0665/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index cf8a77f3..1673b0bc 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -14,6 +14,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用示例
 
+
 ```python
 from bayesian.bbn import build_bbn
 

From a1bcbaf92d8f714e5a87bf98bccabad57263a211 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 1 Apr 2018 22:26:13 +0800
Subject: [PATCH 0666/1406] change page

---
 assets/src/KBO/KBO.0.1.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 assets/src/KBO/KBO.0.1.md

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
new file mode 100644
index 00000000..1cb4e79e
--- /dev/null
+++ b/assets/src/KBO/KBO.0.1.md
@@ -0,0 +1,22 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 贝叶斯算法
+
+贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
+
+从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
+
+在贝叶斯网络中，每个节点代表一个有限状态数的离散随机变量，节点之间的单向箭头代表其间的因果关系。如果某个节点不具有父节点（即没有箭头指向它），那么这个节点就具有一个边缘概率表，其中记录了该节点取不同状态值的概率分布；反之，若某节点有父节点（即存在一条或多条有向箭头指向它），则它就拥有一个条件概率表。条件概率表中的每个元素对应该节点在其父节点处于某种状态组合下，其本身状态值的概率分布规律。
+
+贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
+
+贝叶斯网络（Bayesian networks or Bayesnets）这里的应用算法有：
+
+* 朴素贝叶斯(Naive Bayes)
+* 高斯朴素贝叶斯(Gaussian Naive Bayes)
+* 多项式朴素贝叶斯(Multinomial Naive Bayes)
+* AODE（Averaged One-Dependence Estimators）
+* 多元自适应回归样条（MARS）
+* 贝叶斯网络（Bayesian Belief Network）

From d84b5430c932b5c8470495573485f59ea588fa95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 1 Apr 2018 22:27:30 +0800
Subject: [PATCH 0667/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 213d2118..2fcc09a9 100644
--- a/README.md
+++ b/README.md
@@ -107,7 +107,7 @@
      * [多项式朴素贝叶斯(Multinomial Naive Bayes)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.4.md)
      * [平均单依赖估计量（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
      * [贝叶斯网络（Bayesian Belief Network）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.6.md)
- * [基于核的算法]()   
+ * [基于核的算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.1.md)   
      * [支持向量机（SVM）]()
      * [径向基函数（Radial Basis Function ，RBF)]()
      * [线性判别分析（Linear Discriminate Analysis ，LDA)]()

From 33a697fe6a7ae76e7bc5e12cab6f615a6f81d220 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 1 Apr 2018 22:28:09 +0800
Subject: [PATCH 0668/1406] Update KBO.0.1.md

---
 assets/src/KBO/KBO.0.1.md | 18 +-----------------
 1 file changed, 1 insertion(+), 17 deletions(-)

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
index 1cb4e79e..f4b45b92 100644
--- a/assets/src/KBO/KBO.0.1.md
+++ b/assets/src/KBO/KBO.0.1.md
@@ -2,21 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 贝叶斯算法
+#### 基于核的算法
 
-贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
-
-从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。
-
-在贝叶斯网络中，每个节点代表一个有限状态数的离散随机变量，节点之间的单向箭头代表其间的因果关系。如果某个节点不具有父节点（即没有箭头指向它），那么这个节点就具有一个边缘概率表，其中记录了该节点取不同状态值的概率分布；反之，若某节点有父节点（即存在一条或多条有向箭头指向它），则它就拥有一个条件概率表。条件概率表中的每个元素对应该节点在其父节点处于某种状态组合下，其本身状态值的概率分布规律。
-
-贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
-
-贝叶斯网络（Bayesian networks or Bayesnets）这里的应用算法有：
-
-* 朴素贝叶斯(Naive Bayes)
-* 高斯朴素贝叶斯(Gaussian Naive Bayes)
-* 多项式朴素贝叶斯(Multinomial Naive Bayes)
-* AODE（Averaged One-Dependence Estimators）
-* 多元自适应回归样条（MARS）
-* 贝叶斯网络（Bayesian Belief Network）

From 12bde8375478c4a3b97b3464d788dc24f30862c0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:15:19 +0800
Subject: [PATCH 0669/1406] Update KBO.0.1.md

---
 assets/src/KBO/KBO.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
index f4b45b92..859059ad 100644
--- a/assets/src/KBO/KBO.0.1.md
+++ b/assets/src/KBO/KBO.0.1.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 基于核的算法
 
+ 根据模式识别理论，低维空间线性不可分的模式通过非线性映射到高维特征空间则可能实现线性可分，但是如果直接采用这种技术在高维空间进行分类或回归，则存在确定非线性映射函数的形式和参数、特征空间维数等问题，而最大的障碍则是在高维特征空间运算时存在的“维数灾难”。采用核函数技术可以有效地解决这样问题.
+

From 560b80dd68d02851768ea635301e539ddc1acac7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:18:49 +0800
Subject: [PATCH 0670/1406] Update KBO.0.1.md

---
 assets/src/KBO/KBO.0.1.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
index 859059ad..09fc7510 100644
--- a/assets/src/KBO/KBO.0.1.md
+++ b/assets/src/KBO/KBO.0.1.md
@@ -6,3 +6,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
  根据模式识别理论，低维空间线性不可分的模式通过非线性映射到高维特征空间则可能实现线性可分，但是如果直接采用这种技术在高维空间进行分类或回归，则存在确定非线性映射函数的形式和参数、特征空间维数等问题，而最大的障碍则是在高维特征空间运算时存在的“维数灾难”。采用核函数技术可以有效地解决这样问题.
 
+核函数方法的特点:
+* 核函数的引入避免了“维数灾难”,大大减小了计算量。而输入空间的维数n对核函数矩阵无影响，因此，核函数方法可以有效处理高维输入。
+* 无需知道非线性变换函数的形式和参数。
+* 核函数的形式和参数的变化会隐式地改变从输入空间到特征空间的映射，进而对特征空间的性质产生影响，最终改变各种核函数方法的性能。
+* 核函数方法可以和不同的算法相结合，形成多种不同的基于核函数技术的方法，且这两部分的设计可以单独进行，并可以为不同的应用选择不同的核函数和算法。

From 98efe1d7a1a1bee85e664550ae3f350331f494af Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:24:52 +0800
Subject: [PATCH 0671/1406] Update KBO.0.1.md

---
 assets/src/KBO/KBO.0.1.md | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
index 09fc7510..86762e64 100644
--- a/assets/src/KBO/KBO.0.1.md
+++ b/assets/src/KBO/KBO.0.1.md
@@ -4,7 +4,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 基于核的算法
 
- 根据模式识别理论，低维空间线性不可分的模式通过非线性映射到高维特征空间则可能实现线性可分，但是如果直接采用这种技术在高维空间进行分类或回归，则存在确定非线性映射函数的形式和参数、特征空间维数等问题，而最大的障碍则是在高维特征空间运算时存在的“维数灾难”。采用核函数技术可以有效地解决这样问题.
+ 根据模式识别理论，低维空间线性不可分的模式通过非线性映射到高维特征空间则可能实现线性可分，但是如果直接采用这种技术在高维空间进行分类或回归，则存在确定非线性映射函数的形式和参数、特征空间维数等问题，而最大的障碍则是在高维特征空间运算时存在的“维数灾难”。采用核函数技术可以有效地解决这样问题。
+ 
+ 
+基于核里的应用算法有：
+* 支持向量机（SVM）
+* 径向基函数（Radial Basis Function ，RBF)
+* 线性判别分析（Linear Discriminate Analysis ，LDA)
 
 核函数方法的特点:
 * 核函数的引入避免了“维数灾难”,大大减小了计算量。而输入空间的维数n对核函数矩阵无影响，因此，核函数方法可以有效处理高维输入。

From 32e9d37578694821ca073bba296148cba748b662 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:27:45 +0800
Subject: [PATCH 0672/1406] Update KBO.0.1.md

---
 assets/src/KBO/KBO.0.1.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/KBO/KBO.0.1.md b/assets/src/KBO/KBO.0.1.md
index 86762e64..dcad0455 100644
--- a/assets/src/KBO/KBO.0.1.md
+++ b/assets/src/KBO/KBO.0.1.md
@@ -4,6 +4,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 基于核的算法
 
+支持向量机通过某非线性变换 φ( x) ，将输入空间映射到高维特征空间。特征空间的维数可能非常高。如果支持向量机的求解只用到内积运算，而在低维输入空间又存在某个函数 K(x, x′) ，它恰好等于在高维空间中这个内积，即K( x, x′) =<φ( x) ⋅φ( x′) > 。那么支持向量机就不用计算复杂的非线性变换，而由这个函数 K(x, x′) 直接得到非线性变换的内积，使大大简化了计算。这样的函数 K(x, x′) 称为核函数。
+
+早在1964年Aizermann等在势函数方法的研究中就将该技术引入到机器学习领域，但是直到1992年Vapnik等利用该技术成功地将线性SVMs推广到非线性SVMs时其潜力才得以充分挖掘。而核函数的理论则更为古老，Mercer定理可以追溯到1909年，再生核希尔伯特空间(ReproducingKernel Hilbert Space, RKHS)研究是在20世纪40年代开始的。
+
+核函数包括线性核函数、多项式核函数、高斯核函数等，其中高斯核函数最常用，可以将数据映射到无穷维，也叫做径向基函数（Radial Basis Function 简称 RBF），是某种沿径向对称的标量函数。通常定义为空间中任一点x到某一中心xc之间欧氏距离的单调函数 ，可记作 k（||x-xc||）， 其作用往往是局部的，即当x远离xc时函数取值很小。
+
  根据模式识别理论，低维空间线性不可分的模式通过非线性映射到高维特征空间则可能实现线性可分，但是如果直接采用这种技术在高维空间进行分类或回归，则存在确定非线性映射函数的形式和参数、特征空间维数等问题，而最大的障碍则是在高维特征空间运算时存在的“维数灾难”。采用核函数技术可以有效地解决这样问题。
  
  

From 6ee20117e5a0e0875495b19a97577127867f2c19 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:28:01 +0800
Subject: [PATCH 0673/1406] Update KBO.0.1.md


From be74112b10b47a3137cbc4292a524eed3333267d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 2 Apr 2018 23:29:41 +0800
Subject: [PATCH 0674/1406] change page

---
 README.md                 | 2 +-
 assets/src/KBO/KBO.0.2.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/KBO/KBO.0.2.md

diff --git a/README.md b/README.md
index 2fcc09a9..1d6a194d 100644
--- a/README.md
+++ b/README.md
@@ -108,7 +108,7 @@
      * [平均单依赖估计量（Averaged One-Dependence Estimators）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.5.md)
      * [贝叶斯网络（Bayesian Belief Network）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.6.md)
  * [基于核的算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.1.md)   
-     * [支持向量机（SVM）]()
+     * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.2.md)
      * [径向基函数（Radial Basis Function ，RBF)]()
      * [线性判别分析（Linear Discriminate Analysis ，LDA)]()
  * [聚类算法]()
diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
new file mode 100644
index 00000000..0450f61f
--- /dev/null
+++ b/assets/src/KBO/KBO.0.2.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 支持向量机（SVM）
\ No newline at end of file

From 1a5302faa5b78ce8cae41bed5e3527cbfa703ea9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:33:27 +0800
Subject: [PATCH 0675/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 0450f61f..b57adf7b 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -2,4 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 支持向量机（SVM）
\ No newline at end of file
+#### 支持向量机（SVM）
+支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik等于1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
+在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。

From 1bc9fa1cd8614e85eed9c59bb5b375bb8cd9e870 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Apr 2018 23:34:52 +0800
Subject: [PATCH 0676/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index b57adf7b..a5d34390 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -4,4 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 支持向量机（SVM）
 支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik等于1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
+
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
+支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。
+
+在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。给定一组训练样本，每个标记为属于两类，一个SVM训练算法建立了一个模型，分配新的实例为一类或其他类，使其成为非概率二元线性分类。一个SVM模型的例子，如在空间中的点，映射，使得所述不同的类别的例子是由一个明显的差距是尽可能宽划分的表示。新的实施例则映射到相同的空间中，并预测基于它们落在所述间隙侧上属于一个类别。
+除了进行线性分类，支持向量机可以使用所谓的核技巧，它们的输入隐含映射成高维特征空间中有效地进行非线性分类。

From e14e289f758b4791f229a18b843eaae577e99bd6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Apr 2018 09:02:00 +0800
Subject: [PATCH 0677/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index a5d34390..f29f6127 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -4,7 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 支持向量机（SVM）
 支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik等于1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
-
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
 支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。
 

From edbbdb46f9380fb67e7325de485d612e9191f853 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 4 Apr 2018 00:11:21 +0000
Subject: [PATCH 0678/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index f29f6127..45a40c73 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -3,7 +3,9 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 支持向量机（SVM）
+
 支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik等于1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
+
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
 支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。
 

From eefb9cf5a4299adca99bf8b06244b13c5823f000 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 4 Apr 2018 10:27:30 +0800
Subject: [PATCH 0679/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 45a40c73..fdf7b46d 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -11,3 +11,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。给定一组训练样本，每个标记为属于两类，一个SVM训练算法建立了一个模型，分配新的实例为一类或其他类，使其成为非概率二元线性分类。一个SVM模型的例子，如在空间中的点，映射，使得所述不同的类别的例子是由一个明显的差距是尽可能宽划分的表示。新的实施例则映射到相同的空间中，并预测基于它们落在所述间隙侧上属于一个类别。
 除了进行线性分类，支持向量机可以使用所谓的核技巧，它们的输入隐含映射成高维特征空间中有效地进行非线性分类。
+
+支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。

From 9ab654d16fdfc6bf11430bb385b7150732eb1405 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 6 Apr 2018 23:59:17 +0000
Subject: [PATCH 0680/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index fdf7b46d..f67e7b4e 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -9,6 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
 支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。
 
+
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。给定一组训练样本，每个标记为属于两类，一个SVM训练算法建立了一个模型，分配新的实例为一类或其他类，使其成为非概率二元线性分类。一个SVM模型的例子，如在空间中的点，映射，使得所述不同的类别的例子是由一个明显的差距是尽可能宽划分的表示。新的实施例则映射到相同的空间中，并预测基于它们落在所述间隙侧上属于一个类别。
 除了进行线性分类，支持向量机可以使用所谓的核技巧，它们的输入隐含映射成高维特征空间中有效地进行非线性分类。
 

From eeeeece7ba57b7af6f43186e9b2226c60d044b8f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 7 Apr 2018 00:00:21 +0000
Subject: [PATCH 0681/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index f67e7b4e..2403cc85 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -13,4 +13,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。给定一组训练样本，每个标记为属于两类，一个SVM训练算法建立了一个模型，分配新的实例为一类或其他类，使其成为非概率二元线性分类。一个SVM模型的例子，如在空间中的点，映射，使得所述不同的类别的例子是由一个明显的差距是尽可能宽划分的表示。新的实施例则映射到相同的空间中，并预测基于它们落在所述间隙侧上属于一个类别。
 除了进行线性分类，支持向量机可以使用所谓的核技巧，它们的输入隐含映射成高维特征空间中有效地进行非线性分类。
 
+
+
 支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。

From 7a62aa3d81b9ec66934b70fcc9b2ffa400d1de46 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 7 Apr 2018 00:00:37 +0000
Subject: [PATCH 0682/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 2403cc85..b6a64f2b 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -14,5 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 除了进行线性分类，支持向量机可以使用所谓的核技巧，它们的输入隐含映射成高维特征空间中有效地进行非线性分类。
 
 
-
 支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。

From f87977e732c168c74fffc6acb544cbde6724c591 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 7 Apr 2018 00:01:46 +0000
Subject: [PATCH 0683/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index b6a64f2b..5581e6ba 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 支持向量机（SVM）
 
-支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik等于1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
+支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik在1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
 
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
 支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。

From d182943994f426f307e14896cfb7d7f002018005 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 8 Apr 2018 08:52:58 +0800
Subject: [PATCH 0684/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 5581e6ba..b72f0d2f 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 支持向量机（SVM）
 
-支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik在1995年首先提出的，它在解决小样本、非线性及高维模式识别中表现出许多特有的优势，并能够推广应用到函数拟合等其他机器学习问题中。
+支持向量机(Support Vector Machine，SVM)是Corinna Cortes和Vapnik在1995年首先提出的，是一种监督式学习的方法，可广泛地应用于统计分类以及回归分析。支持向量机属于一般化线性分类器，这族分类器的特点是他们能够同时最小化经验误差与最大化几何边缘区，因此支持向量机也被称为最大边缘区分类器。
 
 在机器学习中，支持向量机（SVM，还支持矢量网络）是与相关的学习算法有关的监督学习模型，可以分析数据，识别模式，用于分类和回归分析。
 支持向量机方法是建立在统计学习理论的VC维理论和结构风险最小原理基础上的，根据有限的样本信息在模型的复杂性（即对特定训练样本的学习精度）和学习能力（即无错误地识别任意样本的能力）之间寻求最佳折中，以求获得最好的推广能力 。

From 3c21741e22b190e67128de2119a8ede0709bf2f6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 8 Apr 2018 08:57:05 +0800
Subject: [PATCH 0685/1406] change KBO

---
 assets/images/219.jpg     | Bin 0 -> 36179 bytes
 assets/src/KBO/KBO.0.2.md |   3 +++
 2 files changed, 3 insertions(+)
 create mode 100644 assets/images/219.jpg

diff --git a/assets/images/219.jpg b/assets/images/219.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..ca6e0116e04d41212d0ba8ae2e9a36ae30079bc1
GIT binary patch
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HcmV?d00001

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index b72f0d2f..31cd5019 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -15,3 +15,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。
+<p align="center">
+<img width="300" align="center" src="../../images/219.jpg" />
+</p>

From 4cec98dc42a3b4a442597b735c7c993b05bf00fd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 8 Apr 2018 08:58:51 +0800
Subject: [PATCH 0686/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 31cd5019..bc096ead 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -16,5 +16,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。
 <p align="center">
-<img width="300" align="center" src="../../images/219.jpg" />
+<img width="500" align="center" src="../../images/219.jpg" />
 </p>

From 2b485e998efdb32423234a06e72055a46ac76b2c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 08:48:06 +0800
Subject: [PATCH 0687/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index bc096ead..64d0c691 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -16,5 +16,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 支持向量机将向量映射到一个更高维的空间里，在这个空间里建立有一个最大间隔超平面。在分开数据的超平面的两边建有两个互相平行的超平面。建立方向合适的分隔超平面使两个与之平行的超平面间的距离最大化。其假定为，平行超平面间的距离或差距越大，分类器的总误差越小。
 <p align="center">
-<img width="500" align="center" src="../../images/219.jpg" />
+<img width="530" align="center" src="../../images/219.jpg" />
 </p>

From c4cfcf55386858aaf76bdcc4fed963f3a119b3b8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:08:20 +0800
Subject: [PATCH 0688/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 44 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 64d0c691..f0ed5c59 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -18,3 +18,47 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="530" align="center" src="../../images/219.jpg" />
 </p>
+
+
+#### 应用示例
+```python
+# Data driven farmer goes to the Rodeoimport numpy as npimport pylab as plfrom sklearn import svmfrom sklearn import linear_modelfrom sklearn import treeimport pandas as pddef
+
+plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
+    x_min, x_max = df.x.min() - .5, df.x.max() + .5
+    y_min, y_max = df.y.min() - .5, df.y.max() + .5
+
+    # step between points. i.e. [0, 0.02, 0.04, ...]
+    step = .02
+    # to plot the boundary, we're going to create a matrix of every possible point
+    # then label each point as a wolf or cow using our classifier
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, step), np.arange(y_min, y_max, step))
+    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
+    # this gets our predictions back into a matrix
+    Z = Z.reshape(xx.shape)
+
+    # create a subplot (we're going to have more than 1 plot on a given image)
+    pl.subplot(2, 2, plt_nmbr)
+    # plot the boundaries
+    pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
+
+    # plot the wolves and cows
+    for animal in df.animal.unique():
+        pl.scatter(df[df.animal==animal].x,
+                   df[df.animal==animal].y,
+                   marker=animal,
+                   label="cows" if animal=="x" else "wolves",
+                   color='black')
+    pl.title(clf_name)
+    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]animals = []for y, row in enumerate(data):
+    for x, item in enumerate(row):
+        # x's are cows, o's are wolves
+        if item in ['o', 'x']:
+            animals.append([x, y, item])df = pd.DataFrame(animals, columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)# train using the x and y position coordiantestrain_cols = ["x", "y"]clfs = {
+    "SVM": svm.SVC(),
+    "Logistic" : linear_model.LogisticRegression(),
+    "Decision Tree": tree.DecisionTreeClassifier(),}plt_nmbr = 1for clf_name, clf in clfs.iteritems():
+    clf.fit(df[train_cols], df.animal_type)
+    plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
+    plt_nmbr += 1pl.show()
+```

From ecf18745e870c16f5d8bec9aee5f75b79e8c81e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:09:30 +0800
Subject: [PATCH 0689/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index f0ed5c59..3e93793b 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -55,9 +55,12 @@ plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
         # x's are cows, o's are wolves
         if item in ['o', 'x']:
             animals.append([x, y, item])df = pd.DataFrame(animals, columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)# train using the x and y position coordiantestrain_cols = ["x", "y"]clfs = {
+    
     "SVM": svm.SVC(),
     "Logistic" : linear_model.LogisticRegression(),
-    "Decision Tree": tree.DecisionTreeClassifier(),}plt_nmbr = 1for clf_name, clf in clfs.iteritems():
+    "Decision Tree": tree.DecisionTreeClassifier(),}
+    
+    plt_nmbr = 1for clf_name, clf in clfs.iteritems():
     clf.fit(df[train_cols], df.animal_type)
     plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
     plt_nmbr += 1pl.show()

From a0543e5ed8c98842526a5938874c0aaf7a0a626d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:09:56 +0800
Subject: [PATCH 0690/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 3e93793b..1cd8cfa5 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -60,8 +60,8 @@ plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
     "Logistic" : linear_model.LogisticRegression(),
     "Decision Tree": tree.DecisionTreeClassifier(),}
     
-    plt_nmbr = 1for clf_name, clf in clfs.iteritems():
+    plt_nmbr = for clf_name, clf in clfs.iteritems():
     clf.fit(df[train_cols], df.animal_type)
     plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
-    plt_nmbr += 1pl.show()
+    plt_nmbr += pl.show()
 ```

From c86c252505440968d6493d3f06a24b8dcf9868c6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:12:46 +0800
Subject: [PATCH 0691/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 90 +++++++++++++++++++++------------------
 1 file changed, 49 insertions(+), 41 deletions(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 1cd8cfa5..5d89fdcf 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -22,46 +22,54 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用示例
 ```python
-# Data driven farmer goes to the Rodeoimport numpy as npimport pylab as plfrom sklearn import svmfrom sklearn import linear_modelfrom sklearn import treeimport pandas as pddef
-
-plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
-    x_min, x_max = df.x.min() - .5, df.x.max() + .5
-    y_min, y_max = df.y.min() - .5, df.y.max() + .5
-
-    # step between points. i.e. [0, 0.02, 0.04, ...]
-    step = .02
-    # to plot the boundary, we're going to create a matrix of every possible point
-    # then label each point as a wolf or cow using our classifier
-    xx, yy = np.meshgrid(np.arange(x_min, x_max, step), np.arange(y_min, y_max, step))
-    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
-    # this gets our predictions back into a matrix
-    Z = Z.reshape(xx.shape)
-
-    # create a subplot (we're going to have more than 1 plot on a given image)
-    pl.subplot(2, 2, plt_nmbr)
-    # plot the boundaries
-    pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
-
-    # plot the wolves and cows
-    for animal in df.animal.unique():
-        pl.scatter(df[df.animal==animal].x,
-                   df[df.animal==animal].y,
-                   marker=animal,
-                   label="cows" if animal=="x" else "wolves",
-                   color='black')
-    pl.title(clf_name)
-    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]animals = []for y, row in enumerate(data):
-    for x, item in enumerate(row):
-        # x's are cows, o's are wolves
-        if item in ['o', 'x']:
-            animals.append([x, y, item])df = pd.DataFrame(animals, columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)# train using the x and y position coordiantestrain_cols = ["x", "y"]clfs = {
-    
-    "SVM": svm.SVC(),
+import numpy as npimport pylab as plimport pandas as pdfrom sklearn 
+import svmfrom sklearn 
+import linear_modelfrom sklearn 
+import treefrom sklearn.metrics import confusion_matrix
+
+x_min, 
+x_max = 0, 
+15y_min, 
+y_max = 0, 
+10step = .1# to plot the boundary, we're going to create a matrix of every possible point# then label each point as a wolf or cow using our classifierxx, yy = np.meshgrid(np.arange(x_min, x_max, step),np.arange(y_min, y_max, step))df = pd.DataFrame(data={'x': xx.ravel(), 'y': yy.ravel()})df['color_gauge'] = (df.x-7.5)**2 + (df.y-5)**2df['color'] = df.color_gauge.apply(lambda x: "red" if x <= 15 else "green")df['color_as_int'] = df.color.apply(lambda x: 0 if x=="red" else 1)print "Points on flag:"print df.groupby('color').size()printfigure = 1# plot a figure for the entire datasetfor color in df.color.unique():
+    idx = df.color==color
+    pl.subplot(2, 2, figure)
+    pl.scatter(df[idx].x, df[idx].y, color=color)
+    pl.title('Actual')train_idx = df.x < 10train = df[train_idx]test = df[-train_idx]print "Training Set Size: %d" % len(train)print "Test Set Size: %d" % len(test)# train using the x and y position coordiantescols = ["x", "y"]clfs = {
+    "SVM": svm.SVC(degree=0.5),
     "Logistic" : linear_model.LogisticRegression(),
-    "Decision Tree": tree.DecisionTreeClassifier(),}
-    
-    plt_nmbr = for clf_name, clf in clfs.iteritems():
-    clf.fit(df[train_cols], df.animal_type)
-    plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
-    plt_nmbr += pl.show()
+    "Decision Tree": tree.DecisionTreeClassifier()}# racehorse different classifiers and plot the resultsfor clf_name, clf in clfs.iteritems():
+    figure += 1
+
+    # train the classifier
+    clf.fit(train[cols], train.color_as_int)
+
+    # get the predicted values from the test set
+    test['predicted_color_as_int'] = clf.predict(test[cols])
+    test['pred_color'] = test.predicted_color_as_int.apply(lambda x: "red" if x==0 else "green")
+
+    # create a new subplot on the plot
+    pl.subplot(2, 2, figure)
+    # plot each predicted color
+    for color in test.pred_color.unique():
+        # plot only rows where pred_color is equal to color
+        idx = test.pred_color==color
+        pl.scatter(test[idx].x, test[idx].y, color=color)
+
+    # plot the training set as well
+    for color in train.color.unique():
+        idx = train.color==color
+        pl.scatter(train[idx].x, train[idx].y, color=color)
+
+    # add a dotted line to show the boundary between the training and test set
+    # (everything to the right of the line is in the test set)
+    #this plots a vertical line
+    train_line_y = np.linspace(y_min, y_max) #evenly spaced array from 0 to 10
+    train_line_x = np.repeat(10, len(train_line_y)) #repeat 10 (threshold for traininset) n times
+    # add a black, dotted line to the subplot
+    pl.plot(train_line_x, train_line_y, 'k--', color="black")
+
+    pl.title(clf_name)
+
+    print "Confusion Matrix for %s:" % clf_name    print confusion_matrix(test.color, test.pred_color)pl.show()
 ```

From 5acd39d4b4520576a32785ca611908e594ec8877 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:14:35 +0800
Subject: [PATCH 0692/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 88 ++++++++++++++++++---------------------
 1 file changed, 41 insertions(+), 47 deletions(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 5d89fdcf..1a868f15 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -22,54 +22,48 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用示例
 ```python
-import numpy as npimport pylab as plimport pandas as pdfrom sklearn 
+# Data driven farmer goes to the Rodeo
+import numpy as npimport pylab as plfrom sklearn 
 import svmfrom sklearn 
 import linear_modelfrom sklearn 
-import treefrom sklearn.metrics import confusion_matrix
-
-x_min, 
-x_max = 0, 
-15y_min, 
-y_max = 0, 
-10step = .1# to plot the boundary, we're going to create a matrix of every possible point# then label each point as a wolf or cow using our classifierxx, yy = np.meshgrid(np.arange(x_min, x_max, step),np.arange(y_min, y_max, step))df = pd.DataFrame(data={'x': xx.ravel(), 'y': yy.ravel()})df['color_gauge'] = (df.x-7.5)**2 + (df.y-5)**2df['color'] = df.color_gauge.apply(lambda x: "red" if x <= 15 else "green")df['color_as_int'] = df.color.apply(lambda x: 0 if x=="red" else 1)print "Points on flag:"print df.groupby('color').size()printfigure = 1# plot a figure for the entire datasetfor color in df.color.unique():
-    idx = df.color==color
-    pl.subplot(2, 2, figure)
-    pl.scatter(df[idx].x, df[idx].y, color=color)
-    pl.title('Actual')train_idx = df.x < 10train = df[train_idx]test = df[-train_idx]print "Training Set Size: %d" % len(train)print "Test Set Size: %d" % len(test)# train using the x and y position coordiantescols = ["x", "y"]clfs = {
-    "SVM": svm.SVC(degree=0.5),
-    "Logistic" : linear_model.LogisticRegression(),
-    "Decision Tree": tree.DecisionTreeClassifier()}# racehorse different classifiers and plot the resultsfor clf_name, clf in clfs.iteritems():
-    figure += 1
-
-    # train the classifier
-    clf.fit(train[cols], train.color_as_int)
-
-    # get the predicted values from the test set
-    test['predicted_color_as_int'] = clf.predict(test[cols])
-    test['pred_color'] = test.predicted_color_as_int.apply(lambda x: "red" if x==0 else "green")
-
-    # create a new subplot on the plot
-    pl.subplot(2, 2, figure)
-    # plot each predicted color
-    for color in test.pred_color.unique():
-        # plot only rows where pred_color is equal to color
-        idx = test.pred_color==color
-        pl.scatter(test[idx].x, test[idx].y, color=color)
-
-    # plot the training set as well
-    for color in train.color.unique():
-        idx = train.color==color
-        pl.scatter(train[idx].x, train[idx].y, color=color)
-
-    # add a dotted line to show the boundary between the training and test set
-    # (everything to the right of the line is in the test set)
-    #this plots a vertical line
-    train_line_y = np.linspace(y_min, y_max) #evenly spaced array from 0 to 10
-    train_line_x = np.repeat(10, len(train_line_y)) #repeat 10 (threshold for traininset) n times
-    # add a black, dotted line to the subplot
-    pl.plot(train_line_x, train_line_y, 'k--', color="black")
-
+import treeimport pandas as pddef 
+
+plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
+    x_min, x_max = df.x.min() - .5, df.x.max() + .5
+    y_min, y_max = df.y.min() - .5, df.y.max() + .5
+
+    # step between points. i.e. [0, 0.02, 0.04, ...]
+    step = .02
+    # to plot the boundary, we're going to create a matrix of every possible point
+    # then label each point as a wolf or cow using our classifier
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, step), np.arange(y_min, y_max, step))
+    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
+    # this gets our predictions back into a matrix
+    Z = Z.reshape(xx.shape)
+
+    # create a subplot (we're going to have more than 1 plot on a given image)
+    pl.subplot(2, 2, plt_nmbr)
+    # plot the boundaries
+    pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
+
+    # plot the wolves and cows
+    for animal in df.animal.unique():
+        pl.scatter(df[df.animal==animal].x,
+                   df[df.animal==animal].y,
+                   marker=animal,
+                   label="cows" if animal=="x" else "wolves",
+                   color='black')
     pl.title(clf_name)
-
-    print "Confusion Matrix for %s:" % clf_name    print confusion_matrix(test.color, test.pred_color)pl.show()
+    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]animals = []for y, row in enumerate(data):
+    for x, item in enumerate(row):
+        # x's are cows, o's are wolves
+        if item in ['o', 'x']:
+            animals.append([x, y, item])df = pd.DataFrame(animals, columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)# train using the x and y position coordiantestrain_cols = ["x", "y"]clfs = {
+    "SVM": svm.SVC(),
+    "Logistic" : linear_model.LogisticRegression(),
+    "Decision Tree": tree.DecisionTreeClassifier(),}
+    plt_nmbr = for clf_name, clf in clfs.iteritems():
+    clf.fit(df[train_cols], df.animal_type)
+    plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
+    plt_nmbr += pl.show()
 ```

From 3ff12dc0ef2a7b0456fef26c6a0b721b03cb00bc Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 9 Apr 2018 21:16:59 +0800
Subject: [PATCH 0693/1406] change page of kbo

---
 README.md                 | 2 +-
 assets/src/KBO/KBO.0.3.md | 6 ++++++
 2 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/KBO/KBO.0.3.md

diff --git a/README.md b/README.md
index 1d6a194d..0a77a7cc 100644
--- a/README.md
+++ b/README.md
@@ -109,7 +109,7 @@
      * [贝叶斯网络（Bayesian Belief Network）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/BNS/BNS.0.6.md)
  * [基于核的算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.1.md)   
      * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.2.md)
-     * [径向基函数（Radial Basis Function ，RBF)]()
+     * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
      * [线性判别分析（Linear Discriminate Analysis ，LDA)]()
  * [聚类算法]()
      * [K-均值]()
diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
new file mode 100644
index 00000000..4489a00b
--- /dev/null
+++ b/assets/src/KBO/KBO.0.3.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 径向基函数（Radial Basis Function ，RBF)
+

From ab4b9b778e5fb0e5e2e9cd6f9de3d2a8956697c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:19:03 +0800
Subject: [PATCH 0694/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 1a868f15..39c677dd 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -67,3 +67,4 @@ plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
     plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
     plt_nmbr += pl.show()
 ```
+相比于神经网络这样更先进的算法，支持向量机有两大主要优势：更高的速度、用更少的样本（千以内）取得更好的表现。这使得该算法非常适合文本分类问题。

From 4ae703ec22dade5fe797ef7671706f6f1ae300f2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:20:41 +0800
Subject: [PATCH 0695/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 24 +++++++++++++++---------
 1 file changed, 15 insertions(+), 9 deletions(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 39c677dd..a68d7290 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -54,17 +54,23 @@ plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
                    label="cows" if animal=="x" else "wolves",
                    color='black')
     pl.title(clf_name)
-    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]animals = []for y, row in enumerate(data):
+    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]
+    animals = []for y, row in enumerate(data):
     for x, item in enumerate(row):
         # x's are cows, o's are wolves
         if item in ['o', 'x']:
-            animals.append([x, y, item])df = pd.DataFrame(animals, columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)# train using the x and y position coordiantestrain_cols = ["x", "y"]clfs = {
-    "SVM": svm.SVC(),
-    "Logistic" : linear_model.LogisticRegression(),
-    "Decision Tree": tree.DecisionTreeClassifier(),}
-    plt_nmbr = for clf_name, clf in clfs.iteritems():
-    clf.fit(df[train_cols], df.animal_type)
-    plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
-    plt_nmbr += pl.show()
+            animals.append([x, y, item])df = pd.DataFrame(animals,
+            columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)
+            # train using the x and y position 
+            coordiantestrain_cols = ["x", "y"]
+            clfs = {
+            "SVM": svm.SVC(),
+            "Logistic" : linear_model.LogisticRegression(),
+            "Decision Tree": tree.DecisionTreeClassifier(),}
+            plt_nmbr = for clf_name, clf in clfs.iteritems():
+            clf.fit(df[train_cols], df.animal_type)
+            plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
+            plt_nmbr += pl.show()
+            }
 ```
 相比于神经网络这样更先进的算法，支持向量机有两大主要优势：更高的速度、用更少的样本（千以内）取得更好的表现。这使得该算法非常适合文本分类问题。

From 525e9e294e29e5a20688309ceec2b540f63687c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:21:12 +0800
Subject: [PATCH 0696/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index a68d7290..03c9315a 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -54,7 +54,8 @@ plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
                    label="cows" if animal=="x" else "wolves",
                    color='black')
     pl.title(clf_name)
-    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()data = [row.split('\t') for row in data.strip().split('\n')]
+    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()
+    data = [row.split('\t') for row in data.strip().split('\n')]
     animals = []for y, row in enumerate(data):
     for x, item in enumerate(row):
         # x's are cows, o's are wolves

From af3b2dd67b1977a9cffd382bdedc96e64fa8c2be Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:34:04 +0800
Subject: [PATCH 0697/1406] Update KBO.0.2.md

---
 assets/src/KBO/KBO.0.2.md | 349 ++++++++++++++++++++++++++++++++------
 1 file changed, 298 insertions(+), 51 deletions(-)

diff --git a/assets/src/KBO/KBO.0.2.md b/assets/src/KBO/KBO.0.2.md
index 03c9315a..577aa70f 100644
--- a/assets/src/KBO/KBO.0.2.md
+++ b/assets/src/KBO/KBO.0.2.md
@@ -22,56 +22,303 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 应用示例
 ```python
-# Data driven farmer goes to the Rodeo
-import numpy as npimport pylab as plfrom sklearn 
-import svmfrom sklearn 
-import linear_modelfrom sklearn 
-import treeimport pandas as pddef 
-
-plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr):
-    x_min, x_max = df.x.min() - .5, df.x.max() + .5
-    y_min, y_max = df.y.min() - .5, df.y.max() + .5
-
-    # step between points. i.e. [0, 0.02, 0.04, ...]
-    step = .02
-    # to plot the boundary, we're going to create a matrix of every possible point
-    # then label each point as a wolf or cow using our classifier
-    xx, yy = np.meshgrid(np.arange(x_min, x_max, step), np.arange(y_min, y_max, step))
-    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
-    # this gets our predictions back into a matrix
-    Z = Z.reshape(xx.shape)
-
-    # create a subplot (we're going to have more than 1 plot on a given image)
-    pl.subplot(2, 2, plt_nmbr)
-    # plot the boundaries
-    pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
-
-    # plot the wolves and cows
-    for animal in df.animal.unique():
-        pl.scatter(df[df.animal==animal].x,
-                   df[df.animal==animal].y,
-                   marker=animal,
-                   label="cows" if animal=="x" else "wolves",
-                   color='black')
-    pl.title(clf_name)
-    pl.legend(loc="best")data = open("cows_and_wolves.txt").read()
-    data = [row.split('\t') for row in data.strip().split('\n')]
-    animals = []for y, row in enumerate(data):
-    for x, item in enumerate(row):
-        # x's are cows, o's are wolves
-        if item in ['o', 'x']:
-            animals.append([x, y, item])df = pd.DataFrame(animals,
-            columns=["x", "y", "animal"])df['animal_type'] = df.animal.apply(lambda x: 0 if x=="x" else 1)
-            # train using the x and y position 
-            coordiantestrain_cols = ["x", "y"]
-            clfs = {
-            "SVM": svm.SVC(),
-            "Logistic" : linear_model.LogisticRegression(),
-            "Decision Tree": tree.DecisionTreeClassifier(),}
-            plt_nmbr = for clf_name, clf in clfs.iteritems():
-            clf.fit(df[train_cols], df.animal_type)
-            plot_results_with_hyperplane(clf, clf_name, df, plt_nmbr)
-            plt_nmbr += pl.show()
-            }
+# coding: utf8
+# svm/smo.py
+
+import numpy as np
+
+from sklearn.metrics.pairwise import rbf_kernel
+
+"""
+svm模型
+"""
+
+def linearKernel():
+    """线性核函数
+    """
+    def calc(X, A):
+        return X * A.T
+    return calc
+
+def rbfKernel(delta):
+    """rbf核函数
+    """
+    gamma = 1.0 / (2 * delta**2)
+
+    def calc(X, A):
+        return np.mat(rbf_kernel(X, A, gamma=gamma))
+    return calc
+
+def getSmo(X, y, C, tol, maxIter, kernel=linearKernel()):
+    """SMO
+
+    Args:
+        X 训练样本
+        y 标签集
+        C 正规化参数
+        tol 容忍值
+        maxIter 最大迭代次数
+        K 所用核函数
+
+    Returns:
+        trainSimple 简化版训练算法
+        train 完整版训练算法
+        predict 预测函数
+    """
+    # 存放核函数的转化结果
+    K = kernel(X, X)
+    # Cache存放预测误差，用以加快计算速度
+    ECache = np.zeros((m,2))
+
+    def predict(X, alphas, b, supportVectorsIndex, supportVectors):
+        """计算权值向量
+
+        Args:
+            X 预测矩阵
+            alphas alphas
+            b b
+            supportVectorsIndex 支持向量坐标集
+            supportVectors 支持向量
+        Returns:
+            predicts 预测结果
+        """
+        Ks = kernel(supportVectors, X)
+        predicts = (np.multiply(alphas[supportVectorsIndex], y[
+            supportVectorsIndex]).T * Ks + b).T
+        predicts = np.sign(predicts)
+        return predicts
+
+    def w(alphas, b, supportVectorsIndex, supportVectors):
+        """计算权值
+
+        Args:
+            alphas alphas
+            b b
+            supportVectorsIndex 支持向量坐标
+            supportVectors 支持向量
+        Returns:
+            w 权值向量
+        """
+        return (np.multiply(alphas[supportVectorsIndex], y[
+            supportVectorsIndex]).T * supportVectors).T
+
+    def E(i, alphas, b):
+        """计算预测误差
+
+        Args:
+            i i
+            alphas alphas
+            b b
+        Returns:
+            E_i 第i个样本的预测误差
+        """
+        FXi = float(np.multiply(alphas, y).T * K[:, i]) + b
+        E = FXi - float(y[i])
+        return E
+
+    def updateE(i, alphas, b):
+        ECache[i] = [1, E(i, alphas, b)]
+
+    def selectJRand(i):
+        """
+        """
+        j = i
+        while j == i:
+            j = int(np.random.uniform(0, m))
+        return j
+
+    def selectJ(i, Ei, alphas, b):
+        """选择权值 {% math %}\alpha^{(i)}{% endmath %}
+        """
+        maxJ = 0; maxDist=0; Ej = 0
+        ECache[i] = [1, Ei]
+        validCaches = np.nonzero(ECache[:, 0])[0]
+        if len(validCaches) > 1:
+            for k in validCaches:
+                if k==i: continue
+                Ek = E(k, alphas, b)
+                dist = np.abs(abs(Ei-Ek))
+                if maxDist < dist:
+                    Ej = Ek
+                    maxJ = k
+                    maxDist = dist
+            return maxJ, Ej
+        else:
+            ### 随机选择
+            j = selectJRand(i)
+            Ej = E(j, alphas, b)
+            return j, Ej
+
+    def select(i, alphas, b):
+        """alpha对选择
+        """
+        Ei = E(i, alphas, b)
+        # 选择违背KKT条件的，作为alpha2
+        Ri = y[i] * Ei
+        if (Ri < -tol and alphas[i] < C) or \
+                (Ri > tol and alphas[i] > 0):
+            # 选择第二个参数
+            j = selectJRand(i)
+            Ej = E(j, alphas, b)
+            # j, Ej = selectJ(i, Ei, alphas, b)
+            # get bounds
+            if y[i] != y[j]:
+                L = max(0, alphas[j] - alphas[i])
+                H = min(C, C + alphas[j] - alphas[i])
+            else:
+                L = max(0, alphas[j] + alphas[i] - C)
+                H = min(C, alphas[j] + alphas[i])
+            if L == H:
+                return 0, alphas, b
+            Kii = K[i, i]
+            Kjj = K[j, j]
+            Kij = K[i, j]
+            eta = 2.0 * Kij - Kii - Kjj
+            if eta >= 0:
+                return 0, alphas, b
+            iOld = alphas[i].copy()
+            jOld = alphas[j].copy()
+            alphas[j] = jOld - y[j] * (Ei - Ej) / eta
+            if alphas[j] > H:
+                alphas[j] = H
+            elif alphas[j] < L:
+                alphas[j] = L
+            if abs(alphas[j] - jOld) < tol:
+                alphas[j] = jOld
+                return 0, alphas, b
+            alphas[i] = iOld + y[i] * y[j] * (jOld - alphas[j])
+            # update ECache
+            updateE(i, alphas, b)
+            updateE(j, alphas, b)
+            # update b
+            bINew = b - Ei - y[i] * (alphas[i] - iOld) * Kii - y[j] * \
+                (alphas[j] - jOld) * Kij
+            bJNew = b - Ej - y[i] * (alphas[i] - iOld) * Kij - y[j] * \
+                (alphas[j] - jOld) * Kjj
+            if alphas[i] > 0 and alphas[i] < C:
+                bNew = bINew
+            elif alphas[j] > 0 and alphas[j] < C:
+                bNew = bJNew
+            else:
+                bNew = (bINew + bJNew) / 2
+            return 1, alphas, b
+        else:
+            return 0, alphas, b
+
+    def train():
+        """完整版训练算法
+
+        Returns:
+            alphas alphas
+            w w
+            b b
+            supportVectorsIndex 支持向量的坐标集
+            supportVectors 支持向量
+            iterCount 迭代次数
+        """
+        numChanged = 0
+        examineAll = True
+        iterCount = 0
+        alphas = np.mat(np.zeros((m, 1)))
+        b = 0
+        # 如果所有alpha都遵从 KKT 条件，则在整个训练集上迭代
+        # 否则在处于边界内 (0, C) 的 alpha 中迭代
+        while (numChanged > 0 or examineAll) and (iterCount < maxIter):
+            numChanged = 0
+            if examineAll:
+                for i in range(m):
+                    changed, alphas, b = select(i, alphas, b)
+                    numChanged += changed
+            else:
+                nonBoundIds = np.nonzero((alphas.A > 0) * (alphas.A < C))[0]
+                for i in nonBoundIds:
+                    changed, alphas, b = select(i, alphas, b)
+                    numChanged += changed
+            iterCount += 1
+
+            if examineAll:
+                examineAll = False
+            elif numChanged == 0:
+                examineAll = True
+        supportVectorsIndex = np.nonzero(alphas.A > 0)[0]
+        supportVectors = np.mat(X[supportVectorsIndex])
+        return alphas, w(alphas, b, supportVectorsIndex, supportVectors), b, \
+            supportVectorsIndex, supportVectors, iterCount
+
+    def trainSimple():
+        """简化版训练算法
+
+        Returns:
+            alphas alphas
+            w w
+            b b
+            supportVectorsIndex 支持向量的坐标集
+            supportVectors 支持向量
+            iterCount 迭代次数
+        """
+        numChanged = 0
+        iterCount = 0
+        alphas = np.mat(np.zeros((m, 1)))
+        b = 0
+        L = 0
+        H = 0
+        while iterCount < maxIter:
+            numChanged = 0
+            for i in range(m):
+                Ei = E(i, alphas, b)
+                Ri = y[i] * Ei
+                # 选择违背KKT条件的，作为alpha2
+                if (Ri < -tol and alphas[i] < C) or \
+                        (Ri > tol and alphas[i] > 0):
+                    # 选择第二个参数
+                    j = selectJRand(i)
+                    Ej = E(j, alphas, b)
+                    # get bounds
+                    if y[i] != y[j]:
+                        L = max(0, alphas[j] - alphas[i])
+                        H = min(C, C + alphas[j] - alphas[i])
+                    else:
+                        L = max(0, alphas[j] + alphas[i] - C)
+                        H = min(C, alphas[j] + alphas[i])
+                    if L == H:
+                        continue
+                    Kii = K[i, i]
+                    Kjj = K[j, j]
+                    Kij = K[i, j]
+                    eta = 2.0 * Kij - Kii - Kjj
+                    if eta >= 0:
+                        continue
+                    iOld = alphas[i].copy();
+                    jOld = alphas[j].copy()
+                    alphas[j] = jOld - y[j] * (Ei - Ej) / eta
+                    if alphas[j] > H:
+                        alphas[j] = H
+                    elif alphas[j] < L:
+                        alphas[j] = L
+                    if abs(alphas[j] - jOld) < tol:
+                        alphas[j] = jOld
+                        continue
+                    alphas[i] = iOld + y[i] * y[j] * (jOld - alphas[j])
+                    # update b
+                    bINew = b - Ei - y[i] * (alphas[i] - iOld) * Kii - y[j] * \
+                        (alphas[j] - jOld) * Kij
+                    bJNew = b - Ej - y[i] * (alphas[i] - iOld) * Kij - y[j] * \
+                        (alphas[j] - jOld) * Kjj
+                    if alphas[i] > 0 and alphas[i] < C:
+                        b = bINew
+                    elif alphas[j] > 0 and alphas[j] < C:
+                        b = bJNew
+                    else:
+                        b = (bINew + bJNew) / 2.0
+                    numChanged += 1
+            if numChanged == 0:
+                iterCount += 1
+            else:
+                iterCount = 0
+        supportVectorsIndex = np.nonzero(alphas.A > 0)[0]
+        supportVectors = np.mat(X[supportVectorsIndex])
+        return alphas, w(alphas, b, supportVectorsIndex, supportVectors), b, \
+            supportVectorsIndex, supportVectors, iterCount
+    return trainSimple, train, predict
 ```
 相比于神经网络这样更先进的算法，支持向量机有两大主要优势：更高的速度、用更少的样本（千以内）取得更好的表现。这使得该算法非常适合文本分类问题。

From eb49aa149b5e33f2ae5383188a9ca41b81dbee75 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 9 Apr 2018 21:45:37 +0800
Subject: [PATCH 0698/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index 4489a00b..11e94de9 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -3,4 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 径向基函数（Radial Basis Function ，RBF)
+核函数指所谓径向基函数（Radial Basis Function 简称 RBF），就是某种沿径向对称的标量函数。 通常定义为空间中任一点x到某一中心xc之间欧氏距离的单调函数 , 可记作 k（||x-xc||）， 其作用往往是局部的 , 即当x远离xc时函数取值很小。
 

From 67816f75ff2da6afe8e392fb5eda302a3aa43046 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 08:51:09 +0800
Subject: [PATCH 0699/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 48 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 47 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index 11e94de9..8fa8a93a 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -3,5 +3,51 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 径向基函数（Radial Basis Function ，RBF)
-核函数指所谓径向基函数（Radial Basis Function 简称 RBF），就是某种沿径向对称的标量函数。 通常定义为空间中任一点x到某一中心xc之间欧氏距离的单调函数 , 可记作 k（||x-xc||）， 其作用往往是局部的 , 即当x远离xc时函数取值很小。
+
+径向基函数（RBF，Radial Basis Function）神经网络，是一种对局部逼近的神经网络。是由J.Moody 和C.Darken于20世纪80年代末提出的一种神经网络，径向基函数方法在某种程度上利用了多维空间中传统的严格插值法的研究成果。在神经网络的背景下，隐藏单元提供一个“函数”集，该函数集在输入模式向量扩展至隐层空间时为其构建了一个任意的“基”；这个函数集中的函数就被称为径向基函数。径向基函数首先是在实多变量插值问题的解中引入的。径向基函数是目前数值分析研究中的一个主要领域之一。
+
+最基本的径向基函数（RBF）神经网络的构成包括三层，其中每一层都有着完全不同的作用。输入层由一些感知单元组成，它们将网络与外界环境连接起来；第二层是网络中仅有的一个隐层，它的作用是从输入空间到隐层空间之间进行非线性变换，在大多数情况下，隐层空间有较高的维数；输出层是线性的，它为作用于输入层的激活模式提供响应。
+
+基本的径向基函数RBF网络是具有单稳层的三层前馈网络。由于它模拟了人脑中局部调整、相互覆盖接受域（或称感受域，Receptive Field）的神经网络结构，因此，RBF网络是一种局部逼近网络，现已证明它能以任意精度逼近任一连续函数。
+
+RBF 神经网络是一种三层前向网络，通过输入层空间到隐含层空间的非线性变换以及隐含层空间到输出层空间的线性变换，实现输入层空间到输出层空间的映射。这两个层间变换参数的学习可以分别进行，使得 RBF 神经网络的学习速度较快且可避免局部极小问题。
+
+
+RBF(Radial Basis Function，径向基函数)是某种沿径向对称的标量函数，通常定义为空间中一点到某一中心之间欧氏距离的单调函数，最常用的径向基函数是高斯函数，形式为：
+
+<p align="center">
+<img width="300" align="center" src="../../images/7.jpg" />
+</p>
+
+中为函数中心向量，为宽度向量。高斯函数的作用域表现出局部性，即当远离时函数取值较小。
+
+如下图所示，RBF 神经网络的结构从左至右分为三层，依次是输入层、隐含层和输出层：
+
+<p align="center">
+<img width="300" align="center" src="../../images/8.jpg" />
+</p>
+
+RBF神经网络结构图
+
+网络的输出如下式所示：
+
+<p align="center">
+<img width="300" align="center" src="../../images/9.jpg" />
+</p>
+
+与BP神经网络类似，理论上RBF神经网络对任何非线性连续映射能够用任意精度近似。但RBF神经网络有其自身的特点：
+
+RBF 神经网络结构的物理意义比较明确。RBF 网络可以看成是输入层数据空间（通常是低维空间）到隐含层空间（通常是高维空间）的一种非线性映射，以及隐含层空间到输出层的线性映射。通过选择适当的非线性映射变换 RBF 函数，从而将原低维空间非线性不可分的问题转换成高维空间的近似线性可分的问题。
+
+RBF 神经网络的学习分成两阶段，自组织学习阶段和监督学习阶段。在自组织学习阶段获取隐含层中心，在监督学习阶段获取隐含层到输出层之间的权值，各部分参数都可以快速学习，因此速度较快。
+
+分阶段学习的 RBF 神经网络无局部极小值问题。由于 RBF 神经网络的学习与输入样本聚类中心密切相关，因此 RBF 神经网络比较适合应用于有类别特征的数据。
+
+模型隐含层中心个数设定原则：
+
+由于RBF神经网络的思想是将低维空间非线性不可分问题转换成高维空间线性可分问题，因此隐含层中心个数应该大于输入变量个数，一般设为输入变量个数的 2 倍以上。
+
+由于隐含层中心点坐标代表了输入数据的聚类中心，因此隐含层中心个数应该大于输入数据集的按记录划分的类别个数，这样才能有效提取各种类别输入数据的特征。这需要对输入数据集的业务特征有一定了解，然后给出输入数据类别个数的大致范围。一般设隐含层中心个数为输入数据类别个数的 2 倍以上。
+
+综合以上两个原则设定隐含层中心个数，然后可以根据训练和测试的效果，对中心个数进行适当调整。一般情况下，中心个数设得越多，训练的效果越好，但所需要的时间越长；而当中心个数多到一定程度的时候，增多中心个数对训练效果的改善已不大。另外，隐含层中心数应该不大于训练数据记录数。
 

From a6d6004822e77a748ee452c84548f73ce138046e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 09:00:15 +0800
Subject: [PATCH 0700/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index 8fa8a93a..b01f687c 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -4,6 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 径向基函数（Radial Basis Function ，RBF)
 
+
 径向基函数（RBF，Radial Basis Function）神经网络，是一种对局部逼近的神经网络。是由J.Moody 和C.Darken于20世纪80年代末提出的一种神经网络，径向基函数方法在某种程度上利用了多维空间中传统的严格插值法的研究成果。在神经网络的背景下，隐藏单元提供一个“函数”集，该函数集在输入模式向量扩展至隐层空间时为其构建了一个任意的“基”；这个函数集中的函数就被称为径向基函数。径向基函数首先是在实多变量插值问题的解中引入的。径向基函数是目前数值分析研究中的一个主要领域之一。
 
 最基本的径向基函数（RBF）神经网络的构成包括三层，其中每一层都有着完全不同的作用。输入层由一些感知单元组成，它们将网络与外界环境连接起来；第二层是网络中仅有的一个隐层，它的作用是从输入空间到隐层空间之间进行非线性变换，在大多数情况下，隐层空间有较高的维数；输出层是线性的，它为作用于输入层的激活模式提供响应。

From 8b88325e2313681e327f42890ec73a80bd001b03 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 09:01:02 +0800
Subject: [PATCH 0701/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index b01f687c..8fa8a93a 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -4,7 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 径向基函数（Radial Basis Function ，RBF)
 
-
 径向基函数（RBF，Radial Basis Function）神经网络，是一种对局部逼近的神经网络。是由J.Moody 和C.Darken于20世纪80年代末提出的一种神经网络，径向基函数方法在某种程度上利用了多维空间中传统的严格插值法的研究成果。在神经网络的背景下，隐藏单元提供一个“函数”集，该函数集在输入模式向量扩展至隐层空间时为其构建了一个任意的“基”；这个函数集中的函数就被称为径向基函数。径向基函数首先是在实多变量插值问题的解中引入的。径向基函数是目前数值分析研究中的一个主要领域之一。
 
 最基本的径向基函数（RBF）神经网络的构成包括三层，其中每一层都有着完全不同的作用。输入层由一些感知单元组成，它们将网络与外界环境连接起来；第二层是网络中仅有的一个隐层，它的作用是从输入空间到隐层空间之间进行非线性变换，在大多数情况下，隐层空间有较高的维数；输出层是线性的，它为作用于输入层的激活模式提供响应。

From 34bfbf434ef099407cbea9fd0016be2da7e35913 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 20:53:08 +0800
Subject: [PATCH 0702/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 81 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 81 insertions(+)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index 8fa8a93a..203f3021 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -51,3 +51,84 @@ RBF 神经网络的学习分成两阶段，自组织学习阶段和监督学习
 
 综合以上两个原则设定隐含层中心个数，然后可以根据训练和测试的效果，对中心个数进行适当调整。一般情况下，中心个数设得越多，训练的效果越好，但所需要的时间越长；而当中心个数多到一定程度的时候，增多中心个数对训练效果的改善已不大。另外，隐含层中心数应该不大于训练数据记录数。
 
+
+#### 应用示例
+```python
+def kernelTrans(X, A, kTup):  # calc the kernel or transform data to a higher dimensional space
+    """
+    核转换函数
+    Args:
+        X     dataMatIn数据集
+        A     dataMatIn数据集的第i行的数据
+        kTup  核函数的信息
+
+    Returns:
+
+    """
+    m, n = shape(X)
+    K = mat(zeros((m, 1)))
+    if kTup[0] == 'lin':
+        # linear kernel:   m*n * n*1 = m*1
+        K = X * A.T
+    elif kTup[0] == 'rbf':
+        for j in range(m):
+            deltaRow = X[j, :] - A
+            K[j] = deltaRow * deltaRow.T
+        # 径向基函数的高斯版本
+        K = exp(K / (-1 * kTup[1] ** 2))  # divide in NumPy is element-wise not matrix like Matlab
+    else:
+        raise NameError('Houston We Have a Problem -- That Kernel is not recognized')
+    return K
+
+def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
+    """
+    Args:
+        dataMatIn    数据集
+        classLabels  类别标签
+        C   松弛变量(常量值)，允许有些数据点可以处于分隔面的错误一侧。
+            控制最大化间隔和保证大部分的函数间隔小于1.0这两个目标的权重。
+            可以通过调节该参数达到不同的结果。
+        toler   容错率
+        maxIter 退出前最大的循环次数
+        kTup    包含核函数信息的元组
+    Returns:
+        b       模型的常量值
+        alphas  拉格朗日乘子
+    """
+
+    # 创建一个 optStruct 对象
+    oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler, kTup)
+    iter = 0
+    entireSet = True
+    alphaPairsChanged = 0
+
+    # 循环遍历：循环maxIter次 并且 （alphaPairsChanged存在可以改变 or 所有行遍历一遍）
+    while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
+        alphaPairsChanged = 0
+
+        #  当entireSet=true or 非边界alpha对没有了；就开始寻找 alpha对，然后决定是否要进行else。
+        if entireSet:
+            # 在数据集上遍历所有可能的alpha
+            for i in range(oS.m):
+                # 是否存在alpha对，存在就+1
+                alphaPairsChanged += innerL(i, oS)
+                # print("fullSet, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
+            iter += 1
+
+        # 对已存在 alpha对，选出非边界的alpha值，进行优化。
+        else:
+            # 遍历所有的非边界alpha值，也就是不在边界0或C上的值。
+            nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
+            for i in nonBoundIs:
+                alphaPairsChanged += innerL(i, oS)
+                # print("non-bound, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
+            iter += 1
+
+        # 如果找到alpha对，就优化非边界alpha值，否则，就重新进行寻找，如果寻找一遍 遍历所有的行还是没找到，就退出循环。
+        if entireSet:
+            entireSet = False  # toggle entire set loop
+        elif (alphaPairsChanged == 0):
+            entireSet = True
+        print("iteration number: %d" % iter)
+    return oS.b, oS.alphas
+```

From 288acc8e58cb41ca32e80a3d00a4aa517c588f80 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 20:54:07 +0800
Subject: [PATCH 0703/1406] Update KBO.0.3.md

---
 assets/src/KBO/KBO.0.3.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/assets/src/KBO/KBO.0.3.md b/assets/src/KBO/KBO.0.3.md
index 203f3021..4e81aaf2 100644
--- a/assets/src/KBO/KBO.0.3.md
+++ b/assets/src/KBO/KBO.0.3.md
@@ -132,3 +132,17 @@ def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
         print("iteration number: %d" % iter)
     return oS.b, oS.alphas
 ```
+
+#### RBF优点
+优点：
+1. 它具有唯一最佳的特性，且无局部极小问题存在；
+2. RBF神经网络具有较强的输入和输出映射功能，并且理论证明在前向网络中RBF神经网络是完成映射功能的最有效网络；
+3. 分类能力好；
+4. 学习过程收敛速度快。
+
+
+#### RBF缺点
+缺点：
+1. 没有能力来解释自己的推理过程和推理依据；
+2. 当样本数据不足时，预测结果不太准确。
+

From acf71f9bf636e82868500378864d28d9b83ee874 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 20:55:38 +0800
Subject: [PATCH 0704/1406] change page of readme

---
 README.md                 | 2 +-
 assets/src/KBO/KBO.0.4.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/KBO/KBO.0.4.md

diff --git a/README.md b/README.md
index 0a77a7cc..2d1b8efe 100644
--- a/README.md
+++ b/README.md
@@ -110,7 +110,7 @@
  * [基于核的算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.1.md)   
      * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.2.md)
      * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
-     * [线性判别分析（Linear Discriminate Analysis ，LDA)]()
+     * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法]()
      * [K-均值]()
      * [K-中位数]()
diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
new file mode 100644
index 00000000..be8f1b7a
--- /dev/null
+++ b/assets/src/KBO/KBO.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 线性判别分析（Linear Discriminate Analysis ，LDA)

From 82a3d6c96b14e3d97638f7c7939dc50585db8041 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 20:58:20 +0800
Subject: [PATCH 0705/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index be8f1b7a..199d5ab1 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 线性判别分析（Linear Discriminate Analysis ，LDA)
+
+线性判别式分析(Linear Discriminant Analysis, LDA)，也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。性鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。就是说，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。

From ae449bae0493d92d8162f1e49e9aed459e6d3d7e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:02:30 +0800
Subject: [PATCH 0706/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 199d5ab1..6789c644 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -4,4 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 线性判别分析（Linear Discriminate Analysis ，LDA)
 
-线性判别式分析(Linear Discriminant Analysis, LDA)，也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。性鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。就是说，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
+线性判别式分析(Linear Discriminant Analysis, LDA)，也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。线性判别分析是一种经典的线性分类方法。它设法将数据集投影到一条直线上，使得同类样例的投影点尽可能接近，异类样例的投影点尽可能远。这样，在分类时，新样本同样投影到这条直线上，根据投影点的位置来确定类别。
+
+由于LDA把原来N维的样本投影到了N-1维空间，因而也常被视为一种经典的降维技术。
+

From 137f3a39aff3de5b9933a2bc45b5dc7b54618a82 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 21:11:35 +0800
Subject: [PATCH 0707/1406] change page of kbo

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 assets/images/227.jpg | Bin 0 -> 2760 bytes
 assets/images/228.jpg | Bin 0 -> 1662 bytes
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From 985ae99030345b2a1acc9c984b530347df3caca8 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 21:13:46 +0800
Subject: [PATCH 0708/1406] change page

---
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 assets/images/224.jpg | Bin 0 -> 3506 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
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From 5d41cd41c6b85b3e820b61f6cca81cd2aeaa4e80 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:20:50 +0800
Subject: [PATCH 0709/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 6789c644..9de05118 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -8,3 +8,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 由于LDA把原来N维的样本投影到了N-1维空间，因而也常被视为一种经典的降维技术。
 
+预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="80" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="80" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="80" align="center" src="../../images/222.jpg" />.
+
+类内散度矩阵<img width="80" align="center" src="../../images/223.jpg" />.
+类间散度矩阵<img width="80" align="center" src="../../images/224.jpg" />.
+
+使用拉格朗日乘子法<img width="80" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
+
+对多分类情况，<img width="80" align="center" src="../../images/227.jpg" />，W的解是<img width="80" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From 8438089cf1c2f85396ffe1dc6626c0355416abf3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:21:08 +0800
Subject: [PATCH 0710/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 9de05118..8391cd7e 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 由于LDA把原来N维的样本投影到了N-1维空间，因而也常被视为一种经典的降维技术。
 
-预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="80" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="80" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="80" align="center" src="../../images/222.jpg" />.
+预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="130" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="80" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="80" align="center" src="../../images/222.jpg" />.
 
 类内散度矩阵<img width="80" align="center" src="../../images/223.jpg" />.
 类间散度矩阵<img width="80" align="center" src="../../images/224.jpg" />.

From 1d7c6630701a71955469debaa7fef0e5f93f7926 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:21:37 +0800
Subject: [PATCH 0711/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 8391cd7e..099c2f8b 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -8,11 +8,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 由于LDA把原来N维的样本投影到了N-1维空间，因而也常被视为一种经典的降维技术。
 
-预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="130" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="80" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="80" align="center" src="../../images/222.jpg" />.
+预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="150" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="150" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="150" align="center" src="../../images/222.jpg" />.
 
-类内散度矩阵<img width="80" align="center" src="../../images/223.jpg" />.
-类间散度矩阵<img width="80" align="center" src="../../images/224.jpg" />.
+类内散度矩阵<img width="150" align="center" src="../../images/223.jpg" />.
+类间散度矩阵<img width="150" align="center" src="../../images/224.jpg" />.
 
-使用拉格朗日乘子法<img width="80" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
+使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
 
-对多分类情况，<img width="80" align="center" src="../../images/227.jpg" />，W的解是<img width="80" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。
+对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="150" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From d883f461d535d1518d0d99d2f3cad439e05bf10f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:21:55 +0800
Subject: [PATCH 0712/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 099c2f8b..b0777501 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -15,4 +15,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
 
-对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="150" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。
+对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="100" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From 2a674bb75c5c16ac2af306104d0e52dad7b7b821 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:22:35 +0800
Subject: [PATCH 0713/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index b0777501..db1cc694 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -10,8 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="150" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="150" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="150" align="center" src="../../images/222.jpg" />.
 
-类内散度矩阵<img width="150" align="center" src="../../images/223.jpg" />.
-类间散度矩阵<img width="150" align="center" src="../../images/224.jpg" />.
+其中类内散度矩阵<img width="400" align="center" src="../../images/223.jpg" />,类间散度矩阵<img width="400" align="center" src="../../images/224.jpg" />.
 
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
 

From 1b35cfebc539162362c64a13d45e095fae5a8044 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:23:04 +0800
Subject: [PATCH 0714/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index db1cc694..d005693c 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -10,8 +10,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="150" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="150" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="150" align="center" src="../../images/222.jpg" />.
 
-其中类内散度矩阵<img width="400" align="center" src="../../images/223.jpg" />,类间散度矩阵<img width="400" align="center" src="../../images/224.jpg" />.
+其中类内散度矩阵<img width="460" align="center" src="../../images/223.jpg" />,类间散度矩阵<img width="400" align="center" src="../../images/224.jpg" />.
 
-使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="80" align="center" src="../../images/226.jpg" />.
+使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="130" align="center" src="../../images/226.jpg" />.
 
 对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="100" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From d1f8f48a5b870a5e47be718616c7f0f1ee5fbaee Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:24:04 +0800
Subject: [PATCH 0715/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index d005693c..e38fc3cb 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="130" align="center" src="../../images/226.jpg" />.
 
-对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="100" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。
+对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="80" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From 35f5b06bbfeeeccefda10b40c3b9d9aa2590d1b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:24:31 +0800
Subject: [PATCH 0716/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index e38fc3cb..9c98bc6a 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -14,4 +14,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="130" align="center" src="../../images/226.jpg" />.
 
-对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="80" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。
+对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="60" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。

From 3f85cf68a5cbe4f21669397e5cea7e6508e1ee08 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:24:47 +0800
Subject: [PATCH 0717/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 9c98bc6a..0c1c21ac 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -10,7 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 预使得同类样例的投影点尽可能接近，可以让同类样例投影点的协方差尽可能小，即<img width="150" align="center" src="../../images/220.jpg" />尽可能小。预使得异类样例的投影点尽可能远，可以让不同类样例的投影点尽可能远，即让类中心距离尽可能大，即<img width="150" align="center" src="../../images/221.jpg" /> 尽可能大。这样，目标函数为<img width="150" align="center" src="../../images/222.jpg" />.
 
-其中类内散度矩阵<img width="460" align="center" src="../../images/223.jpg" />,类间散度矩阵<img width="400" align="center" src="../../images/224.jpg" />.
+其中类内散度矩阵<img width="460" align="center" src="../../images/223.jpg" />,类间散度矩阵<img width="300" align="center" src="../../images/224.jpg" />.
 
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="130" align="center" src="../../images/226.jpg" />.
 

From c8a801482d179dbcd12df9743961830a7e1a0e44 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 21:34:44 +0800
Subject: [PATCH 0718/1406] change page of kBO

---
 assets/images/223.jpg | Bin 9916 -> 13959 bytes
 assets/images/229.jpg | Bin 0 -> 1202 bytes
 assets/images/230.jpg | Bin 0 -> 1242 bytes
 assets/images/231.jpg | Bin 0 -> 3246 bytes
 assets/images/232.png | Bin 0 -> 1448 bytes
 5 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/229.jpg
 create mode 100644 assets/images/230.jpg
 create mode 100644 assets/images/231.jpg
 create mode 100644 assets/images/232.png

diff --git a/assets/images/223.jpg b/assets/images/223.jpg
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From 938ce24b26e4d2d05062a0e8bbe55a297020895d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:35:53 +0800
Subject: [PATCH 0719/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 0c1c21ac..9498258e 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -15,3 +15,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 使用拉格朗日乘子法<img width="150" align="center" src="../../images/225.jpg" />可以求解得到<img width="130" align="center" src="../../images/226.jpg" />.
 
 对多分类情况，<img width="150" align="center" src="../../images/227.jpg" />，W的解是<img width="60" align="center" src="../../images/228.jpg" />的N−1 个最大广义特征值所对应的特征向量组成的矩阵。
+
+线性判别分析降维一般分为5个步骤：
+* 计算数据集中每个类别样本的均值向量。
+* 通过均值向量，计算类间散度矩阵<img width="60" align="center" src="../../images/229.jpg" />和类内散度矩阵<img width="60" align="center" src="../../images/230.jpg" />

From 26b643532eec94d4f4e8acdf81715ab4336c501e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:37:51 +0800
Subject: [PATCH 0720/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 9498258e..628600d3 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -18,4 +18,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性判别分析降维一般分为5个步骤：
 * 计算数据集中每个类别样本的均值向量。
-* 通过均值向量，计算类间散度矩阵<img width="60" align="center" src="../../images/229.jpg" />和类内散度矩阵<img width="60" align="center" src="../../images/230.jpg" />
+* 通过均值向量，计算类间散度矩阵<img width="50" align="center" src="../../images/229.jpg" />和类内散度矩阵<img width="50" align="center" src="../../images/230.jpg" />。
+* 对<img width="50" align="center" src="../../images/231.jpg" />进行特征值求解， 求出<img width="60" align="center" src="../../images/228.jpg" />的特征向量和特征值。
+* 对特征向量按照特征值的大小降序排列，并选择前K个特征向量组成投影矩阵W。
+* 通过D*K维的特征值矩阵将样本点投影到新的子空间中，Y=X*W。

From ca5e73c515bc69d776818f2f8eaa0bb1f7fc9ecf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:38:31 +0800
Subject: [PATCH 0721/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 628600d3..cf3a7bad 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -19,6 +19,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 线性判别分析降维一般分为5个步骤：
 * 计算数据集中每个类别样本的均值向量。
 * 通过均值向量，计算类间散度矩阵<img width="50" align="center" src="../../images/229.jpg" />和类内散度矩阵<img width="50" align="center" src="../../images/230.jpg" />。
-* 对<img width="50" align="center" src="../../images/231.jpg" />进行特征值求解， 求出<img width="60" align="center" src="../../images/228.jpg" />的特征向量和特征值。
+* 对<img width="120" align="center" src="../../images/231.jpg" />进行特征值求解， 求出<img width="60" align="center" src="../../images/228.jpg" />的特征向量和特征值。
 * 对特征向量按照特征值的大小降序排列，并选择前K个特征向量组成投影矩阵W。
-* 通过D*K维的特征值矩阵将样本点投影到新的子空间中，Y=X*W。
+* 通过D*K维的特征值矩阵将样本点投影到新的子空间中，<img width="120" align="center" src="../../images/232.jpg" />.

From 49b858e3329af0c220cacae113638caba1fc9b9f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 21:39:30 +0800
Subject: [PATCH 0722/1406] change page of KBO

---
 assets/images/{232.png => 232.jpg} | Bin
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename assets/images/{232.png => 232.jpg} (100%)

diff --git a/assets/images/232.png b/assets/images/232.jpg
similarity index 100%
rename from assets/images/232.png
rename to assets/images/232.jpg

From bda1334fc8b0dbdad3eaeb0a29786f5967989c15 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:40:15 +0800
Subject: [PATCH 0723/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index cf3a7bad..d905cdf5 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -21,4 +21,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 通过均值向量，计算类间散度矩阵<img width="50" align="center" src="../../images/229.jpg" />和类内散度矩阵<img width="50" align="center" src="../../images/230.jpg" />。
 * 对<img width="120" align="center" src="../../images/231.jpg" />进行特征值求解， 求出<img width="60" align="center" src="../../images/228.jpg" />的特征向量和特征值。
 * 对特征向量按照特征值的大小降序排列，并选择前K个特征向量组成投影矩阵W。
-* 通过D*K维的特征值矩阵将样本点投影到新的子空间中，<img width="120" align="center" src="../../images/232.jpg" />.
+* 通过D*K维的特征值矩阵将样本点投影到新的子空间中，<img width="60" align="center" src="../../images/232.jpg" />.

From bd2e6b5627b20fd8ae2327d3b0c6b8f027da23d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:42:53 +0800
Subject: [PATCH 0724/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 206 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 206 insertions(+)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index d905cdf5..3e62ad05 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -22,3 +22,209 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 对<img width="120" align="center" src="../../images/231.jpg" />进行特征值求解， 求出<img width="60" align="center" src="../../images/228.jpg" />的特征向量和特征值。
 * 对特征向量按照特征值的大小降序排列，并选择前K个特征向量组成投影矩阵W。
 * 通过D*K维的特征值矩阵将样本点投影到新的子空间中，<img width="60" align="center" src="../../images/232.jpg" />.
+
+
+#### 应用示例
+```python
+# coding: utf-8
+import pandas as pd
+
+# u may download data from (https://archive.ics.uci.edu/ml/datasets/Iris).
+df = pd.read_csv('iris.data', header=None)
+
+feature_dict = {i:label for i,label in zip(
+                range(4),
+                  ('sepal length in cm',
+                  'sepal width in cm',
+                  'petal length in cm',
+                  'petal width in cm', ))}
+df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']
+df.dropna(how="all", inplace=True) # to drop the empty line at file-end
+
+df.tail()
+
+
+from sklearn.preprocessing import LabelEncoder
+
+X = df[[0,1,2,3]].values
+y = df['class label'].values
+
+enc = LabelEncoder()
+label_encoder = enc.fit(y)
+y = label_encoder.transform(y) + 1
+
+label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}
+
+
+from matplotlib import pyplot as plt
+import numpy as np
+import math
+
+fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12,6))
+
+for ax,cnt in zip(axes.ravel(), range(4)):  
+
+    # set bin sizes
+    min_b = math.floor(np.min(X[:,cnt]))
+    max_b = math.ceil(np.max(X[:,cnt]))
+    bins = np.linspace(min_b, max_b, 25)
+
+    # plottling the histograms
+    for lab,col in zip(range(1,4), ('blue', 'red', 'green')):
+        ax.hist(X[y==lab, cnt],
+                   color=col,
+                   label='class %s' %label_dict[lab],
+                   bins=bins,
+                   alpha=0.5,)
+    ylims = ax.get_ylim()
+
+    # plot annotation
+    leg = ax.legend(loc='upper right', fancybox=True, fontsize=8)
+    leg.get_frame().set_alpha(0.5)
+    ax.set_ylim([0, max(ylims)+2])
+    ax.set_xlabel(feature_dict[cnt])
+    ax.set_title('Iris histogram #%s' %str(cnt+1))
+
+    # hide axis ticks
+    ax.tick_params(axis="both", which="both", bottom="off", top="off",  
+            labelbottom="on", left="off", right="off", labelleft="on")
+
+    # remove axis spines
+    ax.spines["top"].set_visible(False)  
+    ax.spines["right"].set_visible(False)
+    ax.spines["bottom"].set_visible(False)
+    ax.spines["left"].set_visible(False)    
+
+axes[0][0].set_ylabel('count')
+axes[1][0].set_ylabel('count')
+
+fig.tight_layout()       
+
+plt.show()
+
+# 从上图的结果中可以看出，花瓣的长度和宽度看起来在不同的类别有较强的区分性，因为这2个特征的直方图中，不同的类别的样本较为分散。
+# 因此在实际应用中，我们对特征进行降维，除了使用类似于LDA的特征投影方法（或者叫extraction），特征选择（selection）也是一种较好的方式。
+# 像上图这种低纬度的数据集，看一眼直方图我们就可以做出一定的判断。
+
+
+# step1：计算D维特征样本的均值向量
+np.set_printoptions(precision=4)
+
+mean_vectors = []
+for cl in range(1,4):
+    mean_vectors.append(np.mean(X[y==cl], axis=0))
+    print('Mean Vector class %s: %s\n' %(cl, mean_vectors[cl-1]))
+    
+
+# step2: 计算散度矩阵
+
+# 计算类内散度矩阵：Sw
+S_W = np.zeros((4,4))
+for cl,mv in zip(range(1,4), mean_vectors):
+    class_sc_mat = np.zeros((4,4))                  # scatter matrix for every class
+    for row in X[y == cl]:
+        row, mv = row.reshape(4,1), mv.reshape(4,1) # make column vectors
+        class_sc_mat += (row-mv).dot((row-mv).T)
+    S_W += class_sc_mat                             # sum class scatter matrices
+    
+    
+# 计算类间三度矩阵:Sb
+overall_mean = np.mean(X, axis=0)
+
+S_B = np.zeros((4,4))
+for i,mean_vec in enumerate(mean_vectors):  
+    n = X[y==i+1,:].shape[0]
+    mean_vec = mean_vec.reshape(4,1) # make column vector
+    overall_mean = overall_mean.reshape(4,1) # make column vector
+    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)
+
+print('between-class Scatter Matrix:\n', S_B)
+
+
+
+# step3：求解S?1WSB的特征值问题：
+eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
+
+for i in range(len(eig_vals)):
+    eigvec_sc = eig_vecs[:,i].reshape(4,1)   
+    print('\nEigenvector {}: \n{}'.format(i+1, eigvec_sc.real))
+    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))
+print('within-class Scatter Matrix:\n', S_W)
+
+
+
+# step4：选择新的特征空间
+# 先将特征向量按照特征值的大小降序排列，线代中告诉我我们，矩阵乘法可以看做一种线性变换，而特征向量和特征值代表了变换后的方向以及该方向上的
+# 缩放比例，因此特征值越大，说明这个方向在变换中越显著，也就是信息量最大。因此我们需要抛弃的是特征值较小的方向，因此我们只需要选取前topk个特征值
+# 对应的特征向量，就得到了映射矩阵W
+
+# Make a list of (eigenvalue, eigenvector) tuples
+eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
+
+# Sort the (eigenvalue, eigenvector) tuples from high to low
+eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)
+
+# Visually confirm that the list is correctly sorted by decreasing eigenvalues
+
+print('Eigenvalues in decreasing order:\n')
+for i in eig_pairs:
+    print (i[0], i[1])
+    
+    
+# 从上面的特征值可以看到有2个特征值非常接近0，这2个值之所以接近0，一是代表了他们不包含信息量，第二是因为浮点运算的精确度问题。
+# 实际上这2分特征值应该就是0， 因为在LDA中，如果有C类，线性判别式最多只有C-1个，因此对于之前3类的数据集，最多只有2个特征值。
+# 由于类间散度矩阵S_B是不同类别C矩阵的和，而C矩阵的秩是1，对于最特殊的完美共线性情况（即所有样本点都在一条直线上），协方差矩阵的秩就会是1，
+# 这就导致了只会有一个非0的特征值。
+# 我们通过特征值的比例来体现方差的分布：
+print('Variance explained:\n')
+eigv_sum = sum(eig_vals)
+for i,j in enumerate(eig_pairs):
+    print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))
+    
+W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))
+
+
+# step5：将样本投影到新的空间
+X_lda = X.dot(W)
+assert X_lda.shape == (150,2), "The matrix is not 150x2 dimensional."
+
+
+from matplotlib import pyplot as plt
+
+def plot_step_lda():
+
+    ax = plt.subplot(111)
+    for label,marker,color in zip(
+        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):
+
+        plt.scatter(x=X_lda[:,0].real[y == label],
+                y=X_lda[:,1].real[y == label],
+                marker=marker,
+                color=color,
+                alpha=0.5,
+                label=label_dict[label]
+                )
+
+    plt.xlabel('LD1')
+    plt.ylabel('LD2')
+
+    leg = plt.legend(loc='upper right', fancybox=True)
+    leg.get_frame().set_alpha(0.5)
+    plt.title('LDA: Iris projection onto the first 2 linear discriminants')
+
+    # hide axis ticks
+    plt.tick_params(axis="both", which="both", bottom="off", top="off",  
+            labelbottom="on", left="off", right="off", labelleft="on")
+
+    # remove axis spines
+    ax.spines["top"].set_visible(False)  
+    ax.spines["right"].set_visible(False)
+    ax.spines["bottom"].set_visible(False)
+    ax.spines["left"].set_visible(False)    
+
+    plt.grid()
+    plt.tight_layout
+    plt.show()
+
+plot_step_lda()
+```

From 821146c4e2d51042809f276f78d5f954733109e1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:44:49 +0800
Subject: [PATCH 0725/1406] Update KBO.0.4.md

---
 assets/src/KBO/KBO.0.4.md | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/assets/src/KBO/KBO.0.4.md b/assets/src/KBO/KBO.0.4.md
index 3e62ad05..6bf36dbe 100644
--- a/assets/src/KBO/KBO.0.4.md
+++ b/assets/src/KBO/KBO.0.4.md
@@ -102,7 +102,6 @@ fig.tight_layout()
 
 plt.show()
 
-# 从上图的结果中可以看出，花瓣的长度和宽度看起来在不同的类别有较强的区分性，因为这2个特征的直方图中，不同的类别的样本较为分散。
 # 因此在实际应用中，我们对特征进行降维，除了使用类似于LDA的特征投影方法（或者叫extraction），特征选择（selection）也是一种较好的方式。
 # 像上图这种低纬度的数据集，看一眼直方图我们就可以做出一定的判断。
 
@@ -117,7 +116,6 @@ for cl in range(1,4):
     
 
 # step2: 计算散度矩阵
-
 # 计算类内散度矩阵：Sw
 S_W = np.zeros((4,4))
 for cl,mv in zip(range(1,4), mean_vectors):
@@ -170,7 +168,6 @@ print('Eigenvalues in decreasing order:\n')
 for i in eig_pairs:
     print (i[0], i[1])
     
-    
 # 从上面的特征值可以看到有2个特征值非常接近0，这2个值之所以接近0，一是代表了他们不包含信息量，第二是因为浮点运算的精确度问题。
 # 实际上这2分特征值应该就是0， 因为在LDA中，如果有C类，线性判别式最多只有C-1个，因此对于之前3类的数据集，最多只有2个特征值。
 # 由于类间散度矩阵S_B是不同类别C矩阵的和，而C矩阵的秩是1，对于最特殊的完美共线性情况（即所有样本点都在一条直线上），协方差矩阵的秩就会是1，

From 8653c21a7fab4ef5b5d11b63fbf75bc1e5b22ab8 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 21:51:38 +0800
Subject: [PATCH 0726/1406] change page of CA

---
 assets/src/CA/CA.0.1.md | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 assets/src/CA/CA.0.1.md

diff --git a/assets/src/CA/CA.0.1.md b/assets/src/CA/CA.0.1.md
new file mode 100644
index 00000000..cfc5a959
--- /dev/null
+++ b/assets/src/CA/CA.0.1.md
@@ -0,0 +1,25 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 聚类分析
+
+聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
+
+一般把数据聚类归纳为一种非监督学习。
+
+数据聚类算法可以分为结构性或者分散性。结构性算法利用以前成功使用过的聚类器进行分类，而分散型算法则是一次确定所有分类。结构性算法可以从上至下或者从下至上双向进行计算。从下至上算法从每个对象作为单独分类开始，不断融合其中相近的对象。而从上至下算法则是把所有对象作为一个整体分类，然后逐渐分小。
+
+分割式聚类算法，是一次性确定要产生的类别，这种算法也已应用于从下至上聚类算法。
+
+基于密度的聚类算法，是为了挖掘有任意形状特性的类别而发明的。此算法把一个类别视为数据集中大于某阈值的一个区域。DBSCAN和OPTICS是两个典型的算法。
+
+许多聚类算法在执行之前，需要指定从输入数据集中产生的分类个数。除非事先准备好一个合适的值，否则必须决定一个大概值，关于这个问题已经有一些现成的技术。
+
+在已经得到距离值之后，元素间可以被联系起来。通过分离和融合可以构建一个结构。传统上，表示的方法是树形数据结构， 然后对该结构进行修剪。树的根节点表示一个包含所有项目的类别，树叶表示与个别的项目相关的类别。
+
+层次聚类算法，要么是自下向上聚集型的，即从叶子节点开始，最终汇聚到根节点；要么是自顶向下分裂型的，即从根节点开始，递归的向下分裂。
+
+任意非负值的函数都可以用于衡量一对观测值之间的相似度。决定一个类别是否分裂或者合并的是一个连动的标准，它是两两观测值之间距离的函数。
+
+在一个指定高度上切割此树，可以得到一个相应精度的分类。

From 6c82c3d972ed7519c6b268ebb6c613b2d65aa8db Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:52:25 +0800
Subject: [PATCH 0727/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 2d1b8efe..6a031728 100644
--- a/README.md
+++ b/README.md
@@ -111,7 +111,7 @@
      * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.2.md)
      * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
- * [聚类算法]()
+ * [聚类算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
      * [K-均值]()
      * [K-中位数]()
      * [EM算法]()

From 82dde72b767cdaaa78a0fcf58d410a03da612770 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 21:54:28 +0800
Subject: [PATCH 0728/1406] Update CA.0.1.md

---
 assets/src/CA/CA.0.1.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/CA/CA.0.1.md b/assets/src/CA/CA.0.1.md
index cfc5a959..6751681a 100644
--- a/assets/src/CA/CA.0.1.md
+++ b/assets/src/CA/CA.0.1.md
@@ -23,3 +23,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 任意非负值的函数都可以用于衡量一对观测值之间的相似度。决定一个类别是否分裂或者合并的是一个连动的标准，它是两两观测值之间距离的函数。
 
 在一个指定高度上切割此树，可以得到一个相应精度的分类。
+
+
+聚类分析的应用算法有：
+* K-均值
+* K-中位数
+* EM算法
+* 分层聚类

From 0f91fb3e559f94d99a5241a5d141d429281ea60d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 22:03:16 +0800
Subject: [PATCH 0729/1406] change page readme

---
 README.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index 6a031728..46416542 100644
--- a/README.md
+++ b/README.md
@@ -111,11 +111,11 @@
      * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.2.md)
      * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
- * [聚类算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
-     * [K-均值]()
-     * [K-中位数]()
-     * [EM算法]()
-     * [分层聚类]()
+ * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
+     * [K-均值(K-Means Algorithm)]()
+     * [k-均值聚类(K-Means Clustering)]()
+     * [期望最大化(Expectation-Maximization)]()
+     * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   
      * [Apriori算法]() 
      * [Eclat算法]() 

From 73a9abb84867cc008cc2591cf93c54fce0fd72b1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 22:04:47 +0800
Subject: [PATCH 0730/1406] Update CA.0.1.md

---
 assets/src/CA/CA.0.1.md | 8 ++------
 1 file changed, 2 insertions(+), 6 deletions(-)

diff --git a/assets/src/CA/CA.0.1.md b/assets/src/CA/CA.0.1.md
index 6751681a..2d89c073 100644
--- a/assets/src/CA/CA.0.1.md
+++ b/assets/src/CA/CA.0.1.md
@@ -2,13 +2,9 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 聚类分析
+#### 聚类算法
 
-聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
-
-一般把数据聚类归纳为一种非监督学习。
-
-数据聚类算法可以分为结构性或者分散性。结构性算法利用以前成功使用过的聚类器进行分类，而分散型算法则是一次确定所有分类。结构性算法可以从上至下或者从下至上双向进行计算。从下至上算法从每个对象作为单独分类开始，不断融合其中相近的对象。而从上至下算法则是把所有对象作为一个整体分类，然后逐渐分小。
+聚类算法是一种非监督学习。数据聚类算法可以分为结构性或者分散性。结构性算法利用以前成功使用过的聚类器进行分类，而分散型算法则是一次确定所有分类。结构性算法可以从上至下或者从下至上双向进行计算。从下至上算法从每个对象作为单独分类开始，不断融合其中相近的对象。而从上至下算法则是把所有对象作为一个整体分类，然后逐渐分小。
 
 分割式聚类算法，是一次性确定要产生的类别，这种算法也已应用于从下至上聚类算法。
 

From 2a3ecd389cfa0f3bf7486d1485362a7fd1f6e9bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 10 Apr 2018 22:10:42 +0800
Subject: [PATCH 0731/1406] Update CA.0.1.md

---
 assets/src/CA/CA.0.1.md | 25 ++++++++-----------------
 1 file changed, 8 insertions(+), 17 deletions(-)

diff --git a/assets/src/CA/CA.0.1.md b/assets/src/CA/CA.0.1.md
index 2d89c073..b9570708 100644
--- a/assets/src/CA/CA.0.1.md
+++ b/assets/src/CA/CA.0.1.md
@@ -4,25 +4,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 聚类算法
 
-聚类算法是一种非监督学习。数据聚类算法可以分为结构性或者分散性。结构性算法利用以前成功使用过的聚类器进行分类，而分散型算法则是一次确定所有分类。结构性算法可以从上至下或者从下至上双向进行计算。从下至上算法从每个对象作为单独分类开始，不断融合其中相近的对象。而从上至下算法则是把所有对象作为一个整体分类，然后逐渐分小。
+聚类分析又称群分析，它是研究（样品或指标）分类问题的一种统计分析方法，同时也是数据挖掘的一个重要算法。聚类（Cluster）分析是由若干模式（Pattern）组成的，通常，模式是一个度量（Measurement）的向量，或者是多维空间中的一个点。聚类分析以相似性为基础，在一个聚类中的模式之间比不在同一聚类中的模式之间具有更多的相似性。
 
-分割式聚类算法，是一次性确定要产生的类别，这种算法也已应用于从下至上聚类算法。
-
-基于密度的聚类算法，是为了挖掘有任意形状特性的类别而发明的。此算法把一个类别视为数据集中大于某阈值的一个区域。DBSCAN和OPTICS是两个典型的算法。
+聚类算法是一种非监督学习。聚类分析起源于分类学，在古老的分类学中，人们主要依靠经验和专业知识来实现分类，很少利用数学工具进行定量的分类。随着人类科学技术的发展，对分类的要求越来越高，以致有时仅凭经验和专业知识难以确切地进行分类，于是人们逐渐地把数学工具引用到了分类学中，形成了数值分类学，之后又将多元分析的技术引入到数值分类学形成了聚类分析。聚类分析内容非常丰富，有系统聚类法、有序样品聚类法、动态聚类法、模糊聚类法、图论聚类法、聚类预报法等。
 
 许多聚类算法在执行之前，需要指定从输入数据集中产生的分类个数。除非事先准备好一个合适的值，否则必须决定一个大概值，关于这个问题已经有一些现成的技术。
 
-在已经得到距离值之后，元素间可以被联系起来。通过分离和融合可以构建一个结构。传统上，表示的方法是树形数据结构， 然后对该结构进行修剪。树的根节点表示一个包含所有项目的类别，树叶表示与个别的项目相关的类别。
-
-层次聚类算法，要么是自下向上聚集型的，即从叶子节点开始，最终汇聚到根节点；要么是自顶向下分裂型的，即从根节点开始，递归的向下分裂。
-
-任意非负值的函数都可以用于衡量一对观测值之间的相似度。决定一个类别是否分裂或者合并的是一个连动的标准，它是两两观测值之间距离的函数。
-
-在一个指定高度上切割此树，可以得到一个相应精度的分类。
-
+聚类算法主要可分为：划分方法（partitioning method），层次方法(hierarchical method)，基于密度的方法(density-basedmethod)，基于网格的方法(grid-based method)，和基于模型的方法(model-based method)。
 
-聚类分析的应用算法有：
-* K-均值
-* K-中位数
-* EM算法
-* 分层聚类
+聚类算法(Cluster analysis)的应用算法有：
+* K-均值(K-Means Algorithm)
+* 模糊聚类Fuzzy Clustering
+* 期望最大化(Expectation-Maximization)
+* 聚类分析(Cluster Analysis)

From cd5cf7a4d18b211b91be550551bbb24ec848551b Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 10 Apr 2018 22:11:43 +0800
Subject: [PATCH 0732/1406] change page of Ca

---
 assets/src/CA/CA.0.2.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/CA/CA.0.2.md

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
new file mode 100644
index 00000000..12238b64
--- /dev/null
+++ b/assets/src/CA/CA.0.2.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### K-均值(K-Means Algorithm)

From 7217ff925b5da849d50056c6b9580c0e7358e1c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 08:49:28 +0800
Subject: [PATCH 0733/1406] change page of readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 46416542..62bcc5e7 100644
--- a/README.md
+++ b/README.md
@@ -112,7 +112,7 @@
      * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
-     * [K-均值(K-Means Algorithm)]()
+     * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
      * [k-均值聚类(K-Means Clustering)]()
      * [期望最大化(Expectation-Maximization)]()
      * [聚类分析(Cluster Analysis)]()

From 4a82ca7e3e854ff406f7b680ba25eae7f41fb332 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 20:56:57 +0800
Subject: [PATCH 0734/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 12238b64..facc2256 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### K-均值(K-Means Algorithm)
+
+k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。

From c51ee3a915e98ea0473ebfd80be2db0f01ed1cbf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:23:18 +0800
Subject: [PATCH 0735/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index facc2256..7949fbfa 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### K-均值(K-Means Algorithm)
 
 k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
+
+聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.

From cef9e8ecbd6bb34be351a87f9ac14fc88b72359e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:24:32 +0800
Subject: [PATCH 0736/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 7949fbfa..5d322b0a 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -7,3 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
 
 聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.
+
+k-means算法是一种基于样本间相似性度量的间接聚类方法，属于非监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点

From e0f0f0a7d90fd58a02c0342fb0d336363d5c25b4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:27:40 +0800
Subject: [PATCH 0737/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 5d322b0a..7d68a3d3 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -6,6 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
 
+k-means算法属于非监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点
+
 聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.
 
-k-means算法是一种基于样本间相似性度量的间接聚类方法，属于非监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点

From f723709bce70a322292e0af7b492c7841d1e600d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:29:35 +0800
Subject: [PATCH 0738/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 7d68a3d3..bbcca8a1 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -10,3 +10,13 @@ k-means算法属于非监督学习方法。此算法以k为参数，把n 个对
 
 聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.
 
+
+#### 优点
+
+* 简单、快速，可并行计算
+* 已经获得防范的应用
+
+#### 缺点
+
+* 必须事先给出k（要生成的簇的数目），而且对初值敏感，对于不同的初始值，可能会导致不同结果。
+* 对于“躁声”和孤立点数据是敏感的，少量的该类数据能够对平均值产生极大的影响。

From b5d57819edacd31192e043ac6dc386e3c835b606 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:32:29 +0800
Subject: [PATCH 0739/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 111 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 111 insertions(+)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index bbcca8a1..5d490533 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -10,6 +10,117 @@ k-means算法属于非监督学习方法。此算法以k为参数，把n 个对
 
 聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.
 
+#### 应用示例
+
+输入：簇的数目k和包含n个对象的数据库。 输出：k个簇，使平方误差准则最小。
+
+算法步骤：
+
+* 1.为每个聚类确定一个初始聚类中心，这样就有K 个初始聚类中心。 
+* 2.将样本集中的样本按照最小距离原则分配到最邻近聚类
+* 3.使用每个聚类中的样本均值作为新的聚类中心。
+* 4.重复步骤2.3直到聚类中心不再变化。 
+* 5.结束，得到K个聚类
+
+```python
+#!/usr/bin/env python
+# coding: utf-8
+%matplotlib inline
+import time
+import numpy as np
+import tensorflow as tf
+import matplotlib.pyplot as plt
+
+from sklearn.datasets.samples_generator import make_blobs
+from sklearn.datasets.samples_generator import make_circles
+
+N = 200
+K = 4
+DATA_TYPE = 'blobs'
+MAX_ITERS = 1000
+colourindexes = [2, 1, 4, 3]
+# k-means不适用于circles数据，2个类足以demo这个问题
+if (DATA_TYPE == 'circle'):
+    K = 2
+    colourindexes = [2, 1]
+
+# 根据聚类中心生成测试数据
+centers = [(-2, -2), (-2, 1.5), (1.5, -2), (2, 1.5)]
+if (DATA_TYPE == 'circle'):
+    data, features = make_circles(
+        n_samples=N, shuffle=True, noise=0.01, factor=0.4)
+else:
+    data, features = make_blobs(n_samples=N, centers=centers,
+                                n_features=2, cluster_std=0.8,
+                                shuffle=False, random_state=42)
+    #fig, ax = plt.subplots()
+    #ax.scatter(np.asarray(centers).transpose()[0], np.asarray(
+    #    centers).transpose()[1], marker='o', s=250)
+    #plt.show()
+
+    fig, ax = plt.subplots()
+    ax.scatter(np.asarray(centers).transpose()[0], np.asarray(
+        centers).transpose()[1], marker='o', s=250)
+    ax.scatter(data.transpose()[0], data.transpose()[
+               1], marker='o', s=100, c=features, cmap=plt.cm.coolwarm)
+    plt.show()
+
+def bucket_mean(data, bucket_ids, num_buckets):
+    total = tf.unsorted_segment_sum(data, bucket_ids, num_buckets)
+    count = tf.unsorted_segment_sum(
+        tf.ones_like(data), bucket_ids, num_buckets)
+    return total / count
+
+start = time.time()
+points = tf.Variable(data)
+cluster_assignments = tf.Variable(tf.zeros([N], dtype=tf.int64))
+centroids = tf.Variable(tf.slice(points.initialized_value(), [0, 0], [K, 2]))
+
+rep_centroids = tf.reshape(tf.tile(centroids, [N, 1]), [N, K, 2])
+rep_points = tf.reshape(tf.tile(points, [1, K]), [N, K, 2])
+sum_squares = tf.reduce_sum(tf.square(rep_points - rep_centroids),
+                            reduction_indices=2)
+best_centroids = tf.argmin(sum_squares, 1)
+did_assignments_change = tf.reduce_any(
+    tf.not_equal(best_centroids, cluster_assignments))
+means = bucket_mean(points, best_centroids, K)
+
+with tf.control_dependencies([did_assignments_change]):
+    do_updates = tf.group(
+        centroids.assign(means),
+        cluster_assignments.assign(best_centroids))
+
+changed = True
+iters = 0
+
+sess = tf.Session()
+sess.run(tf.initialize_all_variables())
+while changed and iters < MAX_ITERS:
+    iters += 1
+    [changed, _] = sess.run([did_assignments_change, do_updates])
+    [centers, assignments] = sess.run([centroids, cluster_assignments])
+    fig, ax = plt.subplots()
+    ax.scatter(sess.run(points).transpose()[0], sess.run(points).transpose()[
+               1], marker='o', s=200, c=assignments, cmap=plt.cm.coolwarm)
+    ax.scatter(centers[:, 0], centers[:, 1], marker='^',
+               s=550, c=colourindexes, cmap=plt.cm.plasma)
+    ax.set_title('Iteration ' + str(iters))
+    # plt.savefig("kmeans" + str(iters) + ".png")
+    plt.show()
+
+fig, ax = plt.subplots()
+ax.scatter(sess.run(points).transpose()[0], sess.run(points).transpose()[
+           1], marker='o', s=200, c=assignments, cmap=plt.cm.coolwarm)
+ax.scatter(np.asarray(centers).transpose()[0], np.asarray(
+        centers).transpose()[1], marker='o', s=250, c=colourindexes, cmap=plt.cm.plasma)
+plt.show()
+
+
+end = time.time()
+print ("Found in %.2f seconds" % (end - start)), iters, "iterations"
+print "Centroids:", centers
+print "Cluster assignments:", assignments
+```
 
 #### 优点
 

From 287e1e31e3c713a3ca8a86b47a0aead8c96e38ea Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 11 Apr 2018 21:47:50 +0800
Subject: [PATCH 0740/1406] change page of CA

---
 assets/images/233.jpg   | Bin 0 -> 69519 bytes
 assets/images/234.jpg   | Bin 0 -> 80644 bytes
 assets/src/CA/CA.0.2.md |  16 ++++++++++++++++
 3 files changed, 16 insertions(+)
 create mode 100644 assets/images/233.jpg
 create mode 100644 assets/images/234.jpg

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Hq3{0zv;@Fk

literal 0
HcmV?d00001

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 5d490533..f27061b4 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -122,6 +122,22 @@ print "Centroids:", centers
 print "Cluster assignments:", assignments
 ```
 
+
+
+```python
+Found in 2.15 seconds 8 iterations
+Centroids: [[ 1.65289262 -2.04643427]
+ [-2.0763623   1.61204964]
+ [-2.08862822 -2.07255306]
+ [ 2.09831502  1.55936014]]
+Cluster assignments: [2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
+ 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 3 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
+ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3]
+```
+
 #### 优点
 
 * 简单、快速，可并行计算

From 0197bd0e3961eb484e99c3ef9f809325139d38d8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 21:51:41 +0800
Subject: [PATCH 0741/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index f27061b4..655a2e58 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -121,8 +121,13 @@ print ("Found in %.2f seconds" % (end - start)), iters, "iterations"
 print "Centroids:", centers
 print "Cluster assignments:", assignments
 ```
+<p align="center">
+<img width="400" align="center" src="../../images/233.jpg" />
+</p>
 
-
+<p align="center">
+<img width="400" align="center" src="../../images/234.jpg" />
+</p>
 
 ```python
 Found in 2.15 seconds 8 iterations

From 77fd409110efd816d1795cbf797020e019e20b02 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 22:05:15 +0800
Subject: [PATCH 0742/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 196 +++++++++++++++++-----------------------
 1 file changed, 83 insertions(+), 113 deletions(-)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 17e495fd..2d533d11 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -74,105 +74,79 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 ```python
 
 function [dw,ls] = learnlv3(w,p,z,n,a,t,e,gW,gA,d,lp,ls)
-%LEARNLV2 LVQ2 weight learning function.
-%
-% Syntax
-% 
-% [dW,LS] = learnlv3(w,p,n,a,T,lp,ls,Ttrain,C)
-% info = learnlv2(code)
-%
-% Description
-%
-% LEARNLV3 is the OLVQ weight learning function.
-%
-% LEARNLV2(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,
-% W - SxR weight matrix (or Sx1 bias vector).
-% P - RxQ input vectors (or ones(1,Q)).
-% Z - SxQ weighted input vectors.
-% N - SxQ net input vectors.
-% A - SxQ output vectors.
-% T - SxQ layer target vectors.
-% E - SxQ layer error vectors.
-% gW - SxR weight gradient with respect to performance.
-% gA - SxQ output gradient with respect to performance.
-% D - SxS neuron distances.
-% LP - Learning parameters, none, LP = [].
-% LS - Learning state, initially should be = [].
-% and returns,
-% dW - SxR weight (or bias) change matrix.
-% LS - New learning state.
-%
-% Learning occurs according to LEARNLV1's learning parameter,
-% shown here with its default value.
-% LP.lr - 0.01 - Learning rate
-%
-% LEARNLV2(CODE) returns useful information for each CODE string:
-% 'pnames' - Returns names of learning parameters.
-% 'pdefaults' - Returns default learning parameters.
-% 'needg' - Returns 1 if this function uses gW or gA.
-%
-% Examples
-%
-% Here we define a sample input P, output A, weight matrix W, and
-% output gradient gA for a layer with a 2-element input and 3 neurons.
-% We also define the learning rate LR.
-%
-% p = rand(2,1);
-% w = rand(3,2);
-% n = negdist(w,p);
-% a = compet(n);
-% gA = [-1;1; 1];
-% lp.lr = 0.5;
-%
-% Since LEARNLV2 only needs these values to calculate a weight
-% change (see Algorithm below), we will use them to do so.
-%
-% dW = learnlv3(w,p,n,a,lp,Ttrain,C)
-%
-% Network Use
-%
-% You can create a standard network that uses LEARNLV2 with NEWLVQ.
-%
-% To prepare the weights of layer i of a custom network
-% to learn with LEARNLV1:
-% 1) Set NET.trainFcn to 'trainwb1'.
-% (NET.trainParam will automatically become TRAINWB1's default parameters.)
-% 2) Set NET.adaptFcn to 'adaptwb'.
-% (NET.adaptParam will automatically become TRAINWB1's default parameters.)
-% 3) Set each NET.inputWeights{i,j}.learnFcn to 'learnlv2'.
-% Set each NET.layerWeights{i,j}.learnFcn to 'learnlv2'.
-% (Each weight learning parameter property will automatically
-% be set to LEARNLV2's default parameters.)
-%
-% To train the network (or enable it to adapt):
-% 1) Set NET.trainParam (or NET.adaptParam) properties as desired.
-% 2) Call TRAIN (or ADAPT).
-%
-% Algorithm
-%
-% LEARNLV3 calculates the weight change dW for a given neuron from
-% the neuron's input P, output A, train vector target T train, output
-% conexion matrix C and learning rate LR
-% according to the OLVQ rule, given i the index of the neuron whose
-% output a(i) is 1:
-%
-% dw(i,:) = +lr*(p-w(i,:)) if C(:,i) = Ttrain
-% = -lr*(p-w(i,:)) if C(:,i) ~= Ttrain
-%
-% if C(:,i) ~= Ttrain then the index j is found of the neuron with the
-% greatest net input n(k), from the neurons whose C(:,k)=Ttrain. This
-% neuron's weights are updated as follows:
-%
-% dw(j,:) = +lr*(p-w(i,:))
-%
-% See also LEARNLV1, ADAPTWB, TRAINWB, ADAPT, TRAIN.
-
-% Mark Beale, 11-31-97
-% Copyright (c) 1992-1998 by The MathWorks, Inc.
-% $Revision: 1.1.1.1 $
-
-% FUNCTION INFO
-% =============
+ LEARNLV2 LVQ2 weight learning function.
+
+ Syntax
+ 
+ [dW,LS] = learnlv3(w,p,n,a,T,lp,ls,Ttrain,C)
+ info = learnlv2(code)
+
+ Description
+
+ LEARNLV3 is the OLVQ weight learning function.
+
+ LEARNLV2(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,
+ W - SxR weight matrix (or Sx1 bias vector).
+ P - RxQ input vectors (or ones(1,Q)).
+ Z - SxQ weighted input vectors.
+ N - SxQ net input vectors.
+ A - SxQ output vectors.
+ T - SxQ layer target vectors.
+ E - SxQ layer error vectors.
+ gW - SxR weight gradient with respect to performance.
+ gA - SxQ output gradient with respect to performance.
+ D - SxS neuron distances.
+ LP - Learning parameters, none, LP = [].
+ LS - Learning state, initially should be = [].
+ and returns,
+ dW - SxR weight (or bias) change matrix.
+ LS - New learning state.
+
+ Learning occurs according to LEARNLV1's learning parameter,
+ shown here with its default value.
+ LP.lr - 0.01 - Learning rate
+
+ LEARNLV2(CODE) returns useful information for each CODE string:
+ 'pnames' - Returns names of learning parameters.
+ 'pdefaults' - Returns default learning parameters.
+ 'needg' - Returns 1 if this function uses gW or gA.
+
+# Examples
+
+# Here we define a sample input P, output A, weight matrix W, and
+# output gradient gA for a layer with a 2-element input and 3 neurons.
+# We also define the learning rate LR.
+
+ p = rand(2,1);
+ w = rand(3,2);
+ n = negdist(w,p);
+ a = compet(n);
+ gA = [-1;1; 1];
+ lp.lr = 0.5;
+
+# Since LEARNLV2 only needs these values to calculate a weight
+# change (see Algorithm below), we will use them to do so.
+
+ dW = learnlv3(w,p,n,a,lp,Ttrain,C)
+
+# Network Use
+
+ dw(i,:) = +lr*(p-w(i,:)) if C(:,i) = Ttrain
+ = -lr*(p-w(i,:)) if C(:,i) ~= Ttrain
+
+# if C(:,i) ~= Ttrain then the index j is found of the neuron with the
+# greatest net input n(k), from the neurons whose C(:,k)=Ttrain. This
+# neuron's weights are updated as follows:
+
+ dw(j,:) = +lr*(p-w(i,:))
+
+# See also LEARNLV1, ADAPTWB, TRAINWB, ADAPT, TRAIN.
+
+# Mark Beale, 11-31-97
+# Copyright (c) 1992-1998 by The MathWorks, Inc.
+# Revision: 1.1.1.1 $
+
+# FUNCTION INFO
 if isstr(w)
   switch lower(w)
   case 'name'
@@ -191,39 +165,35 @@ if isstr(w)
   return
 end
 
-
-% CALCULATION
-% ===========
-
 [S,R] = size(w);
 Q = size(p,2);
 pt = p';
 dw = zeros(S,R);
-% For each q...
+ For each q...
 for q=1:Q
 
-  % Find closest neuron k1 
+  Find closest neuron k1 
   nq = n(:,q);
   k1 = find(nq == max(nq));
   k1 = k1(1);
 
-  % Find next closest neuron k2 
+  Find next closest neuron k2 
   nq(k1) = -inf;
   k2 = find(nq == max(nq));
   k2 = k2(1);
 
 
-  % and if x falls into the window...
-  d1 = abs(n(k1,q)); % Shorter distance
-  d2 = abs(n(k2,q)); % Greater distance
+   and if x falls into the window...
+  d1 = abs(n(k1,q)); Shorter distance
+  d2 = abs(n(k2,q)); Greater distance
 
   if d2/d1 > ((1-lp.window)/(1+lp.window))
 
-      % then move incorrect neuron away from input,
-      % and the correct neuron towards the input
+      then move incorrect neuron away from input,
+      and the correct neuron towards the input
       ptq = pt(q,:);
       if gA(k1,q) ~= gA(k2,q)
-          % indicate the incorrect neuron with i, the other with j
+          indicate the incorrect neuron with i, the other with j
           if gA(k1,q) ~= 0
               i = k1;
               j = k2;
@@ -235,7 +205,7 @@ for q=1:Q
           dw(j,:) = dw(j,:) + lp.lr*(ptq - w(j,:));
       else
           dw(k1,:) = dw(k1,:) + 0.11*lp.window*(ptq-w(k1,:));
-       % dw(k2,:) = dw(k2,:) + 0.11*lp.window*(ptq-w(k2,:));
+       dw(k2,:) = dw(k2,:) + 0.11*lp.window*(ptq-w(k2,:));
       end
   end
 end

From 258bec9cf6021885f1084b74afabe1de0dbcb000 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 11 Apr 2018 22:08:28 +0800
Subject: [PATCH 0743/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 655a2e58..e711c852 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -25,7 +25,7 @@ k-means算法属于非监督学习方法。此算法以k为参数，把n 个对
 ```python
 #!/usr/bin/env python
 # coding: utf-8
-%matplotlib inline
+# matplotlib inline
 import time
 import numpy as np
 import tensorflow as tf

From c8098df002546ff104479f5c0dc9e4a781c4526f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 11 Apr 2018 22:10:56 +0800
Subject: [PATCH 0744/1406] change page of Ca

---
 README.md               | 4 ++--
 assets/src/CA/CA.0.3.md | 5 +++++
 2 files changed, 7 insertions(+), 2 deletions(-)
 create mode 100644 assets/src/CA/CA.0.3.md

diff --git a/README.md b/README.md
index 62bcc5e7..ba20d10e 100644
--- a/README.md
+++ b/README.md
@@ -112,8 +112,8 @@
      * [径向基函数（Radial Basis Function ，RBF)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.3.md)
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
-     * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
-     * [k-均值聚类(K-Means Clustering)]()
+     * [k-均值聚类(K-Means Clustering)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
+     * [模糊聚类(Fuzzy Clustering)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)]()
      * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   
diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
new file mode 100644
index 00000000..801ad100
--- /dev/null
+++ b/assets/src/CA/CA.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 模糊聚类(Fuzzy Clustering)

From 0b5738538a50fb6483b1ce231b90049707e4975c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 08:54:43 +0800
Subject: [PATCH 0745/1406] change page CA

---
 README.md               | 2 +-
 assets/src/CA/CA.0.3.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/CA/CA.0.3.md

diff --git a/README.md b/README.md
index 62bcc5e7..df52d96d 100644
--- a/README.md
+++ b/README.md
@@ -113,7 +113,7 @@
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
      * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
-     * [k-均值聚类(K-Means Clustering)]()
+     * [模糊聚类(Fuzzy Clustering)]()
      * [期望最大化(Expectation-Maximization)]()
      * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   
diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
new file mode 100644
index 00000000..801ad100
--- /dev/null
+++ b/assets/src/CA/CA.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 模糊聚类(Fuzzy Clustering)

From e1bf89dc3c40cc04e1deb4e244658a0d30b50aa7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 09:05:02 +0800
Subject: [PATCH 0746/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index df52d96d..05ee082d 100644
--- a/README.md
+++ b/README.md
@@ -113,7 +113,7 @@
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
      * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
-     * [模糊聚类(Fuzzy Clustering)]()
+     * [模糊聚类(Fuzzy Clustering)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)]()
      * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   

From 0d24e816b29f15d29e52b4f2a304eecae81eb88a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 09:06:14 +0800
Subject: [PATCH 0747/1406] Update CA.0.3.md

---
 assets/src/CA/CA.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
index 801ad100..ed53e8d1 100644
--- a/assets/src/CA/CA.0.3.md
+++ b/assets/src/CA/CA.0.3.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 模糊聚类(Fuzzy Clustering)
+模糊聚类算法,是一种基于目标函数的模糊聚类算法，主要用于数据的聚类分析。理论成熟，应用广泛，是一种优秀的聚类算法。

From e5cabbfd71a9d2ec7c888a2cc39ed69fd79e07d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 21:45:25 +0800
Subject: [PATCH 0748/1406] Update CA.0.3.md

---
 assets/src/CA/CA.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
index ed53e8d1..056274f9 100644
--- a/assets/src/CA/CA.0.3.md
+++ b/assets/src/CA/CA.0.3.md
@@ -2,5 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 模糊聚类(Fuzzy Clustering)
-模糊聚类算法,是一种基于目标函数的模糊聚类算法，主要用于数据的聚类分析。理论成熟，应用广泛，是一种优秀的聚类算法。
+#### 模糊c-均值聚类算法(Fuzzy C-means Algorithm)
+模糊c-均值聚类算法算法,是一种基于目标函数的模糊聚类算法，主要用于数据的聚类分析。理论成熟，应用广泛，是一种优秀的聚类算法。

From fe9227536bebfc3c2e06c88213f7a7eb09947779 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 21:46:30 +0800
Subject: [PATCH 0749/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 05ee082d..6132faa0 100644
--- a/README.md
+++ b/README.md
@@ -113,7 +113,7 @@
      * [线性判别分析（Linear Discriminate Analysis ，LDA)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/KBO/KBO.0.4.md)
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
      * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
-     * [模糊聚类(Fuzzy Clustering)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
+     * [模糊c-均值聚类算法(Fuzzy C-means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)]()
      * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   

From 458388ebe4977cbaaccaae99d0cfed9777eedf47 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 12 Apr 2018 21:56:39 +0800
Subject: [PATCH 0750/1406] change page of CA

---
 assets/images/235.jpg   | Bin 0 -> 706 bytes
 assets/src/CA/CA.0.3.md |   8 +++++++-
 2 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/235.jpg

diff --git a/assets/images/235.jpg b/assets/images/235.jpg
new file mode 100644
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GIT binary patch
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diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
index 056274f9..5f7f8d32 100644
--- a/assets/src/CA/CA.0.3.md
+++ b/assets/src/CA/CA.0.3.md
@@ -3,4 +3,10 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 模糊c-均值聚类算法(Fuzzy C-means Algorithm)
-模糊c-均值聚类算法算法,是一种基于目标函数的模糊聚类算法，主要用于数据的聚类分析。理论成熟，应用广泛，是一种优秀的聚类算法。
+模糊c-均值聚类算法,是一种基于目标函数的模糊聚类算法，主要用于数据的聚类分析。理论成熟，应用广泛，是一种优秀的聚类算法。
+模糊c-均值聚类算法输入就是一个待聚类的数据集，每一个数据都有p个特征。它的输出是一个c行n列的矩阵U，c刚才提到是聚类数目，n是数据集中元素的个数，用这个矩阵就可以表示分类的结果，因为你看某一列，表示的就是这个元素对各个类的隶属程度，哪一个值最大，就说这个元素属于哪一类。
+
+还有一个输出是各个类的聚类中心向量集合V，一共有c个元素。每个元素也是有p维的。
+<p align="center">
+<img width="400" align="center" src="../../images/235.jpg" />
+</p>
\ No newline at end of file

From 22e42051904e87abbd6554be5abb048dbb7071d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 12 Apr 2018 21:59:03 +0800
Subject: [PATCH 0751/1406] change page of CA

---
 assets/images/236.jpg   | Bin 0 -> 706 bytes
 assets/images/237.jpg   | Bin 0 -> 1282 bytes
 assets/src/CA/CA.0.3.md |  10 +++++++++-
 3 files changed, 9 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/236.jpg
 create mode 100644 assets/images/237.jpg

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diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
index 5f7f8d32..805afd3c 100644
--- a/assets/src/CA/CA.0.3.md
+++ b/assets/src/CA/CA.0.3.md
@@ -8,5 +8,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 还有一个输出是各个类的聚类中心向量集合V，一共有c个元素。每个元素也是有p维的。
 <p align="center">
-<img width="400" align="center" src="../../images/235.jpg" />
+<img width="200" align="center" src="../../images/235.jpg" />
+</p>
+
+<p align="center">
+<img width="200" align="center" src="../../images/236.jpg" />
+</p>
+
+<p align="center">
+<img width="200" align="center" src="../../images/237.jpg" />
 </p>
\ No newline at end of file

From b75a15dcd908bfacaafde61dc134c48b972e6ef7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 22:13:49 +0800
Subject: [PATCH 0752/1406] Update CA.0.3.md

---
 assets/src/CA/CA.0.3.md | 186 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 185 insertions(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.3.md b/assets/src/CA/CA.0.3.md
index 805afd3c..47772662 100644
--- a/assets/src/CA/CA.0.3.md
+++ b/assets/src/CA/CA.0.3.md
@@ -17,4 +17,188 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 <p align="center">
 <img width="200" align="center" src="../../images/237.jpg" />
-</p>
\ No newline at end of file
+</p>
+
+
+#### 应用示例
+
+```python
+typedef struct{
+    double x;
+    double y;
+} Position;
+
+
+//len:节点数量
+//range：节点x、y值的范围
+Position *randomPosition(int len, int range){
+    srand((unsigned)time(NULL));
+    Position *allPos = (Position *)malloc(len * sizeof(Position));
+
+    short a = 1; 
+    for (int i = 0; i < len; ++i)
+    {
+        if (a)
+        {
+            allPos[i].x = (double)rand() / 2147483647 * range;
+            allPos[i].y = (double)rand() / 2147483647 * range;
+            a = 0;
+        }
+        else if (!a)
+        {
+            allPos[i].x = (double)rand() / 2147483647 * range+50;
+            allPos[i].y = (double)rand() / 2147483647 * range+50;
+            a = 1;
+        }
+    }
+    return allPos;
+}
+
+//posNum：节点数量
+//clusterNum：聚类中心数量
+double **init(int posNum, int clusterNum){
+    double **u = (double **)malloc(sizeof(double *) * clusterNum);
+    for (int i = 0; i <clusterNum; ++i)
+    {
+        u[i] = (double *)malloc(sizeof(double) * posNum);
+    }
+    srand((unsigned)time(NULL));
+    double sum;
+    //初始化u：sigmaU[i]=1
+    for (int i = 0; i < posNum; ++i)
+    {
+        sum=1;
+        for (int x = 0; x < clusterNum - 1; ++x)
+        {
+            u[x][i] = ((double)rand() / 2147483647) * sum;
+            sum -= u[x][i];
+            printf("u[%d][%d]:%f ",x,i,u[x][i]);
+        }
+        u[clusterNum-1][i]=sum;
+        printf("u[%d][%d]:%f\n",clusterNum-1,i,u[clusterNum-1][i]);
+    }
+    return u;
+}
+
+//allPos：节点数组
+//len：节点数量
+void outputPos(Position *allPos, int len){
+
+    for (int i = 0; i < len; ++i)
+        printf("position %d:(%f,%f)\n", i, allPos[i].x, allPos[i].y);
+    return;
+}
+
+
+//u：隶属度矩阵
+//posNum：节点数量
+//i:第i个聚类中心
+//m：隶属度因子
+double sumUi(double** u,int posNum,int i,int m){
+    double res=0;
+    for(int x=0;x<posNum;++x)
+        res+=pow(u[i][x],m);
+    return res;
+}
+
+//u：隶属度矩阵
+//allPos:节点数组
+//posNum：节点数量
+//i:第i个聚类中心
+//m：隶属度因子
+double sumXi(double** u,Position* allPos,int posNum,int i,int m){
+    double res=0;
+    for(int x=0;x<posNum;++x)
+        res+=allPos[x].x*pow(u[i][x],m);
+    return res;
+}
+
+//u：隶属度矩阵
+//posNum：节点数量
+//i:第i个聚类中心
+//m：隶属度因子
+double sumYi(double** u,Position* allPos,int posNum,int i,int m){
+    double res=0;
+    for(int x=0;x<posNum;++x)
+        res+=allPos[x].y*pow(u[i][x],m);
+    return res;
+}
+
+//pos:第j个节点
+//cluster:聚类中心数组
+//clusterNum：聚类中心数量
+//m：隶属度因子
+double sumDis(Position pos,Position* cluster,int clusterNum,int m){
+    double res=0;
+    for(int i=0;i<clusterNum;++i)
+        res+=(double)1/pow(pow(pos.x-cluster[i].x,2)+pow(pos.y-cluster[i].y,2),(double)1/(m-1));
+    return res;
+}
+
+//allPos:节点数组
+//cluster:聚类中心数组
+//u：隶属度矩阵
+//posNum：节点数量
+//clusterNum：聚类中心数量
+//m：隶属度因子
+void updateCluster(Position* allPos,Position* cluster,double** u,int posNum,int clusterNum,int m){
+    for(int i=0;i<clusterNum;++i){
+        cluster[i].x=sumXi(u,allPos,posNum,i,m)/sumUi(u,posNum,i,m);
+        cluster[i].y=sumYi(u,allPos,posNum,i,m)/sumUi(u,posNum,i,m);
+    }
+}
+
+//allPos:节点数组
+//cluster:聚类中心数组
+//u：隶属度矩阵
+//posNum：节点数量
+//clusterNum：聚类中心数量
+//m：隶属度因子
+void updateU(Position* allPos,Position* cluster,double** u,int posNum,int clusterNum,int m){
+    double disXI;
+    for(int i=0;i<clusterNum;++i)
+    for(int x=0;x<posNum;++x){
+        disXI=pow(pow(allPos[x].x-cluster[i].x,2)+pow(allPos[x].y-cluster[i].y,2),(double)1/(m-1));
+        u[i][x]=(double)1/(disXI*sumDis(allPos[x],cluster,clusterNum,m));
+    }
+}
+
+//allPos:节点数组
+//cluster:聚类中心数组
+//u：隶属度矩阵
+//posNum：节点数量
+//clusterNum：聚类中心数量
+//m：隶属度因子
+void outpuCost_fun(Position* allPos,Position* cluster,double** u,int posNum,int clusterNum,int m){
+    double res=0;
+    for(int i=0;i<clusterNum;++i)
+    for(int x=0;x<posNum;++x)
+        res+=(pow(u[i][x],m)*(pow(allPos[x].x-cluster[i].x,2)+pow(allPos[x].y-cluster[i].y,2)));
+    printf("costFun:%f\n",res);
+}
+
+void outputU(double** u,int posNum,int clusterNum){
+    for(int i=0;i<posNum;++i){
+        for(int x=0;x<clusterNum;++x)
+            printf("u[%d][%d]:%f ",x,i,u[x][i]);
+        printf("\n");
+    }
+}
+void fuzzy_Cmeans(int posNum,int clusterNum, int m, int iterTime,int range)
+{
+    Position* allPos=randomPosition(posNum,range);
+    Position* cluster=(Position*)malloc(sizeof(Position)*clusterNum);
+    double** u=init(posNum,clusterNum);
+    for (int i = 0; i < iterTime; ++i)
+    {   
+        updateCluster(allPos,cluster,u,posNum,clusterNum,m);
+        updateU(allPos,cluster,u,posNum,clusterNum,m);
+        outpuCost_fun(allPos,cluster,u,posNum,clusterNum,m);
+        //outputU(u,posNum,clusterNum);
+    }
+}
+int main(){
+    fuzzy_Cmeans(100,10,3,500,500);
+    return 0;
+}
+```

From 98522d1988ed4e363338105ee38c55603ffb8d55 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 12 Apr 2018 22:17:28 +0800
Subject: [PATCH 0753/1406] change page of CA

---
 assets/src/CA/CA.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/CA/CA.0.4.md

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
new file mode 100644
index 00000000..cada466a
--- /dev/null
+++ b/assets/src/CA/CA.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 期望最大化(Expectation-Maximization)

From 834590f369df20dcdd752c342984b492708ead73 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 12 Apr 2018 22:19:04 +0800
Subject: [PATCH 0754/1406] change page of CA

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 6132faa0..ae4407e5 100644
--- a/README.md
+++ b/README.md
@@ -114,7 +114,7 @@
  * [聚类算法(Cluster analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.1.md)
      * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
      * [模糊c-均值聚类算法(Fuzzy C-means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
-     * [期望最大化(Expectation-Maximization)]()
+     * [期望最大化(Expectation-Maximization)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.4.md)
      * [聚类分析(Cluster Analysis)]()
  * [关联规则学习]()   
      * [Apriori算法]() 

From 11b0c4056d1b186a7dc9bce9686f412f45e5513a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 12 Apr 2018 22:22:19 +0800
Subject: [PATCH 0755/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index cada466a..00d932fa 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 期望最大化(Expectation-Maximization)
+期望最大化（Expectation-maximization）算法在统计中被用于寻找，依赖于不可观察的隐性变量的概率模型中，参数的最大似然估计。

From 73857e04353601568980feb99848b8ddd4854fb0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 20:40:20 +0800
Subject: [PATCH 0756/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 00d932fa..0f686bd0 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 期望最大化(Expectation-Maximization)
-期望最大化（Expectation-maximization）算法在统计中被用于寻找，依赖于不可观察的隐性变量的概率模型中，参数的最大似然估计。
+期望最大化（Expectation-maximization）算法是由Dempster等人1977年提出的统计模型参数估计的一种算法。它采用的迭代交替搜索方式可以简单有效的求解最大似然函数估计问题。已知的概率模型内部存在隐含的变量，导致了不能直接用极大似然法来估计参数，期望最大化（Expectation-maximization）就是通过迭代逼近的方式用实际的值带入求解模型内部参数的算法。它在当代的工业、商业和科学研究领域发挥了重要的作用。

From fa996b1a8d4c388400160038c32e8dfcfaf77936 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 20:41:34 +0800
Subject: [PATCH 0757/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 0f686bd0..061f771e 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -4,3 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 期望最大化(Expectation-Maximization)
 期望最大化（Expectation-maximization）算法是由Dempster等人1977年提出的统计模型参数估计的一种算法。它采用的迭代交替搜索方式可以简单有效的求解最大似然函数估计问题。已知的概率模型内部存在隐含的变量，导致了不能直接用极大似然法来估计参数，期望最大化（Expectation-maximization）就是通过迭代逼近的方式用实际的值带入求解模型内部参数的算法。它在当代的工业、商业和科学研究领域发挥了重要的作用。
+
+期望最大化算法是一种启发式的迭代算法，是一种从“不完全数据”中求极大似然的方法。在人工智能、机器学习、数理统计、模式识别等许多应用都需要进行模型的参数估计，极大似然估计和极大后验似然估计是必要进行的。然而在理想的可观察变量模型中，即变量分布式均匀的时候，做出以上两个估计是显然可以的。但是实际的情况往往不是这样，某些变量并不是可以观察的，对这类模型进行极大似然估计就比较复杂了。期望最大化算法是解决对于不可观察变量进行似然估计的一种方法。
+期望最大化算法的提出主要是用来计算后验分布的众数或极大似然估计。然而，近年来它引起了统计学家的极大兴趣，在统计领域得到了广泛的应用。该方法广泛的应用于缺损数据、截尾数据、成群数据、带有复杂参数的数据等不完整数据。期望最大化算法流行的原因，一是在于它的理论简单化和一般性，二是许多应用都能够纳入到期望最大化算法的范畴，期望最大化算法已经成为统计学上的一个标准工具。
+EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988），而且它是用于学习部分可观察马尔可夫模型（Partially Observable Markov Model）的广泛使用的Baum-Welch前向后向算法的基础。

From 92013488a0b09740f1878b8de6ef2669dc699539 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 13 Apr 2018 20:53:21 +0800
Subject: [PATCH 0758/1406] change page

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From 9a8150bc9c8640cea1536ecbb213c866e458eca5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 20:59:53 +0800
Subject: [PATCH 0759/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 061f771e..8ab835b8 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -8,3 +8,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 期望最大化算法是一种启发式的迭代算法，是一种从“不完全数据”中求极大似然的方法。在人工智能、机器学习、数理统计、模式识别等许多应用都需要进行模型的参数估计，极大似然估计和极大后验似然估计是必要进行的。然而在理想的可观察变量模型中，即变量分布式均匀的时候，做出以上两个估计是显然可以的。但是实际的情况往往不是这样，某些变量并不是可以观察的，对这类模型进行极大似然估计就比较复杂了。期望最大化算法是解决对于不可观察变量进行似然估计的一种方法。
 期望最大化算法的提出主要是用来计算后验分布的众数或极大似然估计。然而，近年来它引起了统计学家的极大兴趣，在统计领域得到了广泛的应用。该方法广泛的应用于缺损数据、截尾数据、成群数据、带有复杂参数的数据等不完整数据。期望最大化算法流行的原因，一是在于它的理论简单化和一般性，二是许多应用都能够纳入到期望最大化算法的范畴，期望最大化算法已经成为统计学上的一个标准工具。
 EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988），而且它是用于学习部分可观察马尔可夫模型（Partially Observable Markov Model）的广泛使用的Baum-Welch前向后向算法的基础。
+
+给定的训练样本是<img width="200" align="center" src="../../images/238.jpg" />，样例间独立，我们想找到每个样例隐含的类别z，能使得p(x,z)最大。p(x,z)的最大似然估计如下：<img width="200" align="center" src="../../images/239.jpg" />

From 15f6cfbc067f19220a72730c90f4defc079202cc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:04:21 +0800
Subject: [PATCH 0760/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 8ab835b8..59e76380 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -9,4 +9,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 期望最大化算法的提出主要是用来计算后验分布的众数或极大似然估计。然而，近年来它引起了统计学家的极大兴趣，在统计领域得到了广泛的应用。该方法广泛的应用于缺损数据、截尾数据、成群数据、带有复杂参数的数据等不完整数据。期望最大化算法流行的原因，一是在于它的理论简单化和一般性，二是许多应用都能够纳入到期望最大化算法的范畴，期望最大化算法已经成为统计学上的一个标准工具。
 EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988），而且它是用于学习部分可观察马尔可夫模型（Partially Observable Markov Model）的广泛使用的Baum-Welch前向后向算法的基础。
 
-给定的训练样本是<img width="200" align="center" src="../../images/238.jpg" />，样例间独立，我们想找到每个样例隐含的类别z，能使得p(x,z)最大。p(x,z)的最大似然估计如下：<img width="200" align="center" src="../../images/239.jpg" />
+给定的训练样本是<img width="80" align="center" src="../../images/238.jpg" />，样例间独立，我们想找到每个样例隐含的类别z，能使得p(x,z)最大。p(x,z)的最大似然估计如下：
+<p align="center">
+<img width="200" align="center" src="../../images/239.jpg" />
+</p>
+
+由jensen不等式可得：
+<p align="center">
+<img width="200" align="center" src="../../images/240.jpg" />
+</p>
+
+对于每一个样例i，让<img width="80" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="80" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：

From 29871d8f5f6ea4c6f7b77923f62a0df1ffb62c28 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:04:47 +0800
Subject: [PATCH 0761/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 59e76380..7263ac06 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -11,12 +11,12 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 给定的训练样本是<img width="80" align="center" src="../../images/238.jpg" />，样例间独立，我们想找到每个样例隐含的类别z，能使得p(x,z)最大。p(x,z)的最大似然估计如下：
 <p align="center">
-<img width="200" align="center" src="../../images/239.jpg" />
+<img width="300" align="center" src="../../images/239.jpg" />
 </p>
 
 由jensen不等式可得：
 <p align="center">
-<img width="200" align="center" src="../../images/240.jpg" />
+<img width="300" align="center" src="../../images/240.jpg" />
 </p>
 
-对于每一个样例i，让<img width="80" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="80" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
+对于每一个样例i，让<img width="30" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="30" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：

From f947cd328d2e08b9a488c76c9bb5c94fc34e4c6c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:05:18 +0800
Subject: [PATCH 0762/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 7263ac06..8fdef8f1 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -16,7 +16,7 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 由jensen不等式可得：
 <p align="center">
-<img width="300" align="center" src="../../images/240.jpg" />
+<img width="500" align="center" src="../../images/240.jpg" />
 </p>
 
-对于每一个样例i，让<img width="30" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="30" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
+对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：

From a702e86d2c7c0f57e9d2b6dd5b9b80fb1f5ca8e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:05:44 +0800
Subject: [PATCH 0763/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 8fdef8f1..98e0a3ea 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -16,7 +16,7 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 由jensen不等式可得：
 <p align="center">
-<img width="500" align="center" src="../../images/240.jpg" />
+<img width="680" align="center" src="../../images/240.jpg" />
 </p>
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：

From 244fb5a0daca16e1e151ce33f4ae530de97f56bb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:06:11 +0800
Subject: [PATCH 0764/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 98e0a3ea..95ce979a 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -20,3 +20,6 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 </p>
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
+<p align="center">
+<img width="680" align="center" src="../../images/244.jpg" />
+</p>

From 911372624e3455fc2e2cc85a1de8c1335ecf7670 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:06:44 +0800
Subject: [PATCH 0765/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 95ce979a..881676a8 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -21,5 +21,11 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
 <p align="center">
-<img width="680" align="center" src="../../images/244.jpg" />
+<img width="300" align="center" src="../../images/244.jpg" />
+</p>
+
+由于Q是随机变量z的概率密度函数，因此，可以得到：分子的和等于c（分子分母都对所有z求和：多个等式分子分母相加不变，这个认为每个样例的两个概率比值都是c）。
+
+<p align="center">
+<img width="300" align="center" src="../../images/245.jpg" />
 </p>

From 0f31d3a9a192fe0c61fd54254a352ca731a27d9a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:07:02 +0800
Subject: [PATCH 0766/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 881676a8..59ed7480 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -21,11 +21,11 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
 <p align="center">
-<img width="300" align="center" src="../../images/244.jpg" />
+<img width="100" align="center" src="../../images/244.jpg" />
 </p>
 
 由于Q是随机变量z的概率密度函数，因此，可以得到：分子的和等于c（分子分母都对所有z求和：多个等式分子分母相加不变，这个认为每个样例的两个概率比值都是c）。
 
 <p align="center">
-<img width="300" align="center" src="../../images/245.jpg" />
+<img width="100" align="center" src="../../images/245.jpg" />
 </p>

From 30d7788217e3b82329e3acb06070dfc79eb99ae5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:07:25 +0800
Subject: [PATCH 0767/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 59ed7480..bb91a37d 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -21,7 +21,7 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
 <p align="center">
-<img width="100" align="center" src="../../images/244.jpg" />
+<img width="280" align="center" src="../../images/244.jpg" />
 </p>
 
 由于Q是随机变量z的概率密度函数，因此，可以得到：分子的和等于c（分子分母都对所有z求和：多个等式分子分母相加不变，这个认为每个样例的两个概率比值都是c）。

From cae9e22d0495ba06e73ca4d51ca8bc0f932a0df5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:07:52 +0800
Subject: [PATCH 0768/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index bb91a37d..d5365051 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -21,11 +21,11 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 
 对于每一个样例i，让<img width="20" align="center" src="../../images/241.jpg" />表示该样例隐含变量z的某种分布，<img width="20" align="center" src="../../images/241.jpg" />满足的条件是<img width="80" align="center" src="../../images/242.jpg" />，<img width="80" align="center" src="../../images/243.jpg" />。由此，可以确定式子的下界，然后不断的提高此下界达到逼近最后真实值的目的值，这个不等式变成等式为止，然后再依据jensen不等式，当不等式变为等式的时候，当且仅当，也就是说X是常量，推出就是下面的公式：
 <p align="center">
-<img width="280" align="center" src="../../images/244.jpg" />
+<img width="130" align="center" src="../../images/244.jpg" />
 </p>
 
 由于Q是随机变量z的概率密度函数，因此，可以得到：分子的和等于c（分子分母都对所有z求和：多个等式分子分母相加不变，这个认为每个样例的两个概率比值都是c）。
 
 <p align="center">
-<img width="100" align="center" src="../../images/245.jpg" />
+<img width="230" align="center" src="../../images/245.jpg" />
 </p>

From 45e1e0cfbb48392c46e687b106015b3740c46342 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:09:21 +0800
Subject: [PATCH 0769/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index d5365051..6e8ee145 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -29,3 +29,17 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 <p align="center">
 <img width="230" align="center" src="../../images/245.jpg" />
 </p>
+
+
+由此可得出EM算法的一般过程：循环重复E步骤和M步骤直到收敛。
+E步骤：对于每一个i，计算：
+
+<p align="center">
+<img width="230" align="center" src="../../images/246.jpg" />
+</p>
+
+M步骤计算:
+
+<p align="center">
+<img width="230" align="center" src="../../images/247.jpg" />
+</p>

From a69aec9496d39fd32e1a3c4f73a3face75d5cd34 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:10:21 +0800
Subject: [PATCH 0770/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 6e8ee145..c9091725 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -35,11 +35,17 @@ EM算法还是许多非监督聚类算法的基础（如Cheeseman et al. 1988）
 E步骤：对于每一个i，计算：
 
 <p align="center">
-<img width="230" align="center" src="../../images/246.jpg" />
+<img width="260" align="center" src="../../images/246.jpg" />
 </p>
 
 M步骤计算:
 
 <p align="center">
-<img width="230" align="center" src="../../images/247.jpg" />
+<img width="280" align="center" src="../../images/247.jpg" />
 </p>
+
+#### EM算法的特点编辑
+
+* 1.EM算法中，由于似然函数是有界的，并且算法的每一步迭代都使似然函数增加，根据单调有界定理可以证明EM算法具有收敛性。
+* 2.EM算法是一种初始值敏感的算法，选取不同初始参数会有不同的最终结果；
+* 3.EM算法得到的不会是全局最优，每次迭代逼近的都是当前的局部最优。

From 9b9e66738677fd1dbe719b01ca3de9e4306222ef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:13:07 +0800
Subject: [PATCH 0771/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index c9091725..5c4cb413 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -44,7 +44,7 @@ M步骤计算:
 <img width="280" align="center" src="../../images/247.jpg" />
 </p>
 
-#### EM算法的特点编辑
+#### 期望最大化算法的特点
 
 * 1.EM算法中，由于似然函数是有界的，并且算法的每一步迭代都使似然函数增加，根据单调有界定理可以证明EM算法具有收敛性。
 * 2.EM算法是一种初始值敏感的算法，选取不同初始参数会有不同的最终结果；

From 84ddf4e7bd672ecd4a3114efc8f0857738be4598 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 13 Apr 2018 21:24:25 +0800
Subject: [PATCH 0772/1406] change page

---
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 assets/images/246.jpg | Bin 9489 -> 2767 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)

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From 43a17749d90c7dad47207b2f0492a1fe73da8b0f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:31:51 +0800
Subject: [PATCH 0773/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 162 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 162 insertions(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 5c4cb413..cd2d4647 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -44,6 +44,168 @@ M步骤计算:
 <img width="280" align="center" src="../../images/247.jpg" />
 </p>
 
+
+#### 应用示例
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import multivariate_normal
+
+DEBUG = True
+
+
+# 调试输出函数
+# 由全局变量 DEBUG 控制输出
+def debug(*args, **kwargs):
+    global DEBUG
+    if DEBUG:
+        print(*args, **kwargs)
+
+
+
+# 第 k 个模型的高斯分布密度函数
+# 每 i 行表示第 i 个样本在各模型中的出现概率
+# 返回一维列表
+
+def phi(Y, mu_k, cov_k):
+    norm = multivariate_normal(mean=mu_k, cov=cov_k)
+    return norm.pdf(Y)
+
+# E 步：计算每个模型对样本的响应度
+# Y 为样本矩阵，每个样本一行，只有一个特征时为列向量
+# mu 为均值多维数组，每行表示一个样本各个特征的均值
+# cov 为协方差矩阵的数组，alpha 为模型响应度数组
+def getExpectation(Y, mu, cov, alpha):
+    # 样本数
+    N = Y.shape[0]
+    # 模型数
+    K = alpha.shape[0]
+
+    # 为避免使用单个高斯模型或样本，导致返回结果的类型不一致
+    # 因此要求样本数和模型个数必须大于1
+    assert N > 1, "There must be more than one sample!"
+    assert K > 1, "There must be more than one gaussian model!"
+
+    # 响应度矩阵，行对应样本，列对应响应度
+    gamma = np.mat(np.zeros((N, K)))
+
+    # 计算各模型中所有样本出现的概率，行对应样本，列对应模型
+    prob = np.zeros((N, K))
+    for k in range(K):
+        prob[:, k] = phi(Y, mu[k], cov[k])
+    prob = np.mat(prob)
+
+    # 计算每个模型对每个样本的响应度
+    for k in range(K):
+        gamma[:, k] = alpha[k] * prob[:, k]
+    for i in range(N):
+        gamma[i, :] /= np.sum(gamma[i, :])
+    return gamma
+
+# M 步：迭代模型参数
+# Y 为样本矩阵，gamma 为响应度矩阵
+def maximize(Y, gamma):
+    # 样本数和特征数
+    N, D = Y.shape
+    # 模型数
+    K = gamma.shape[1]
+
+    #初始化参数值
+    mu = np.zeros((K, D))
+    cov = []
+    alpha = np.zeros(K)
+
+    # 更新每个模型的参数
+    for k in range(K):
+        # 第 k 个模型对所有样本的响应度之和
+        Nk = np.sum(gamma[:, k])
+        # 更新 mu
+        # 对每个特征求均值
+        for d in range(D):
+            mu[k, d] = np.sum(np.multiply(gamma[:, k], Y[:, d])) / Nk
+        # 更新 cov
+        cov_k = np.mat(np.zeros((D, D)))
+        for i in range(N):
+            cov_k += gamma[i, k] * (Y[i] - mu[k]).T * (Y[i] - mu[k]) / Nk
+        cov.append(cov_k)
+        # 更新 alpha
+        alpha[k] = Nk / N
+    cov = np.array(cov)
+    return mu, cov, alpha
+# 数据预处理
+# 将所有数据都缩放到 0 和 1 之间
+def scale_data(Y):
+    # 对每一维特征分别进行缩放
+    for i in range(Y.shape[1]):
+        max_ = Y[:, i].max()
+        min_ = Y[:, i].min()
+        Y[:, i] = (Y[:, i] - min_) / (max_ - min_)
+    debug("Data scaled.")
+    return Y
+
+# 初始化模型参数
+# shape 是表示样本规模的二元组，(样本数, 特征数)
+# K 表示模型个数
+def init_params(shape, K):
+    N, D = shape
+    mu = np.random.rand(K, D)
+    cov = np.array([np.eye(D)] * K)
+    alpha = np.array([1.0 / K] * K)
+    debug("Parameters initialized.")
+    debug("mu:", mu, "cov:", cov, "alpha:", alpha, sep="\n")
+    return mu, cov, alpha
+    
+# 高斯混合模型 EM 算法
+# 给定样本矩阵 Y，计算模型参数
+# K 为模型个数
+# times 为迭代次数
+def GMM_EM(Y, K, times):
+    Y = scale_data(Y)
+    mu, cov, alpha = init_params(Y.shape, K)
+    for i in range(times):
+        gamma = getExpectation(Y, mu, cov, alpha)
+        mu, cov, alpha = maximize(Y, gamma)
+    debug("{sep} Result {sep}".format(sep="-" * 20))
+    debug("mu:", mu, "cov:", cov, "alpha:", alpha, sep="\n")
+    return mu, cov, alpha
+```
+
+```python
+main.py 文件：
+import matplotlib.pyplot as plt
+from gmm import *
+
+# 设置调试模式
+DEBUG = True
+
+# 载入数据
+Y = np.loadtxt("gmm.data")
+matY = np.matrix(Y, copy=True)
+
+# 模型个数，即聚类的类别个数
+K = 2
+
+# 计算 GMM 模型参数
+mu, cov, alpha = GMM_EM(matY, K, 100)
+
+# 根据 GMM 模型，对样本数据进行聚类，一个模型对应一个类别
+N = Y.shape[0]
+# 求当前模型参数下，各模型对样本的响应度矩阵
+gamma = getExpectation(matY, mu, cov, alpha)
+# 对每个样本，求响应度最大的模型下标，作为其类别标识
+category = gamma.argmax(axis=1).flatten().tolist()[0]
+# 将每个样本放入对应类别的列表中
+class1 = np.array([Y[i] for i in range(N) if category[i] == 0])
+class2 = np.array([Y[i] for i in range(N) if category[i] == 1])
+
+# 绘制聚类结果
+plt.plot(class1[:, 0], class1[:, 1], 'rs', label="class1")
+plt.plot(class2[:, 0], class2[:, 1], 'bo', label="class2")
+plt.legend(loc="best")
+plt.title("GMM Clustering By EM Algorithm")
+plt.show()
+```
+
 #### 期望最大化算法的特点
 
 * 1.EM算法中，由于似然函数是有界的，并且算法的每一步迭代都使似然函数增加，根据单调有界定理可以证明EM算法具有收敛性。

From daa4cb2f3e539c343abed655ba7dae969ceca728 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Apr 2018 21:32:26 +0800
Subject: [PATCH 0774/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index cd2d4647..fad35276 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -52,17 +52,12 @@ import matplotlib.pyplot as plt
 from scipy.stats import multivariate_normal
 
 DEBUG = True
-
-
 # 调试输出函数
 # 由全局变量 DEBUG 控制输出
 def debug(*args, **kwargs):
     global DEBUG
     if DEBUG:
         print(*args, **kwargs)
-
-
-
 # 第 k 个模型的高斯分布密度函数
 # 每 i 行表示第 i 个样本在各模型中的出现概率
 # 返回一维列表
@@ -132,6 +127,7 @@ def maximize(Y, gamma):
         alpha[k] = Nk / N
     cov = np.array(cov)
     return mu, cov, alpha
+    
 # 数据预处理
 # 将所有数据都缩放到 0 和 1 之间
 def scale_data(Y):

From dcab5410892e5a4c8cfca00a067974fd2892e619 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 14 Apr 2018 02:30:02 +0000
Subject: [PATCH 0775/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index fad35276..dce7859c 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 期望最大化(Expectation-Maximization)
+
 期望最大化（Expectation-maximization）算法是由Dempster等人1977年提出的统计模型参数估计的一种算法。它采用的迭代交替搜索方式可以简单有效的求解最大似然函数估计问题。已知的概率模型内部存在隐含的变量，导致了不能直接用极大似然法来估计参数，期望最大化（Expectation-maximization）就是通过迭代逼近的方式用实际的值带入求解模型内部参数的算法。它在当代的工业、商业和科学研究领域发挥了重要的作用。
 
 期望最大化算法是一种启发式的迭代算法，是一种从“不完全数据”中求极大似然的方法。在人工智能、机器学习、数理统计、模式识别等许多应用都需要进行模型的参数估计，极大似然估计和极大后验似然估计是必要进行的。然而在理想的可观察变量模型中，即变量分布式均匀的时候，做出以上两个估计是显然可以的。但是实际的情况往往不是这样，某些变量并不是可以观察的，对这类模型进行极大似然估计就比较复杂了。期望最大化算法是解决对于不可观察变量进行似然估计的一种方法。

From f131d2b09328a8facb7bd206921df4502b2fdb00 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 15 Apr 2018 00:20:09 +0000
Subject: [PATCH 0776/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index dce7859c..60ffbba1 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -47,6 +47,7 @@ M步骤计算:
 
 
 #### 应用示例
+
 ```python
 import numpy as np
 import matplotlib.pyplot as plt

From 77d76e2656f836d93b5e8398cb49509153d99d56 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 09:08:48 +0800
Subject: [PATCH 0777/1406] Update CA.0.4.md

---
 assets/src/CA/CA.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.4.md b/assets/src/CA/CA.0.4.md
index 60ffbba1..dad1929f 100644
--- a/assets/src/CA/CA.0.4.md
+++ b/assets/src/CA/CA.0.4.md
@@ -168,6 +168,7 @@ def GMM_EM(Y, K, times):
     return mu, cov, alpha
 ```
 
+
 ```python
 main.py 文件：
 import matplotlib.pyplot as plt

From 3a68623075e74acdce921c58a212201c92cf72f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 16 Apr 2018 21:03:08 +0800
Subject: [PATCH 0778/1406] change page of CA

---
 assets/src/CA/CA.0.5.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/CA/CA.0.5.md

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
new file mode 100644
index 00000000..cada466a
--- /dev/null
+++ b/assets/src/CA/CA.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 期望最大化(Expectation-Maximization)

From 7f3446a42fc9440ee744c1b87da2c00c1e2cf71b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:05:13 +0800
Subject: [PATCH 0779/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ae4407e5..023cf0f4 100644
--- a/README.md
+++ b/README.md
@@ -115,7 +115,7 @@
      * [K-均值(K-Means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.2.md)
      * [模糊c-均值聚类算法(Fuzzy C-means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.4.md)
-     * [聚类分析(Cluster Analysis)]()
+     * [聚类分析(Cluster Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.5.md)
  * [关联规则学习]()   
      * [Apriori算法]() 
      * [Eclat算法]() 

From 1757acf478d5193dc7e7def20ecc7ed0cd73b131 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 16 Apr 2018 21:07:01 +0800
Subject: [PATCH 0780/1406] change page of CA

---
 assets/src/CA/CA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index cada466a..850aa4d1 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 期望最大化(Expectation-Maximization)
+#### 聚类分析(Cluster Analysis)

From 2d9d329cc7d0bf57e154a76e31bd31b6289cffa9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:08:11 +0800
Subject: [PATCH 0781/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index 850aa4d1..e879c4de 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 聚类分析(Cluster Analysis)
+聚类分析指将物理或抽象对象的集合分组为由类似的对象组成的多个类的分析过程。它是一种重要的人类行为。
+聚类分析的目标就是在相似的基础上收集数据来分类。聚类源于很多领域，包括数学，计算机科学，统计学，生物学和经济学。在不同的应用领域，很多聚类技术都得到了发展，这些技术方法被用作描述数据，衡量不同数据源间的相似性，以及把数据源分类到不同的簇中。

From d7dd5d71ed976bf7bf407bc93d4a3ece6ad4ac94 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:09:44 +0800
Subject: [PATCH 0782/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index e879c4de..2ba457a5 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -5,3 +5,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 聚类分析(Cluster Analysis)
 聚类分析指将物理或抽象对象的集合分组为由类似的对象组成的多个类的分析过程。它是一种重要的人类行为。
 聚类分析的目标就是在相似的基础上收集数据来分类。聚类源于很多领域，包括数学，计算机科学，统计学，生物学和经济学。在不同的应用领域，很多聚类技术都得到了发展，这些技术方法被用作描述数据，衡量不同数据源间的相似性，以及把数据源分类到不同的簇中。
+
+聚类与分类的不同在于，聚类所要求划分的类是未知的。
+聚类是将数据分类到不同的类或者簇这样的一个过程，所以同一个簇中的对象有很大的相似性，而不同簇间的对象有很大的相异性。
+从统计学的观点看，聚类分析是通过数据建模简化数据的一种方法。传统的统计聚类分析方法包括系统聚类法、分解法、加入法、动态聚类法、有序样品聚类、有重叠聚类和模糊聚类等。采用k-均值、k-中心点等算法的聚类分析工具已被加入到许多著名的统计分析软件包中，如SPSS、SAS等。
+
+从机器学习的角度讲，簇相当于隐藏模式。聚类是搜索簇的无监督学习过程。与分类不同，无监督学习不依赖预先定义的类或带类标记的训练实例，需要由聚类学习算法自动确定标记，而分类学习的实例或数据对象有类别标记。聚类是观察式学习，而不是示例式的学习。
+聚类分析是一种探索性的分析，在分类的过程中，人们不必事先给出一个分类的标准，聚类分析能够从样本数据出发，自动进行分类。聚类分析所使用方法的不同，常常会得到不同的结论。不同研究者对于同一组数据进行聚类分析，所得到的聚类数未必一致。
+从实际应用的角度看，聚类分析是数据挖掘的主要任务之一。而且聚类能够作为一个独立的工具获得数据的分布状况，观察每一簇数据的特征，集中对特定的聚簇集合作进一步地分析。聚类分析还可以作为其他算法（如分类和定性归纳算法）的预处理步骤。

From 66dd80e1409fc12f012400ec6c2b0d0063b6777e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:11:38 +0800
Subject: [PATCH 0783/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index 2ba457a5..a146fc7a 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -13,3 +13,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 从机器学习的角度讲，簇相当于隐藏模式。聚类是搜索簇的无监督学习过程。与分类不同，无监督学习不依赖预先定义的类或带类标记的训练实例，需要由聚类学习算法自动确定标记，而分类学习的实例或数据对象有类别标记。聚类是观察式学习，而不是示例式的学习。
 聚类分析是一种探索性的分析，在分类的过程中，人们不必事先给出一个分类的标准，聚类分析能够从样本数据出发，自动进行分类。聚类分析所使用方法的不同，常常会得到不同的结论。不同研究者对于同一组数据进行聚类分析，所得到的聚类数未必一致。
 从实际应用的角度看，聚类分析是数据挖掘的主要任务之一。而且聚类能够作为一个独立的工具获得数据的分布状况，观察每一簇数据的特征，集中对特定的聚簇集合作进一步地分析。聚类分析还可以作为其他算法（如分类和定性归纳算法）的预处理步骤。
+
+
+聚类分析是一个富有挑战性的研究领域，对数据挖掘中聚类分析的一些要求:
+* (1) 可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
+
+* (2) 能够处理不同类型的属性。现实中的数据对象己远远超出关系型数据的范畴，比如空间数据、多媒体数据、遗传学数据、时间序列数据、文本数据、万维网上的数据、以及目前逐渐兴起的数据流。这些数据对象的属性类型往往是由多种数据类型综合而成的。
+
+* (3) 能够发现任意形状的簇。

From 4f0fb207ce503dfa37ddd88f2c5c5d22a661fb41 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:12:02 +0800
Subject: [PATCH 0784/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index a146fc7a..d88b8de9 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -16,8 +16,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 聚类分析是一个富有挑战性的研究领域，对数据挖掘中聚类分析的一些要求:
-* (1) 可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
+* 1.可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
 
-* (2) 能够处理不同类型的属性。现实中的数据对象己远远超出关系型数据的范畴，比如空间数据、多媒体数据、遗传学数据、时间序列数据、文本数据、万维网上的数据、以及目前逐渐兴起的数据流。这些数据对象的属性类型往往是由多种数据类型综合而成的。
+* 2.能够处理不同类型的属性。现实中的数据对象己远远超出关系型数据的范畴，比如空间数据、多媒体数据、遗传学数据、时间序列数据、文本数据、万维网上的数据、以及目前逐渐兴起的数据流。这些数据对象的属性类型往往是由多种数据类型综合而成的。
 
-* (3) 能够发现任意形状的簇。
+* 3.能够发现任意形状的簇。

From e33343f51b267781cd8c0803e905ae43be8f0a21 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:16:45 +0800
Subject: [PATCH 0785/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 18 +++++++++++++++---
 1 file changed, 15 insertions(+), 3 deletions(-)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index d88b8de9..e89c8755 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -16,8 +16,20 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 聚类分析是一个富有挑战性的研究领域，对数据挖掘中聚类分析的一些要求:
-* 1.可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
+* 可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
 
-* 2.能够处理不同类型的属性。现实中的数据对象己远远超出关系型数据的范畴，比如空间数据、多媒体数据、遗传学数据、时间序列数据、文本数据、万维网上的数据、以及目前逐渐兴起的数据流。这些数据对象的属性类型往往是由多种数据类型综合而成的。
+* 能够处理不同类型的属性。现实中的数据对象己远远超出关系型数据的范畴，比如空间数据、多媒体数据、遗传学数据、时间序列数据、文本数据、万维网上的数据、以及目前逐渐兴起的数据流。这些数据对象的属性类型往往是由多种数据类型综合而成的。
 
-* 3.能够发现任意形状的簇。
+* 能够发现任意形状的簇。
+
+* 尽量减少用于决定输入参数的领域知识。
+
+* 能够处理噪声数据及孤立点。
+
+* 对输入数据记录的顺序不敏感。
+
+* 高维性(high-dimensional)。一个数据集可能包含若干维。较高的维数给聚类分析带来两个问题：首先，不相关的属性削弱了数据汇聚的趋势，使得数据分布非常稀疏。尽管这种情况在低维空间中并不多见，但是随着维数的增加，不相关属性的出现概率及数量也会增加，最后导致数据空间中几乎不存在簇。其次，高维使得在低维中很有效的区分数据的标准在高维空间中失效了。如在高维空间中，数据点到最近邻点的距离与到其他点的距离没有多少分别，从而导致最近邻查询在高维空间中不稳定，此时若根据接近度来划分簇，结果是不可信的。
+
+* 能够根据用户指定的约束条件进行聚类。
+
+*  聚类结果具有可解释性和可用性

From 4344058c00d907b7e965241c7c9febdb46667ffe Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:17:07 +0800
Subject: [PATCH 0786/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index e89c8755..56e4d3a8 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -32,4 +32,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 * 能够根据用户指定的约束条件进行聚类。
 
-*  聚类结果具有可解释性和可用性
+*  聚类结果具有可解释性和可用性。

From a0afae7bb54e1881ed2b67272dc6859ad06808ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:21:17 +0800
Subject: [PATCH 0787/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index 56e4d3a8..b7a46ef1 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -33,3 +33,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 能够根据用户指定的约束条件进行聚类。
 
 *  聚类结果具有可解释性和可用性。
+
+
+聚类分析是一种分类技术。与多元分析的其他方法相比，该方法较为粗糙，理论上还不完善，但应用方面取得了很大成功。与回归分析、判别分析一起被称为多元分析的三大方法。
+
+聚类的目的——根据已知数据（ 一批观察个体的许多观测指标） ， 按照一定的数学公式计算各观察个体或变量（指标）之间亲疏关系的统计量（距离或相关系数等）。 根据某种准则（ 最短距离法、最长距离法、中间距离法、重心法等），使同一类内的差别较小，而类与类之间的差别较大，最终将观察个体或变量分为若干类。
+
+根据分类的方法可将聚类分析分为：系统聚类、快速聚类、有序聚类。
+根据分类的对象可将聚类分析分为：Q型——样品聚类clustering for individuals；R型——指标聚类clustering for variables。

From 97797fac6a363a7b8c8d8e9918ec1cfe6b2a6da4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 16 Apr 2018 21:32:16 +0800
Subject: [PATCH 0788/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index b7a46ef1..e7a373aa 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -41,3 +41,37 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 根据分类的方法可将聚类分析分为：系统聚类、快速聚类、有序聚类。
 根据分类的对象可将聚类分析分为：Q型——样品聚类clustering for individuals；R型——指标聚类clustering for variables。
+
+#### 应用示例
+```python
+from numpy import vstack 
+from scipy.cluster.vq import kmeans,vq 
+from matplotlib.finance import quotes_historical_yahoo_ochl 
+from datetime import datetime 
+
+start = datetime(2014,7,1) 
+end = datetime(2014,9,30) 
+listDji = ['AXP','BA','CAT','CSCO','CVX','DD','DIS','GE',
+'GS','HD','IBM', 'INTC','JNJ','JPM','KO','MCD','MMM','MRK',
+'MSFT','NKE','PFE','PG','T','TRV', 'UNH','UTX','V','VZ','WMT','XOM']    #30家公司代号
+
+'''初始化两个二维数组'''
+quotes = [ [0 for col in range(90)] for row in range(30)] 
+listTemp = [ [0 for col in range(90)] for row in range(30)]      
+
+for i in range(30):
+    quotes[i] = quotes_historical_yahoo_ochl(listDji[i], start, end)       #摘录数据，放入quotes
+
+days = len(quotes[0])                                           
+for i in range(30):
+    for j in range(days-1):
+        if (quotes[i][j][2] and quotes[i][j+1][2] and (quotes[i][j+1][2]>=quotes[i][j][2])):    #比较前后两天的收盘价
+            listTemp[i][j] = 1.0
+        else:
+            listTemp[i][j] = -1.0 
+
+data = vstack(listTemp) 
+centroids,_ = kmeans(data,4) #float or double is supported  
+result,_= vq(data,centroids) 
+print(result)
+```

From 6be305c67ba8060749dab788a30aa9706bc51de8 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 16 Apr 2018 21:37:40 +0800
Subject: [PATCH 0789/1406] change page of ARL

---
 README.md                 | 7 ++++---
 assets/src/ARL/ARL.0.1.md | 6 ++++++
 2 files changed, 10 insertions(+), 3 deletions(-)
 create mode 100644 assets/src/ARL/ARL.0.1.md

diff --git a/README.md b/README.md
index 023cf0f4..76b7e4f7 100644
--- a/README.md
+++ b/README.md
@@ -116,9 +116,10 @@
      * [模糊c-均值聚类算法(Fuzzy C-means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.4.md)
      * [聚类分析(Cluster Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.5.md)
- * [关联规则学习]()   
-     * [Apriori算法]() 
-     * [Eclat算法]() 
+ * [关联规则学习(Association Rule Learning)]()   
+     * [先验算法(Apriori Algorithm)]() 
+     * [Eclat算法(Eclat Algorithm)]() 
+     * [FP-growth算法(FP-Growth Algorithm)]() 
  * [神经网络]()      
      * [感知器]() 
      * [反向传播算法（BP）]() 
diff --git a/assets/src/ARL/ARL.0.1.md b/assets/src/ARL/ARL.0.1.md
new file mode 100644
index 00000000..6e115256
--- /dev/null
+++ b/assets/src/ARL/ARL.0.1.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 关联规则学习(Association Rule Learning)]
+

From 2f092834ec85c54561d7274eb0d8359574b2cf61 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 16 Apr 2018 21:39:31 +0800
Subject: [PATCH 0790/1406] change ARL

---
 assets/src/ARL/ARL.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARL/ARL.0.1.md b/assets/src/ARL/ARL.0.1.md
index 6e115256..b22a543c 100644
--- a/assets/src/ARL/ARL.0.1.md
+++ b/assets/src/ARL/ARL.0.1.md
@@ -2,5 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 关联规则学习(Association Rule Learning)]
+#### 关联规则学习(Association Rule Learning)
 

From 64e18a1b164b2ab81046afe94e6b552a56bdc8f6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 08:59:46 +0800
Subject: [PATCH 0791/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 76b7e4f7..3dff4fc0 100644
--- a/README.md
+++ b/README.md
@@ -116,7 +116,7 @@
      * [模糊c-均值聚类算法(Fuzzy C-means Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.3.md)
      * [期望最大化(Expectation-Maximization)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.4.md)
      * [聚类分析(Cluster Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.5.md)
- * [关联规则学习(Association Rule Learning)]()   
+ * [关联规则学习(Association Rule Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.1.md)   
      * [先验算法(Apriori Algorithm)]() 
      * [Eclat算法(Eclat Algorithm)]() 
      * [FP-growth算法(FP-Growth Algorithm)]() 

From 172d1ffb9ba56acbb8338442525193cf7da9cf81 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:00:58 +0800
Subject: [PATCH 0792/1406] Update ARL.0.1.md

---
 assets/src/ARL/ARL.0.1.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARL/ARL.0.1.md b/assets/src/ARL/ARL.0.1.md
index b22a543c..5f65d89f 100644
--- a/assets/src/ARL/ARL.0.1.md
+++ b/assets/src/ARL/ARL.0.1.md
@@ -4,3 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 关联规则学习(Association Rule Learning)
 
+关联规则学习（英语：Association rule learning）是一种在大型数据库中发现变量之间的有趣性关系的方法。它的目的是利用一些有趣性的量度来识别数据库中发现的强规则。基于强规则的概念，Rakesh Agrawal等人引入了关联规则以发现由超市的POS系统记录的大批交易数据中产品之间的规律性。例如，从销售数据中发现的规则 {洋葱, 土豆}→{汉堡} 会表明如果顾客一起买洋葱和土豆，他们也有可能买汉堡的肉。此类信息可以作为做出促销定价或产品植入等营销活动决定的根据。除了上面购物篮分析中的例子以外， 关联规则如今还被用在许多应用领域中，包括网络用法挖掘、入侵检测、连续生产及生物信息学中。与序列挖掘相比，关联规则学习通常不考虑在事务中、或事务间的项目的顺序。

From 8b8b88dd449a93a17680226263897046b5a8d728 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:02:41 +0800
Subject: [PATCH 0793/1406] Update ARL.0.1.md

---
 assets/src/ARL/ARL.0.1.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/ARL/ARL.0.1.md b/assets/src/ARL/ARL.0.1.md
index 5f65d89f..dc01a799 100644
--- a/assets/src/ARL/ARL.0.1.md
+++ b/assets/src/ARL/ARL.0.1.md
@@ -5,3 +5,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 关联规则学习(Association Rule Learning)
 
 关联规则学习（英语：Association rule learning）是一种在大型数据库中发现变量之间的有趣性关系的方法。它的目的是利用一些有趣性的量度来识别数据库中发现的强规则。基于强规则的概念，Rakesh Agrawal等人引入了关联规则以发现由超市的POS系统记录的大批交易数据中产品之间的规律性。例如，从销售数据中发现的规则 {洋葱, 土豆}→{汉堡} 会表明如果顾客一起买洋葱和土豆，他们也有可能买汉堡的肉。此类信息可以作为做出促销定价或产品植入等营销活动决定的根据。除了上面购物篮分析中的例子以外， 关联规则如今还被用在许多应用领域中，包括网络用法挖掘、入侵检测、连续生产及生物信息学中。与序列挖掘相比，关联规则学习通常不考虑在事务中、或事务间的项目的顺序。
+
+关联规则学习(Association Rule Learning) 的应用算法：
+* 先验算法(Apriori Algorithm)
+* Eclat算法(Eclat Algorithm)
+* FP-growth算法(FP-Growth Algorithm)

From ff703c03acf5ad9e343f31f172afe8d1a42d188e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:03:43 +0800
Subject: [PATCH 0794/1406] change page

---
 assets/src/ARL/ARL.0.2.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 assets/src/ARL/ARL.0.2.md

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
new file mode 100644
index 00000000..59f662a7
--- /dev/null
+++ b/assets/src/ARL/ARL.0.2.md
@@ -0,0 +1,12 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 先验算法(Apriori Algorithm)
+
+关联规则学习（英语：Association rule learning）是一种在大型数据库中发现变量之间的有趣性关系的方法。它的目的是利用一些有趣性的量度来识别数据库中发现的强规则。基于强规则的概念，Rakesh Agrawal等人引入了关联规则以发现由超市的POS系统记录的大批交易数据中产品之间的规律性。例如，从销售数据中发现的规则 {洋葱, 土豆}→{汉堡} 会表明如果顾客一起买洋葱和土豆，他们也有可能买汉堡的肉。此类信息可以作为做出促销定价或产品植入等营销活动决定的根据。除了上面购物篮分析中的例子以外， 关联规则如今还被用在许多应用领域中，包括网络用法挖掘、入侵检测、连续生产及生物信息学中。与序列挖掘相比，关联规则学习通常不考虑在事务中、或事务间的项目的顺序。
+
+关联规则学习(Association Rule Learning) 的应用算法：
+* 先验算法(Apriori Algorithm)
+* Eclat算法(Eclat Algorithm)
+* FP-growth算法(FP-Growth Algorithm)

From 08b1e91cf3ae096c77fd2d6822d12171f87ced97 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:04:18 +0800
Subject: [PATCH 0795/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3dff4fc0..9bffa934 100644
--- a/README.md
+++ b/README.md
@@ -117,7 +117,7 @@
      * [期望最大化(Expectation-Maximization)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.4.md)
      * [聚类分析(Cluster Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.5.md)
  * [关联规则学习(Association Rule Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.1.md)   
-     * [先验算法(Apriori Algorithm)]() 
+     * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
      * [Eclat算法(Eclat Algorithm)]() 
      * [FP-growth算法(FP-Growth Algorithm)]() 
  * [神经网络]()      

From b1bdfa0a89575aa4d58e18098074f687466111df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:05:09 +0800
Subject: [PATCH 0796/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 59f662a7..f154c362 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -4,9 +4,3 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 先验算法(Apriori Algorithm)
 
-关联规则学习（英语：Association rule learning）是一种在大型数据库中发现变量之间的有趣性关系的方法。它的目的是利用一些有趣性的量度来识别数据库中发现的强规则。基于强规则的概念，Rakesh Agrawal等人引入了关联规则以发现由超市的POS系统记录的大批交易数据中产品之间的规律性。例如，从销售数据中发现的规则 {洋葱, 土豆}→{汉堡} 会表明如果顾客一起买洋葱和土豆，他们也有可能买汉堡的肉。此类信息可以作为做出促销定价或产品植入等营销活动决定的根据。除了上面购物篮分析中的例子以外， 关联规则如今还被用在许多应用领域中，包括网络用法挖掘、入侵检测、连续生产及生物信息学中。与序列挖掘相比，关联规则学习通常不考虑在事务中、或事务间的项目的顺序。
-
-关联规则学习(Association Rule Learning) 的应用算法：
-* 先验算法(Apriori Algorithm)
-* Eclat算法(Eclat Algorithm)
-* FP-growth算法(FP-Growth Algorithm)

From ab1417c6b788fda1a4a8bd0f02d6eaaa38bb6a48 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 09:06:50 +0800
Subject: [PATCH 0797/1406] Update ARL.0.1.md

---
 assets/src/ARL/ARL.0.1.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/assets/src/ARL/ARL.0.1.md b/assets/src/ARL/ARL.0.1.md
index dc01a799..fcc97fd9 100644
--- a/assets/src/ARL/ARL.0.1.md
+++ b/assets/src/ARL/ARL.0.1.md
@@ -6,6 +6,20 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 关联规则学习（英语：Association rule learning）是一种在大型数据库中发现变量之间的有趣性关系的方法。它的目的是利用一些有趣性的量度来识别数据库中发现的强规则。基于强规则的概念，Rakesh Agrawal等人引入了关联规则以发现由超市的POS系统记录的大批交易数据中产品之间的规律性。例如，从销售数据中发现的规则 {洋葱, 土豆}→{汉堡} 会表明如果顾客一起买洋葱和土豆，他们也有可能买汉堡的肉。此类信息可以作为做出促销定价或产品植入等营销活动决定的根据。除了上面购物篮分析中的例子以外， 关联规则如今还被用在许多应用领域中，包括网络用法挖掘、入侵检测、连续生产及生物信息学中。与序列挖掘相比，关联规则学习通常不考虑在事务中、或事务间的项目的顺序。
 
+
+根据关联规则所处理的值的类型
+
+如果考虑关联规则中的数据项是否出现，则这种关联规则是布尔关联规则（Boolean association rules）。例如上面的例子。
+如果关联规则中的数据项是数量型的，这种关联规则是数量关联规则（quantitative association rules）。例如年龄("20-25")=>购买("网球拍")，年龄是一个数量型的数据项。在这种关联规则中，一般将数量离散化（discretize）为区间。
+根据关联规则所涉及的数据维数
+
+如果关联规则各项只涉及一个维，则它是单维关联规则（single-dimensional association rules），例如购买("网球拍")=>购买("网球")只涉及“购买”一个维度。
+如果关联规则涉及两个或两个以上维度，则它是多维关联规则（multi-dimensional association rules），例如年龄("20-25")=>购买("网球拍")涉及“年龄”和“购买”两个维度。
+根据关联规则所涉及的抽象层次
+
+如果不涉及不同层次的数据项，得到的是单层关联规则（single-level association rules）。
+在不同抽象层次中挖掘出的关联规则称为广义关联规则（generalized association rules）。例如年龄("20-25")=>购买("HEAD网球拍")和年龄("20-25") =>购买("网球拍")是广义关联规则，因为"HEAD网球拍"和"网球拍"属于不同的抽象层次。
+
 关联规则学习(Association Rule Learning) 的应用算法：
 * 先验算法(Apriori Algorithm)
 * Eclat算法(Eclat Algorithm)

From 079f0a00cd8e199dd8f977c7fc9d43c9078d05c2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 23:09:19 +0800
Subject: [PATCH 0798/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index f154c362..701cdd82 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -4,3 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 先验算法(Apriori Algorithm)
 
+在计算机科学以及数据挖掘领域中， 先验算法是关联式规则中的经典算法之一。先验算法的设计目的是为了处理包含交易信息内容的数据库（例如,顾客购买的商品清单，或者网页常访清单。）而其他的算法则是设计用来寻找无交易信息（如Winepi算法和Minepi算法）或无时间标记（如DNA测序）的数据之间的联系规则。
+
+在关联式规则中,一般对于给定的项目集合（例如，零售交易集合，每个集合都列出的单个商品的购买信息），算法通常尝试在项目集合中找出至少有C个相同的子集。先验算法采用自底向上的处理方法，即频繁子集每次只扩展一个对象（该步骤被称为候选集产生），并且候选集由数据进行检验。当不再产生符合条件的扩展对象时，算法终止。

From 57a27cde13a735411206658c86ff4ce7d6b4956c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Apr 2018 23:11:01 +0800
Subject: [PATCH 0799/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 701cdd82..0f1ccd37 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -4,6 +4,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 先验算法(Apriori Algorithm)
 
+Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想是通过候选集生成和情节的向下封闭检测两个阶段来挖掘频繁项集。 Apriori（先验的，推测的）算法应用广泛，可用于消费市场价格分析，猜测顾客的消费习惯；网络安全领域中的入侵检测技术；可用在用于高校管理中，根据挖掘规则可以有效地辅助学校管理部门有针对性的开展贫困助学工作；也可用在移动通信领域中，指导运营商的业务运营和辅助业务提供商的决策制定。
+
 在计算机科学以及数据挖掘领域中， 先验算法是关联式规则中的经典算法之一。先验算法的设计目的是为了处理包含交易信息内容的数据库（例如,顾客购买的商品清单，或者网页常访清单。）而其他的算法则是设计用来寻找无交易信息（如Winepi算法和Minepi算法）或无时间标记（如DNA测序）的数据之间的联系规则。
 
 在关联式规则中,一般对于给定的项目集合（例如，零售交易集合，每个集合都列出的单个商品的购买信息），算法通常尝试在项目集合中找出至少有C个相同的子集。先验算法采用自底向上的处理方法，即频繁子集每次只扩展一个对象（该步骤被称为候选集产生），并且候选集由数据进行检验。当不再产生符合条件的扩展对象时，算法终止。

From 7de9bba67cf62554491733124da60af7f75410a5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 18 Apr 2018 09:00:53 +0800
Subject: [PATCH 0800/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 0f1ccd37..66cdf060 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 先验算法(Apriori Algorithm)
-
 Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想是通过候选集生成和情节的向下封闭检测两个阶段来挖掘频繁项集。 Apriori（先验的，推测的）算法应用广泛，可用于消费市场价格分析，猜测顾客的消费习惯；网络安全领域中的入侵检测技术；可用在用于高校管理中，根据挖掘规则可以有效地辅助学校管理部门有针对性的开展贫困助学工作；也可用在移动通信领域中，指导运营商的业务运营和辅助业务提供商的决策制定。
 
 在计算机科学以及数据挖掘领域中， 先验算法是关联式规则中的经典算法之一。先验算法的设计目的是为了处理包含交易信息内容的数据库（例如,顾客购买的商品清单，或者网页常访清单。）而其他的算法则是设计用来寻找无交易信息（如Winepi算法和Minepi算法）或无时间标记（如DNA测序）的数据之间的联系规则。

From 9cbd1606be03f6ecede5f0d62252ee94b87314ed Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 19 Apr 2018 08:49:16 +0800
Subject: [PATCH 0801/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index e7a373aa..1ec8b6c8 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -14,7 +14,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 聚类分析是一种探索性的分析，在分类的过程中，人们不必事先给出一个分类的标准，聚类分析能够从样本数据出发，自动进行分类。聚类分析所使用方法的不同，常常会得到不同的结论。不同研究者对于同一组数据进行聚类分析，所得到的聚类数未必一致。
 从实际应用的角度看，聚类分析是数据挖掘的主要任务之一。而且聚类能够作为一个独立的工具获得数据的分布状况，观察每一簇数据的特征，集中对特定的聚簇集合作进一步地分析。聚类分析还可以作为其他算法（如分类和定性归纳算法）的预处理步骤。
 
-
 聚类分析是一个富有挑战性的研究领域，对数据挖掘中聚类分析的一些要求:
 * 可伸缩性(scalability)。实际应用要求聚类算法能够处理大数据集，且时间复杂度不能太高(最好是多项式时间)，消耗的内存空间也有限。目前，为了将算法拓展到超大数据库(VLDB)领域，研究人员已经进行了许多有益的尝试，包括：增量式挖掘、可靠的采样、数据挤压(data squashing)等。其中，数据挤压技术首先通过扫描数据来获得数据的统计信息，然后在这些统计信息的基础上进行聚类分析。比如BIRCH 算法中使用CF树就是属于数据挤压技术。
 

From 128a837f2b8a823974263a53ca45ee167472c101 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 08:57:23 +0800
Subject: [PATCH 0802/1406] Update CA.0.5.md

---
 assets/src/CA/CA.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CA/CA.0.5.md b/assets/src/CA/CA.0.5.md
index 1ec8b6c8..c2aa4fd3 100644
--- a/assets/src/CA/CA.0.5.md
+++ b/assets/src/CA/CA.0.5.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 聚类分析(Cluster Analysis)
+
 聚类分析指将物理或抽象对象的集合分组为由类似的对象组成的多个类的分析过程。它是一种重要的人类行为。
 聚类分析的目标就是在相似的基础上收集数据来分类。聚类源于很多领域，包括数学，计算机科学，统计学，生物学和经济学。在不同的应用领域，很多聚类技术都得到了发展，这些技术方法被用作描述数据，衡量不同数据源间的相似性，以及把数据源分类到不同的簇中。
 

From 38b74bbca2847281ca7b8b1f0da10e189af30eac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 20:54:51 +0800
Subject: [PATCH 0803/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 66cdf060..e7eeb680 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -8,3 +8,5 @@ Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想
 在计算机科学以及数据挖掘领域中， 先验算法是关联式规则中的经典算法之一。先验算法的设计目的是为了处理包含交易信息内容的数据库（例如,顾客购买的商品清单，或者网页常访清单。）而其他的算法则是设计用来寻找无交易信息（如Winepi算法和Minepi算法）或无时间标记（如DNA测序）的数据之间的联系规则。
 
 在关联式规则中,一般对于给定的项目集合（例如，零售交易集合，每个集合都列出的单个商品的购买信息），算法通常尝试在项目集合中找出至少有C个相同的子集。先验算法采用自底向上的处理方法，即频繁子集每次只扩展一个对象（该步骤被称为候选集产生），并且候选集由数据进行检验。当不再产生符合条件的扩展对象时，算法终止。
+
+先验算法采用广度优先搜索算法进行搜索并采用树结构来对候选项目集进行高效计数。它通过长度为k-1的候选项目集来产生长度为k的候选项目集，然后从中删除包含不常见子模式的候选项。根据向下封闭性引理,该候选项目集包含所有长度为k的频繁项目集。之后，就可以通过扫描交易数据库来决定候选项目集中的频繁项目集。

From a3f4c12b54b0afa6cf8c650baa11543df764dc7a Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 20:59:50 +0800
Subject: [PATCH 0804/1406] change page

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From 9cb525c530495a83867a527308a116f4730022e8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:00:35 +0800
Subject: [PATCH 0805/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index e7eeb680..32577e1d 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -10,3 +10,5 @@ Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想
 在关联式规则中,一般对于给定的项目集合（例如，零售交易集合，每个集合都列出的单个商品的购买信息），算法通常尝试在项目集合中找出至少有C个相同的子集。先验算法采用自底向上的处理方法，即频繁子集每次只扩展一个对象（该步骤被称为候选集产生），并且候选集由数据进行检验。当不再产生符合条件的扩展对象时，算法终止。
 
 先验算法采用广度优先搜索算法进行搜索并采用树结构来对候选项目集进行高效计数。它通过长度为k-1的候选项目集来产生长度为k的候选项目集，然后从中删除包含不常见子模式的候选项。根据向下封闭性引理,该候选项目集包含所有长度为k的频繁项目集。之后，就可以通过扫描交易数据库来决定候选项目集中的频繁项目集。
+
+虽然先验算法具有显著的历史地位，但是其中的一些低效与权衡弊端也进而引致了许多其他的算法的产生。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有<img width="100" align="center" src="../../images/247.jpg" />个可能的子集之后才寻找任意最大子集S。

From ae1fe9f6b9d42b2dabcb6bbbb1cd929750e2a824 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:01:11 +0800
Subject: [PATCH 0806/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 32577e1d..e04c732d 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -11,4 +11,4 @@ Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想
 
 先验算法采用广度优先搜索算法进行搜索并采用树结构来对候选项目集进行高效计数。它通过长度为k-1的候选项目集来产生长度为k的候选项目集，然后从中删除包含不常见子模式的候选项。根据向下封闭性引理,该候选项目集包含所有长度为k的频繁项目集。之后，就可以通过扫描交易数据库来决定候选项目集中的频繁项目集。
 
-虽然先验算法具有显著的历史地位，但是其中的一些低效与权衡弊端也进而引致了许多其他的算法的产生。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有<img width="100" align="center" src="../../images/247.jpg" />个可能的子集之后才寻找任意最大子集S。
+虽然先验算法具有显著的历史地位，但是其中的一些低效与权衡弊端也进而引致了许多其他的算法的产生。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有<img width="100" align="center" src="../../images/248.jpg" />个可能的子集之后才寻找任意最大子集S。

From 8a9260ea199f11c5f6caf4ad3ff0aa56ce5050e1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:04:12 +0800
Subject: [PATCH 0807/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index e04c732d..5275e081 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -12,3 +12,5 @@ Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想
 先验算法采用广度优先搜索算法进行搜索并采用树结构来对候选项目集进行高效计数。它通过长度为k-1的候选项目集来产生长度为k的候选项目集，然后从中删除包含不常见子模式的候选项。根据向下封闭性引理,该候选项目集包含所有长度为k的频繁项目集。之后，就可以通过扫描交易数据库来决定候选项目集中的频繁项目集。
 
 虽然先验算法具有显著的历史地位，但是其中的一些低效与权衡弊端也进而引致了许多其他的算法的产生。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有<img width="100" align="center" src="../../images/248.jpg" />个可能的子集之后才寻找任意最大子集S。
+
+Apriori算法中的一些低效与权衡弊端也进而引致了许多其他的算法的产生，例如FP-growth算法。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有 <img width="100" align="center" src="../../images/248.jpg" />个可能的子集之后才寻找任意最大子集S。

From d1022fbf9ebe54ba08f16a4632c903f6142b3b61 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:07:26 +0800
Subject: [PATCH 0808/1406] Update ARL.0.2.md

---
 assets/src/ARL/ARL.0.2.md | 130 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 130 insertions(+)

diff --git a/assets/src/ARL/ARL.0.2.md b/assets/src/ARL/ARL.0.2.md
index 5275e081..d5a50cf1 100644
--- a/assets/src/ARL/ARL.0.2.md
+++ b/assets/src/ARL/ARL.0.2.md
@@ -14,3 +14,133 @@ Apriori算法是一种挖掘关联规则的频繁项集算法，其核心思想
 虽然先验算法具有显著的历史地位，但是其中的一些低效与权衡弊端也进而引致了许多其他的算法的产生。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有<img width="100" align="center" src="../../images/248.jpg" />个可能的子集之后才寻找任意最大子集S。
 
 Apriori算法中的一些低效与权衡弊端也进而引致了许多其他的算法的产生，例如FP-growth算法。候选集产生过程生成了大量的子集（先验算法在每次对数据库进行扫描之前总是尝试加载尽可能多的候选集）。并且自底而上的子集浏览过程（本质上为宽度优先的子集格遍历）也直到遍历完所有 <img width="100" align="center" src="../../images/248.jpg" />个可能的子集之后才寻找任意最大子集S。
+
+
+#### 应用示例
+```python
+
+class Apriori():
+    def __init__(self):
+        pass
+    '''
+    关联分析的目标包括两项：发现频繁项集和发现关联规则
+    '''
+
+    '''
+    频繁项集：
+        对于包含N种物品的数据集共有2^N-1种项集组合。
+        支持度(support)
+            一个项集的支持度被定义为数据集中包含该项集的记录所占的比例。
+        Apriori算法：如果某个项集是频繁的，那么它的所有子集也是频繁的。
+        如果一个项集是非频繁集，那么它的所有超集也是非频繁集。
+    '''
+    def _createC1(self, dataSet):
+        C1 = []
+        for transaction in dataSet:
+            for item in transaction:
+                if [item] not in C1:
+                    C1.append([item])
+        C1.sort()
+        return map(frozenset, C1) # use frozen set so we can use it as a key in a dict
+
+    def _scanD(self, D, Ck, minSupport=0.5):
+        ssCnt = {}
+        for tid in D:
+            for can in Ck:
+                if can.issubset(tid):
+                    if can in ssCnt:
+                        ssCnt[can] += 1
+                    else:
+                        ssCnt[can] = 1
+                    # if can not in ssCnt:
+                    #     ssCnt[can] = 0
+                    # ssCnt[can] += 1
+        # print ssCnt
+        numItems = len(D)
+        retList = []
+        supportK = {}
+        for key in ssCnt:
+            support = ssCnt[key]/float(numItems) # 计算支持度
+            if support >= minSupport:
+                retList.append(key)
+            supportK[key] = support
+        return retList, supportK
+
+    def aprioriGen(self, Lk, k): # k>=2
+        retList = []
+        lenLk = len(Lk)
+        for i in range(lenLk):
+            for j in range(i+1, lenLk):
+                L1 = list(Lk[i])[:k-2]
+                L2 = list(Lk[j])[:k-2]
+                L1.sort()
+                L2.sort()
+                if L1 == L2: # if first k-2 elements are equal. when k is 3, {0,1},{0,2},{1,2}→{0,1}U{0,2}→{0,1,2}
+                    retList.append(Lk[i] | Lk[j])
+        return retList
+
+    def apriori(self, dataSet, minSupport=0.5): # minSupport 最小支持度
+        D = map(set, dataSet) # 转换为集合set
+        C1 = self._createC1(dataSet) # 创建C1，转换为集合frozenset
+        L1, supp1 = self._scanD(D, C1, minSupport) # 基于C1和minSupport创建L1
+        L = []
+        supportData = {}
+        L.append(L1)
+        supportData.update(supp1)
+        k = 2
+        while len(L[k-2]) > 1:
+            Ck = self.aprioriGen(L[k-2], k) # 创建Ck
+            Lk, suppK = self._scanD(D, Ck, minSupport) # 基于Ck和minSupport创建Lk
+            L.append(Lk)
+            supportData.update(suppK)
+            k += 1
+        return L, supportData
+
+    '''
+    关联规则：→
+        可信度(confidence)：也称置信度
+            可信度(尿布→葡萄酒) = 支持度({尿布,葡萄酒})/支持度({尿布})
+        如果某条规则并不满足最小可信度要求，那么该规则的所有子集也不会满足最小可信度要求。
+    '''
+
+    def _calcConf(self, freqSet, H, supportData, brl, minConf=0.7): # H为出现在右部的规则列表，如{0},{1}
+        prunedH = []
+        for conseq in H:
+            conf = supportData[freqSet]/supportData[freqSet-conseq] # 计算可信度
+            if conf >= minConf:
+                print freqSet-conseq, '-->', conseq, 'conf:', conf
+                brl.append((freqSet-conseq, conseq, conf))
+                prunedH.append(conseq)
+        return prunedH
+
+    def _rulesFromConseq(self, freqSet, H, supportData, brl, minConf=0.7): # H为出现在右部的规则列表，如{0},{1}
+        m = len(H[0])
+        if len(freqSet) > (m+1):
+            Hmp1 = self.aprioriGen(H, m+1) # 合并规则
+            Hmp = self._calcConf(freqSet, Hmp1, supportData, brl, minConf) # Hmp为出现在右部的合并规则列表，如{0,1}
+            if len(Hmp) > 1: # 如果规则列表长度大于1，则进一步合并
+                self._rulesFromConseq(freqSet, Hmp, supportData, brl, minConf)
+
+    def generateRules(self, L, supportData, minConf=0.7): # minConf 最小可信度
+        bigRuleList = []
+        for i in range(1, len(L)): # 从包含两个或者更多元素的项集开始规则构建过程
+            for freqSet in L[i]:
+                H1 = [frozenset([item]) for item in freqSet] # 构建只包含单个元素的列表，即出现在规则右部的规则列表，如{0},{1}
+                if i > 1:
+                    self._rulesFromConseq(freqSet, H1, supportData, bigRuleList, minConf) # 生成候选规则
+                else:
+                    self._calcConf(freqSet, H1, supportData, bigRuleList, minConf) # 对规则进行评估
+        return bigRuleList
+
+def loadDataSet():
+    return [[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]]
+
+if __name__ == '__main__':
+    dataSet = loadDataSet()
+    ap = Apriori()
+    L, suppData = ap.apriori(dataSet, minSupport=0.5)
+    print L
+    print suppData
+    rules = ap.generateRules(L, suppData, minConf=0.6)
+    print rules
+```

From c25b408c183ef0f80e77a97cb231421c4be2349b Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 21:15:21 +0800
Subject: [PATCH 0809/1406] change page

---
 README.md                 | 2 +-
 assets/src/ARL/ARL.0.3.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/ARL/ARL.0.3.md

diff --git a/README.md b/README.md
index 9bffa934..b5c535ec 100644
--- a/README.md
+++ b/README.md
@@ -118,7 +118,7 @@
      * [聚类分析(Cluster Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/CA/CA.0.5.md)
  * [关联规则学习(Association Rule Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.1.md)   
      * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
-     * [Eclat算法(Eclat Algorithm)]() 
+     * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
      * [FP-growth算法(FP-Growth Algorithm)]() 
  * [神经网络]()      
      * [感知器]() 
diff --git a/assets/src/ARL/ARL.0.3.md b/assets/src/ARL/ARL.0.3.md
new file mode 100644
index 00000000..51e1067d
--- /dev/null
+++ b/assets/src/ARL/ARL.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### Eclat算法(Eclat Algorithm)

From 5952374ab06c2a70ae7d89c8d0d209ef5328ed07 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:32:07 +0800
Subject: [PATCH 0810/1406] Update ARL.0.3.md

---
 assets/src/ARL/ARL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ARL/ARL.0.3.md b/assets/src/ARL/ARL.0.3.md
index 51e1067d..30546199 100644
--- a/assets/src/ARL/ARL.0.3.md
+++ b/assets/src/ARL/ARL.0.3.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Eclat算法(Eclat Algorithm)
+Eclat算法是一种深度优先算法,采用垂直数据表示形式,在概念格理论的基础上利用基于前缀的等价关系将搜索空间(概念格)划分为较小的子空间(子概念格)。

From 6f3fb2688f07f4f8d2fb4be8224c8d33862d6dae Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:32:59 +0800
Subject: [PATCH 0811/1406] Update ARL.0.3.md

---
 assets/src/ARL/ARL.0.3.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/ARL/ARL.0.3.md b/assets/src/ARL/ARL.0.3.md
index 30546199..02a5fa38 100644
--- a/assets/src/ARL/ARL.0.3.md
+++ b/assets/src/ARL/ARL.0.3.md
@@ -4,3 +4,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Eclat算法(Eclat Algorithm)
 Eclat算法是一种深度优先算法,采用垂直数据表示形式,在概念格理论的基础上利用基于前缀的等价关系将搜索空间(概念格)划分为较小的子空间(子概念格)。
+
+#### Eclat算法原理
+* 垂直数据表示
+支持度的计算需要访问数据库。在大多数算法中,考虑数据库中事务(即记录)的表示形式。从概念上讲,这样的数据库可以用一个二进制的二维矩阵来表示,矩阵的每一行代表数据库的一条事务,每一列代表项目。
+传统的数据挖掘算法多采用水平数据表示,在水平数据表示中,数据库的一条事务由事务标识符(TID)和项目组成。事务由TID唯一标识,一条事务可以包含一个项目或多个项目。Apriori、FP?Growth等算法都是采用此种表示方法。
+定义1(Tidset)?设有项目X,包含项目X的所有事务的标识符的集合称为项目X的Tidset。在这种数据表示方法中,数据库的事务由项目和该项目的Tidset组成,该事务由项目唯一标识。Tidset垂直数据表示:数据库中的每一条记录由一个项目及其所出现过的所有事务记录的列表(即Tidset表)构成。这样使得任何一个频繁项集的支持度计数都可以通过对Tidset交集运算求得。
+
+

From 9e46ff93f19539d4535a0925d9c0f052e590cfe1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:34:34 +0800
Subject: [PATCH 0812/1406] Update ARL.0.3.md

---
 assets/src/ARL/ARL.0.3.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/assets/src/ARL/ARL.0.3.md b/assets/src/ARL/ARL.0.3.md
index 02a5fa38..f6ac3bee 100644
--- a/assets/src/ARL/ARL.0.3.md
+++ b/assets/src/ARL/ARL.0.3.md
@@ -7,8 +7,20 @@ Eclat算法是一种深度优先算法,采用垂直数据表示形式,在概念
 
 #### Eclat算法原理
 * 垂直数据表示
+
 支持度的计算需要访问数据库。在大多数算法中,考虑数据库中事务(即记录)的表示形式。从概念上讲,这样的数据库可以用一个二进制的二维矩阵来表示,矩阵的每一行代表数据库的一条事务,每一列代表项目。
 传统的数据挖掘算法多采用水平数据表示,在水平数据表示中,数据库的一条事务由事务标识符(TID)和项目组成。事务由TID唯一标识,一条事务可以包含一个项目或多个项目。Apriori、FP?Growth等算法都是采用此种表示方法。
 定义1(Tidset)?设有项目X,包含项目X的所有事务的标识符的集合称为项目X的Tidset。在这种数据表示方法中,数据库的事务由项目和该项目的Tidset组成,该事务由项目唯一标识。Tidset垂直数据表示:数据库中的每一条记录由一个项目及其所出现过的所有事务记录的列表(即Tidset表)构成。这样使得任何一个频繁项集的支持度计数都可以通过对Tidset交集运算求得。
 
+* 支持度计数方法
+
+Eclat算法采用方法二计算支持度。对候选k项集进行支持度计算时,不需再次扫描数据库,仅在一次扫描数据库后得到每个1项集的支持度,而候选k项集的支持度就是在对k-1项集进行交集操作后得到的该k项集Tidset中元素的个数。
+
+* 概念格理论
+
+Eclat算法在概念格理论的基础上,利用基于前缀的等价关系将搜索空间(概念格)划分为较小的子空间(子概念格),各子概念格采用自底向上的搜索方法独立产生频繁项集。
 
+#### eclat算法不足
+在Eclat算法中,它由2个集合的并集产生新的候选集,通过计算这2个项集的Tidset的交集快速得到候选集的支持度,因此,当Tidset的规模庞大时将出现以下问题:
+* 1.求Tidset的交集的操作将消耗大量时间,影响了算法的效率;
+* 2.Tidset的规模相当庞大,消耗系统大量的内存。

From 98decb1ef4562475f73733b0f67e8554a339d2ea Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:36:16 +0800
Subject: [PATCH 0813/1406] Update ARL.0.3.md

---
 assets/src/ARL/ARL.0.3.md | 112 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 112 insertions(+)

diff --git a/assets/src/ARL/ARL.0.3.md b/assets/src/ARL/ARL.0.3.md
index f6ac3bee..9ab36594 100644
--- a/assets/src/ARL/ARL.0.3.md
+++ b/assets/src/ARL/ARL.0.3.md
@@ -24,3 +24,115 @@ Eclat算法在概念格理论的基础上,利用基于前缀的等价关系将
 在Eclat算法中,它由2个集合的并集产生新的候选集,通过计算这2个项集的Tidset的交集快速得到候选集的支持度,因此,当Tidset的规模庞大时将出现以下问题:
 * 1.求Tidset的交集的操作将消耗大量时间,影响了算法的效率;
 * 2.Tidset的规模相当庞大,消耗系统大量的内存。
+
+
+#### 应用案例
+```python
+import sys
+import itertools
+import math
+
+tidlists = {1: {}};
+min_sup = float(sys.argv[1])
+min_conf = float(sys.argv[2])
+
+print('Reading dataset.')
+dataset = open(sys.argv[3])
+tid = 0
+for line in dataset:
+    line = line.strip()
+    if len(line) == 0:
+        continue
+
+    items = line.split(' ')
+
+    for item in items:
+        item = (item,)
+        if item not in tidlists[1]:
+            tidlists[1][item] = set()
+        tidlists[1][item].add(tid)
+
+    tid += 1
+dataset.close()
+print('Dataset reading done.')
+transactions = tid
+min_sup_count = min_sup * transactions
+
+n_items = len(tidlists[1])
+print('Number of items: {}.'.format(n_items))
+
+tidlists[1] = {k:v for k,v in tidlists[1].items() if len(v) >= min_sup_count}
+
+n_frequent_items = len(tidlists[1])
+print('Number of requent items: {}. Removed {}.'.format(n_frequent_items, n_items - n_frequent_items))
+
+def has_same_prefix(itemset1, itemset2, n):
+    for i in range(0, min(len(itemset1), len(itemset2))):
+        if n == 0:
+            return True
+
+        if itemset1[i] != itemset2[i]:
+            return False
+        n -= 1
+    return n == 0
+
+def eclat():
+    k = 2
+    while True:
+        print('Searching for {}-itemsets.'.format(k))
+        tidlists[k] = {}
+        combination_counter = 0
+        #n_combinations = math.factorial(len(tidlists[k-1]))/(2 * math.factorial(len(tidlists[k-1])-2))
+        #print('Possible number of combinations: {}.'.format(n_combinations))
+        for itemset1, itemset2 in itertools.combinations(tidlists[k-1].keys(), r=2):
+            combination_counter += 1
+            if not has_same_prefix(itemset1, itemset2, k-2):
+                continue
+
+            tidlist1, tidlist2 = tidlists[k-1][itemset1], tidlists[k-1][itemset2]
+            intersection = tidlist1.intersection(tidlist2)
+            if len(intersection) < min_sup_count:
+                continue
+
+            tidlists[k][tuple(list(itemset1) + [itemset2[len(itemset2)-1]])] = intersection
+
+
+        if len(tidlists[k]) == 0:
+            del tidlists[k]
+            break
+
+
+        print('Number of frequent {}-itemsets: {}.'.format(k, len(tidlists[k])))
+        k += 1
+        
+    out = open(sys.argv[4], 'w')
+    # Print results
+    out.write('itemsets\n')
+    for i in range(1, k):
+        #print('Frequent {}-itemsets'.format(i))
+        for (itemset, tidlist) in tidlists[i].items():
+            out.write(' '.join(itemset1) + '\n')
+            out.write(str(len(tidlist)/transactions) + '\n')
+
+    out.write('rules\n')
+    for i in range(1, k):
+        #print('Frequent {}-itemsets'.format(i))
+        for (itemset, tidlist) in tidlists[i].items():
+            subsets = []
+            for j in range(1, len(itemset)):
+                subsets = subsets + list(itertools.combinations(itemset, j))
+
+            for subset in subsets:
+                difference = set(itemset).difference(subset)
+                confidence = len(tidlist)/len(tidlists[len(subset)][tuple(subset)])
+                if confidence < min_conf:
+                    continue
+                out.write(' '.join(subset) + '\n')
+                out.write(' '.join(difference) + '\n')
+                out.write(str(confidence) + '\n')
+
+    out.close()
+    
+eclat()
+
+``

From fa83d95f8883539891568b6c27220feeca292565 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 21:40:03 +0800
Subject: [PATCH 0814/1406] change page FP

---
 assets/src/ARL/ARL.0.4.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/ARL/ARL.0.4.md

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
new file mode 100644
index 00000000..0083b7db
--- /dev/null
+++ b/assets/src/ARL/ARL.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### FP-growth算法(FP-Growth Algorithm)

From c153cb940f1f47a0aea35f19ae697986f816ea0d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 21:43:12 +0800
Subject: [PATCH 0815/1406] add FP GRowtg

---
 README.md                 | 2 +-
 assets/src/ARL/ARL.0.4.md | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b5c535ec..3bbe95a6 100644
--- a/README.md
+++ b/README.md
@@ -119,7 +119,7 @@
  * [关联规则学习(Association Rule Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.1.md)   
      * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
      * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
-     * [FP-growth算法(FP-Growth Algorithm)]() 
+     * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
  * [神经网络]()      
      * [感知器]() 
      * [反向传播算法（BP）]() 
diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 0083b7db..07da8c1a 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -3,3 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### FP-growth算法(FP-Growth Algorithm)
+FP-growth算法是基于Apriori原理的，通过将数据集存储在FP（Frequent Pattern)树上发现频繁项集，但不能发现数据之间的关联规则。FP-growth算法只需要对数据库进行两次扫描，而Apriori算法在求每个潜在的频繁项集时都需要扫描一次数据集，所以说Apriori算法是高效的。其中算法发现频繁项集的过程是：
+* 1.构建FP树；
+* 2.从FP树中挖掘频繁项集。
\ No newline at end of file

From 333d2c6a78a2e02400c08510e84beb78681cf87d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:46:05 +0800
Subject: [PATCH 0816/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3bbe95a6..3a346950 100644
--- a/README.md
+++ b/README.md
@@ -29,7 +29,7 @@
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)
  * [机器学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.02.md)
- * [机器学习的框架]()
+ * [机器学习的框架](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.03.md)
  * [机器学习的应用案例]()
 
 

From 3770877678108a5bdf02f219bdcc3724bc5377e6 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 21:49:02 +0800
Subject: [PATCH 0817/1406] add ML

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3bbe95a6..3a346950 100644
--- a/README.md
+++ b/README.md
@@ -29,7 +29,7 @@
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)
  * [机器学习的入门](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.02.md)
- * [机器学习的框架]()
+ * [机器学习的框架](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.03.md)
  * [机器学习的应用案例]()
 
 

From 9b97a267e0c3881b0e2e7de259d48c70aa27972f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 21:53:01 +0800
Subject: [PATCH 0818/1406] Update ARL.0.4.md

---
 assets/src/ARL/ARL.0.4.md | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 07da8c1a..ffcf6f4e 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -5,4 +5,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### FP-growth算法(FP-Growth Algorithm)
 FP-growth算法是基于Apriori原理的，通过将数据集存储在FP（Frequent Pattern)树上发现频繁项集，但不能发现数据之间的关联规则。FP-growth算法只需要对数据库进行两次扫描，而Apriori算法在求每个潜在的频繁项集时都需要扫描一次数据集，所以说Apriori算法是高效的。其中算法发现频繁项集的过程是：
 * 1.构建FP树；
-* 2.从FP树中挖掘频繁项集。
\ No newline at end of file
+* 2.从FP树中挖掘频繁项集。
+
+#### 构建FP树
+FP表示的是频繁模式，其通过链接来连接相似元素，被连起来的元素可以看成是一个链表。将事务数据表中的各个事务对应的数据项按照支持度排序后，把每个事务中的数据项按降序依次插入到一棵以 NULL为根节点的树中，同时在每个结点处记录该结点出现的支持度。
+
+FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁项集。在构造FP树时，需要对数据集扫描两边，第一遍扫描用来统计频率，第二遍扫描至考虑频繁项集。下面举例对FP树加以说明。
+
+假设存在的一个事务数据样例为,构建FP树的步骤如下： 

From 53a5c3e3ab7c9ac5865a01d6cf97b5dc20291ea9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:03:58 +0800
Subject: [PATCH 0819/1406] Update ARL.0.4.md

---
 assets/src/ARL/ARL.0.4.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index ffcf6f4e..141a8ebb 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -13,3 +13,12 @@ FP表示的是频繁模式，其通过链接来连接相似元素，被连起来
 FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁项集。在构造FP树时，需要对数据集扫描两边，第一遍扫描用来统计频率，第二遍扫描至考虑频繁项集。下面举例对FP树加以说明。
 
 假设存在的一个事务数据样例为,构建FP树的步骤如下： 
+
+| 事务ID |  事务中的元素 |
+| ------ | --- | 
+| 001 | r,z,h,j,p | 
+| 002 |z,y,x,w,v,u,t,s|
+| 003 | z |
+| 004 | r,x,n,o,s |
+| 005 | y,r,x,z,q,t,p |
+| 006 | y,z,x,e,q,s,t,m|

From a44fea51fa8c149c4b98ffc50ca257c6757865bc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:04:57 +0800
Subject: [PATCH 0820/1406] Update ARL.0.4.md

change ARL
---
 assets/src/ARL/ARL.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 141a8ebb..90303aa5 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -22,3 +22,5 @@ FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁
 | 004 | r,x,n,o,s |
 | 005 | y,r,x,z,q,t,p |
 | 006 | y,z,x,e,q,s,t,m|
+
+　结合Apriori算法中最小支持度的阈值，在此将最小支持度定义为3，结合上表中的数据，那些不满足最小支持度要求的将不会出现在最后的FP树中，据此构建FP树，并采用一个头指针表来指向给定类型的第一个实例，快速访问FP树中的所有元素，构建的带头指针的FP树如下:

From 168544e5ab68b00f081ebb763195350c64849986 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:09:13 +0800
Subject: [PATCH 0821/1406] change page ARL.0.4

---
 assets/images/249.jpg | Bin 0 -> 26462 bytes
 assets/images/250.jpg | Bin 0 -> 9797 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/249.jpg
 create mode 100644 assets/images/250.jpg

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From 5a36a4cc1baaac9c97ad7a0eb479c336bce5bacb Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:11:03 +0800
Subject: [PATCH 0822/1406] change ARL

---
 assets/src/ARL/ARL.0.4.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 90303aa5..1d6caf0c 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -24,3 +24,6 @@ FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁
 | 006 | y,z,x,e,q,s,t,m|
 
 　结合Apriori算法中最小支持度的阈值，在此将最小支持度定义为3，结合上表中的数据，那些不满足最小支持度要求的将不会出现在最后的FP树中，据此构建FP树，并采用一个头指针表来指向给定类型的第一个实例，快速访问FP树中的所有元素，构建的带头指针的FP树如下:
+<p align="center">
+<img width="300" align="center" src="../../images/249.jpg" />
+</p>

From d50256b226c4b9e5230447a8ecdac12bc97b2033 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:23:02 +0800
Subject: [PATCH 0823/1406] change page of ARL

---
 assets/src/ARL/ARL.0.4.md | 178 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 178 insertions(+)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 1d6caf0c..3d56eefa 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -27,3 +27,181 @@ FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁
 <p align="center">
 <img width="300" align="center" src="../../images/249.jpg" />
 </p>
+
+结合绘制的带头指针表的FP树，对表中数据进行过滤，排序如下：
+| 事务ID |  事务中的元素 |过滤和重排序后的事务|
+| ------ | --- |  --------------------------- | 
+| 001 | r,z,h,j,p |    z,r                    |
+| 002 |z,y,x,w,v,u,t,s|  z,x,y,s,t            |
+| 003 | z |          z                        |
+| 004 | r,x,n,o,s |  x,s,r                    |
+| 005 | y,r,x,z,q,t,p |    	z,x,y,r,t         |
+| 006 | y,z,x,e,q,s,t,m|    z,x,y,s,t         |
+
+在对数据项过滤排序了之后，就可以构建FP树了，从NULL开始，向其中不断添加过滤排序后的频繁项集。过程可表示为：
+<p align="center">
+<img width="300" align="center" src="../../images/250.jpg" />
+</p>
+
+因而我们可以实现FP树的构建，我们知道，在第二次扫描数据集时会构建一棵FP树，并采用一个容器来保存树。首先创建一个类来保存树的每一个节点：
+```python
+from numpy import *
+
+class treeNode:
+    def __init__(self, nameValue, numOccur, parentNode):
+        self.name = nameValue
+        self.count = numOccur
+        self.nodeLink = None
+        self.parent = parentNode      #needs to be updated
+        self.children = {} 
+        
+    def inc(self,numOccur):
+        self.count += numOccur
+
+    def disp(self,ind = 1):
+        print ' '*ind,self.name,' ',self.count
+        for child in self.children.values():
+            child.disp(ind+1)
+'''
+#test
+rootNode = treeNode('pyramid',9,None)
+rootNode.children['eye'] = treeNode('eye',13,None)
+a = rootNode.disp()
+print a
+'''
+```
+
+这样，FP树对应的数据结构就建好了，现在就可以构建FP树了，FP树的构建函数如下:
+
+```python
+#FP构建函数
+def createTree(dataSet,minSup = 1):
+    headerTable = {}
+    for trans in dataSet:
+        for item in trans:
+            headerTable[item] = headerTable.get(item,0) + dataSet[trans]#记录每个元素项出现的频度
+    for k in headerTable.keys():
+        if headerTable[k] < minSup:
+            del(headerTable[k])
+    freqItemSet = set(headerTable.keys())
+    if len(freqItemSet) == 0:#不满足最小值支持度要求的除去
+        return None,None
+    for k in headerTable:
+        headerTable[k] = [headerTable[k],None]
+    retTree = treeNode('Null Set',1,None)
+    for tranSet,count in dataSet.items():
+        localD = {}
+        for item in tranSet:
+            if item in freqItemSet:
+                localD[item] = headerTable[item][0]
+        if len(localD) > 0:
+            orderedItems = [v[0] for v in sorted(localD.items(),key = lambda p:p[1],reverse = True)]
+            updateTree(orderedItems,retTree,headerTable,count)
+    return retTree,headerTable
+
+def updateTree(items, inTree, headerTable, count):
+    if items[0] in inTree.children:
+        inTree.children[items[0]].inc(count) 
+    else:
+        inTree.children[items[0]] = treeNode(items[0], count, inTree)
+        if headerTable[items[0]][1] == None:
+            headerTable[items[0]][1] = inTree.children[items[0]]
+        else:
+            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
+    if len(items) > 1:
+        updateTree(items[1::], inTree.children[items[0]], headerTable, count)
+
+def updateHeader(nodeToTest, targetNode):   
+    while (nodeToTest.nodeLink != None):
+        nodeToTest = nodeToTest.nodeLink
+    nodeToTest.nodeLink = targetNode
+```
+
+在应用示例之前还需要一个真正的数据集，结合之前的数据自定义数据集：
+```python
+def loadSimpDat():
+    simpDat = [['r', 'z', 'h', 'j', 'p'],
+               ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'],
+               ['z'],
+               ['r', 'x', 'n', 'o', 's'],
+               ['y', 'r', 'x', 'z', 'q', 't', 'p'],
+               ['y', 'z', 'x', 'e', 'q', 's', 't', 'm']]
+    return simpDat
+
+def createInitSet(dataSet):
+    retDict = {}
+    for trans in dataSet:
+        retDict[frozenset(trans)] = 1
+    return retDict
+```
+结果：
+```python
+simpDat = loadSimpDat()
+initSet  = createInitSet(simpDat)
+myFPtree,myHeaderTab = createTree(initSet,3)
+a = myFPtree.disp()
+print a
+```
+这样就构建了FP树，接下来就是使用它来进行频繁项集的挖掘。
+
+#### 从FP树中挖掘频繁项集
+在构建了FP树之后，就可以抽取频繁项集了，这里的思想和Apriori算法大致类似，首先从氮元素项集合开始，然后在此基础上逐步构建更大的集合。大致分为三个步骤：
+
+* 1.从FP树中获得条件模式基；
+* 2.利用条件模式基，构建一个条件FP树；
+* 3.迭代重复1和2，直到树包含一个元素项为止。
+首先，获取条件模式基。条件模式基是以所查找元素项为结尾的路径集合，表示的是所查找的元素项与树根节点之间的所有内容。结合构建FP树绘制的图，r的前缀路径就是{x,s}、{z,x,y}和{z},其中的每条前缀路径都与一个计数值有关，该计数值表示的是每条路径上r的数目。
+为了得到这些前缀路径，结合之前所得到的头指针表，头指针表中包含相同类型元素链表的起始指针，根据每一个元素项都可以上溯到这棵树直到根节点为止。该过程对应的代码如下：
+
+```python
+def ascendTree(leafNode, prefixPath): #ascends from leaf node to root
+    if leafNode.parent != None:
+        prefixPath.append(leafNode.name)
+        ascendTree(leafNode.parent, prefixPath)
+    
+def findPrefixPath(basePat, treeNode): #treeNode comes from header table
+    condPats = {}
+    while treeNode != None:
+        prefixPath = []
+        ascendTree(treeNode, prefixPath)
+        if len(prefixPath) > 1: 
+            condPats[frozenset(prefixPath[1:])] = treeNode.count
+        treeNode = treeNode.nodeLink
+    return condPats
+
+#test
+simpDat = loadSimpDat()
+initSet  = createInitSet(simpDat)
+myFPtree,myHeaderTab = createTree(initSet,3)
+a = myFPtree.disp()
+b = findPrefixPath('x',myHeaderTab['x'][1])
+print b
+```
+运行示例，与所给数据一致。接下来就可以创建条件FP树了。对于每一个频繁项，都需要创建一棵条件FP树，使用刚才创建的条件模式基作为输入，采用相同的建树代码来构建树，相应的递归发现频繁项、发现条件模式基和另外的条件树。对应的递归查找频繁项集的函数如下：
+```python
+def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
+    bigL = [v[0] for v in sorted(headerTable.items(), key=lambda p: p[1])]#(sort header table)
+    for basePat in bigL:
+        newFreqSet = preFix.copy()
+        newFreqSet.add(basePat)
+        freqItemList.append(newFreqSet)
+        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
+        myCondTree, myHead = createTree(condPattBases, minSup)
+        if myHead != None:            
+            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)
+```
+结合之前的数据验证发现没有错误。
+
+#### 应用示例
+在自定义的数据中队算法进行了验证，现在选取实际的数据进行测试。在这个数据集合中，包含了100万条记录，文件中的每一行包含某个用户浏览过的新闻报道，用来寻找那些至少被10万人浏览过的报道。代码如下：
+```python
+#从新闻网站点击流中挖掘
+parsedData = [line.split() for line in open('kosarak.dat').readlines()]
+initSet = createInitSet(parsedData)
+myFPtree,myHeaderTab = createTree(initSet,100000)
+myFreqList = []
+a = mineTree(myFPtree,myHeaderTab,100000,set([]),myFreqList)
+b = len(myFreqList)
+print b
+print myFreqList
+```
\ No newline at end of file

From ca6a0b627de158f838c3f05bd7359448927f2725 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:26:10 +0800
Subject: [PATCH 0824/1406] add ARL

---
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 assets/images/252.jpg | Bin 0 -> 17366 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/251.jpg
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From b6f7d750bdfa4138c0bed3bcf81a47b6dd95596e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:35:13 +0800
Subject: [PATCH 0825/1406] Update ARL.0.4.md

---
 assets/src/ARL/ARL.0.4.md | 21 ++++++++++++---------
 1 file changed, 12 insertions(+), 9 deletions(-)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 3d56eefa..f1df0aee 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -29,14 +29,17 @@ FP-growth算法的流程为：首先构造FP树，然后利用它来挖掘频繁
 </p>
 
 结合绘制的带头指针表的FP树，对表中数据进行过滤，排序如下：
-| 事务ID |  事务中的元素 |过滤和重排序后的事务|
-| ------ | --- |  --------------------------- | 
-| 001 | r,z,h,j,p |    z,r                    |
-| 002 |z,y,x,w,v,u,t,s|  z,x,y,s,t            |
-| 003 | z |          z                        |
-| 004 | r,x,n,o,s |  x,s,r                    |
-| 005 | y,r,x,z,q,t,p |    	z,x,y,r,t         |
-| 006 | y,z,x,e,q,s,t,m|    z,x,y,s,t         |
+
+| 事务ID | 事务ID | 过滤和重排序后的事务 |
+| --- | --- | --- |
+| 001 | r,z,h,j,p | z,r|
+| 002 |z,y,x,w,v,u,t,s|z,x,y,s,t|
+| 003 | z |z|
+| 004 | r,x,n,o,s |x,s,r|
+| 005 | y,r,x,z,q,t,p |z,x,y,r,t|
+| 006 | y,z,x,e,q,s,t,m|z,x,y,s,t|
+
+
 
 在对数据项过滤排序了之后，就可以构建FP树了，从NULL开始，向其中不断添加过滤排序后的频繁项集。过程可表示为：
 <p align="center">
@@ -204,4 +207,4 @@ a = mineTree(myFPtree,myHeaderTab,100000,set([]),myFreqList)
 b = len(myFreqList)
 print b
 print myFreqList
-```
\ No newline at end of file
+```

From b11e12f6c97d8dab386eb9c9f08048320771f3ba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:36:16 +0800
Subject: [PATCH 0826/1406] Update ARL.0.4.md

---
 assets/src/ARL/ARL.0.4.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index f1df0aee..2c270d47 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -74,6 +74,10 @@ print a
 '''
 ```
 
+<p align="center">
+<img width="300" align="center" src="../../images/251.jpg" />
+</p>
+
 这样，FP树对应的数据结构就建好了，现在就可以构建FP树了，FP树的构建函数如下:
 
 ```python
@@ -154,7 +158,11 @@ print a
 * 2.利用条件模式基，构建一个条件FP树；
 * 3.迭代重复1和2，直到树包含一个元素项为止。
 首先，获取条件模式基。条件模式基是以所查找元素项为结尾的路径集合，表示的是所查找的元素项与树根节点之间的所有内容。结合构建FP树绘制的图，r的前缀路径就是{x,s}、{z,x,y}和{z},其中的每条前缀路径都与一个计数值有关，该计数值表示的是每条路径上r的数目。
-为了得到这些前缀路径，结合之前所得到的头指针表，头指针表中包含相同类型元素链表的起始指针，根据每一个元素项都可以上溯到这棵树直到根节点为止。该过程对应的代码如下：
+为了得到这些前缀路径，结合之前所得到的头指针表，头指针表中包含相同类型元素链表的起始指针，根据每一个元素项都可以上溯到这棵树直到根节点为止。该过程对应的如下：
+
+<p align="center">
+<img width="300" align="center" src="../../images/252.jpg" />
+</p>
 
 ```python
 def ascendTree(leafNode, prefixPath): #ascends from leaf node to root

From 04327b379b3c0fe1b3b9962b526f311a79f24208 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:39:26 +0800
Subject: [PATCH 0827/1406] Update ARL.0.4.md

---
 assets/src/ARL/ARL.0.4.md | 176 +++++++++++++++++++++++++++++++++++---
 1 file changed, 164 insertions(+), 12 deletions(-)

diff --git a/assets/src/ARL/ARL.0.4.md b/assets/src/ARL/ARL.0.4.md
index 2c270d47..c711da74 100644
--- a/assets/src/ARL/ARL.0.4.md
+++ b/assets/src/ARL/ARL.0.4.md
@@ -75,7 +75,7 @@ print a
 ```
 
 <p align="center">
-<img width="300" align="center" src="../../images/251.jpg" />
+<img width="500" align="center" src="../../images/251.jpg" />
 </p>
 
 这样，FP树对应的数据结构就建好了，现在就可以构建FP树了，FP树的构建函数如下:
@@ -161,7 +161,7 @@ print a
 为了得到这些前缀路径，结合之前所得到的头指针表，头指针表中包含相同类型元素链表的起始指针，根据每一个元素项都可以上溯到这棵树直到根节点为止。该过程对应的如下：
 
 <p align="center">
-<img width="300" align="center" src="../../images/252.jpg" />
+<img width="500" align="center" src="../../images/252.jpg" />
 </p>
 
 ```python
@@ -204,15 +204,167 @@ def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
 结合之前的数据验证发现没有错误。
 
 #### 应用示例
-在自定义的数据中队算法进行了验证，现在选取实际的数据进行测试。在这个数据集合中，包含了100万条记录，文件中的每一行包含某个用户浏览过的新闻报道，用来寻找那些至少被10万人浏览过的报道。代码如下：
 ```python
-#从新闻网站点击流中挖掘
-parsedData = [line.split() for line in open('kosarak.dat').readlines()]
-initSet = createInitSet(parsedData)
-myFPtree,myHeaderTab = createTree(initSet,100000)
-myFreqList = []
-a = mineTree(myFPtree,myHeaderTab,100000,set([]),myFreqList)
-b = len(myFreqList)
-print b
-print myFreqList
+# -*- coding: utf-8 -* 
+# 树节点
+class treeNode:
+    def __init__(self, nameValue, numOccur, parentNode):
+        self.name = nameValue
+        self.count = numOccur         # 计数值
+        self.nodeLink = None          # 连接相似变量
+        self.parent = parentNode      #needs to be updated
+        self.children = {} 
+    
+    def inc(self, numOccur):
+        self.count += numOccur
+    
+    # 递归输出树节点
+    def disp(self, ind=1):
+        print '  '*ind, self.name, ' ', self.count
+        for child in self.children.values():
+            child.disp(ind+1)
+
+
+# 根据 dataSet 创建 FP-growth 树
+# 参数 minSup 指的是最小支持度
+def createTree(dataSet, minSup=1): 
+    headerTable = {}
+    
+    # 遍历所有元素项, 记录其出现次数
+    # 内容类似为 {'t': 3, 'w': 1, 'v': 1, 'y': 3, 'x': 4, 'z': 5}
+    for trans in dataSet:
+        for item in trans:
+            headerTable[item] = headerTable.get(item, 0) + dataSet[trans]
+
+    # 移除未达到最小支持度的元素项
+    for k in headerTable.keys():  
+        if headerTable[k] < minSup: 
+            del(headerTable[k])
+
+    freqItemSet = set(headerTable.keys())
+    if len(freqItemSet) == 0: return None, None  # 没有达到最小支持度的元素项, 返回
+
+    # 格式化后格式为: 
+    # {'t': [3, None], 'y': [3, None], 'x': [4, None], 'z': [5, None]}
+    for k in headerTable:
+        headerTable[k] = [headerTable[k], None] 
+
+    retTree = treeNode('Null Set', 1, None)     # 只包含空值的根节点
+    
+    for tranSet, count in dataSet.items():      # count 都初始化为 1
+        localD = {}
+        for item in tranSet:                    # 取满足最小支持度的元素项
+            if item in freqItemSet:
+                localD[item] = headerTable[item][0]
+
+        # 对每个项集中的元素项, 按支持度从大到小排序
+        if len(localD) > 0:
+            orderedItems = [v[0] for v in sorted(localD.items(), 
+                            key=lambda p: p[1], reverse=True)]
+            updateTree(orderedItems, retTree, headerTable, count)   # 填充树
+    return retTree, headerTable                 # 返回树与各个元素的头指针
+
+
+# 使用 items 使树生长, FP-growth 的来历
+# inTree 为树的根节点
+def updateTree(items, inTree, headerTable, count):
+    # 如果 items 的第一个元素是 树的第一层子节点, 则将此子节点对应的计算 加1
+    if items[0] in inTree.children:
+        inTree.children[items[0]].inc(count) 
+    else:   # 如果此节点不存在, 则给树添加新子节点
+        inTree.children[items[0]] = treeNode(items[0], count, inTree)
+        # 更新头指针表
+        if headerTable[items[0]][1] == None: 
+            headerTable[items[0]][1] = inTree.children[items[0]]
+        else:
+            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
+
+    # 对除去第一个元素之外的 items 递归建树
+    if len(items) > 1:
+        updateTree(items[1::], inTree.children[items[0]], headerTable, count)
+        
+
+# 更新头指针链表, targetNode 接到 nodeToTest 所指链表的最后
+# 这里不用递归, 因为递归在链表长度过长时, 可能会栈溢出
+def updateHeader(nodeToTest, targetNode):   
+    while (nodeToTest.nodeLink != None):    
+        nodeToTest = nodeToTest.nodeLink
+    nodeToTest.nodeLink = targetNode
+        
+
+# 迭代上溯整棵树
+# 即将叶节点到根节点的所有元素都存到 prefixPath 中
+def ascendTree(leafNode, prefixPath): 
+    if leafNode.parent != None:
+        prefixPath.append(leafNode.name)
+        ascendTree(leafNode.parent, prefixPath)
+
+
+# 按给定元素项生成一个条件模式基
+# 遍历头指针链表, 对每一个元素都向根节点上溯, 记录找到的前缀式及元素出现次数
+def findPrefixPath(basePat, treeNode): #treeNode comes from header table
+    condPats = {}
+    # 遍历以 treeNode 为头节点的头指针链表
+    while treeNode != None:
+        prefixPath = []
+        ascendTree(treeNode, prefixPath)
+        # 保存前缀及其次数
+        if len(prefixPath) > 1: 
+            condPats[frozenset(prefixPath[1:])] = treeNode.count
+        treeNode = treeNode.nodeLink
+    return condPats
+
+
+# 递归查找频繁项集
+# 参 freqItemList 返回频繁项集列表
+def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
+    # 头指针按其元素项出现的频率从小到大进行排序
+    bigL = [v[0] for v in sorted(headerTable.items(), key=lambda p: p[1])]
+
+    for basePat in bigL:  #start from bottom of header table
+        newFreqSet = preFix.copy()   # 生成一个频繁项集
+        newFreqSet.add(basePat)
+
+        # 创造条件基
+        freqItemList.append(newFreqSet)  # 繁频项集添加到参数中, 以待最后返回
+        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
+
+        # 创建条件 FP 树
+        myCondTree, myHead = createTree(condPattBases, minSup)
+
+        # 递归挖掘条件 FP 树
+        if myHead != None:
+            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)
+
+
+# 载入数据
+def loadSimpDat():
+    simpDat = [['r', 'z', 'h', 'j', 'p'],
+               ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'],
+               ['z'],
+               ['r', 'x', 'n', 'o', 's'],
+               ['y', 'r', 'x', 'z', 'q', 't', 'p'],
+               ['y', 'z', 'x', 'e', 'q', 's', 't', 'm']]
+    return simpDat
+
+
+# 初始化每个项集的次数为 1
+def createInitSet(dataSet):
+    retDict = {}
+    for trans in dataSet:
+        retDict[frozenset(trans)] = 1
+    return retDict
+
+
+if __name__ == "__main__":
+    # 建树
+    simpDat = loadSimpDat()
+    initSet = createInitSet(simpDat)
+    myFPtree, myHeaderTab = createTree(initSet, 3)          # 3 为最小支持度
+    myFPtree.disp()  # 显示树
+
+    # 根据树挖掘 频繁项集
+    freqItems = []
+    mineTree(myFPtree, myHeaderTab, 3, set([]), freqItems)  # 3 为最小支持度
+    print freqItems
 ```

From 8911fc0fb32ecff70da30975bdd69a5e56ef1c1c Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:52:27 +0800
Subject: [PATCH 0828/1406] change page

---
 README.md | 30 ++++++++++++++++++++----------
 1 file changed, 20 insertions(+), 10 deletions(-)

diff --git a/README.md b/README.md
index 3a346950..c19e8d4e 100644
--- a/README.md
+++ b/README.md
@@ -120,16 +120,26 @@
      * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
      * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
      * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
- * [神经网络]()      
-     * [感知器]() 
-     * [反向传播算法（BP）]() 
-     * [Hopfield网络]() 
-     * [径向基函数网络（RBFN）]() 
- * [深度学习]() 
-     * [深度玻尔兹曼机（DBM）]() 
-     * [卷积神经网络（CNN）]() 
-     * [递归神经网络（RNN、LSTM）]()
-     * [栈式自编码算法（Stacked Auto-Encoder）]()
+ * [人工神经网络(Artificial  neural network)]()      
+     * [自动编码器(Autoencoder)]() 
+     * [反向传播(Backpropagation)]() 
+     * [回归神经网络(Recurrent Neural Network)]() 
+     * [多层感知器(Multilayer Perceptron)]() 
+     * [玻尔兹曼机(Boltzmann Machine)]() 
+     * [卷积神经网络(Convolutional Neural Network)]() 
+     * [Hopfield网络(Hopfield Network)]() 
+     * [径向基函数网络(Radial Basis Function Network)]() 
+     * [受限玻尔兹曼机(Restricted Boltzmann Machine)]() 
+     * [自组织映射(Self-Organizing Map)]() 
+     * [尖峰神经网络(Spiking Neural Network)]() 
+ * [深度学习(Deep learning)]() 
+     * [深度信念网络(Deep Belief Machines)]() 
+     * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
+     * [深度递归神经网络(Deep Recurrent Neural Networks)]() 
+     * [分层时间记忆(Hierarchical Temporal Memory)]() 
+     * [深度玻尔兹曼机(Deep Boltzmann Machine)]() 
+     * [堆叠自动编码器(Stacked Boltzmann Machine)]() 
+     * [生成式对抗网络(Generative Adversarial Networks)]()
  * [降维算法]()
      * [主成分分析法（PCA）]()
      * [主成分回归（PCR）]()

From a7029a1d4cd4f856313e99ee7ef1a3721c583d3b Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 22:56:42 +0800
Subject: [PATCH 0829/1406] change page of ANN

---
 README.md                 |  4 ++--
 assets/src/ANN/ANN.0.1.md | 14 ++++++++++++++
 2 files changed, 16 insertions(+), 2 deletions(-)
 create mode 100644 assets/src/ANN/ANN.0.1.md

diff --git a/README.md b/README.md
index c19e8d4e..254cec93 100644
--- a/README.md
+++ b/README.md
@@ -120,7 +120,7 @@
      * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
      * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
      * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
- * [人工神经网络(Artificial  neural network)]()      
+ * [人工神经网络(Artificial Neural Network)]()      
      * [自动编码器(Autoencoder)]() 
      * [反向传播(Backpropagation)]() 
      * [回归神经网络(Recurrent Neural Network)]() 
@@ -132,7 +132,7 @@
      * [受限玻尔兹曼机(Restricted Boltzmann Machine)]() 
      * [自组织映射(Self-Organizing Map)]() 
      * [尖峰神经网络(Spiking Neural Network)]() 
- * [深度学习(Deep learning)]() 
+ * [深度学习(Deep Learning)]() 
      * [深度信念网络(Deep Belief Machines)]() 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
      * [深度递归神经网络(Deep Recurrent Neural Networks)]() 
diff --git a/assets/src/ANN/ANN.0.1.md b/assets/src/ANN/ANN.0.1.md
new file mode 100644
index 00000000..1c67e1d7
--- /dev/null
+++ b/assets/src/ANN/ANN.0.1.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 人工神经网络(Artificial Neural Network)

From 78d515d07a572e6dbe77bacb04d3bc0465b0163b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 22:57:41 +0800
Subject: [PATCH 0830/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 254cec93..538dcec5 100644
--- a/README.md
+++ b/README.md
@@ -120,7 +120,7 @@
      * [先验算法(Apriori Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.2.md) 
      * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
      * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
- * [人工神经网络(Artificial Neural Network)]()      
+ * [人工神经网络(Artificial Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.1.md)      
      * [自动编码器(Autoencoder)]() 
      * [反向传播(Backpropagation)]() 
      * [回归神经网络(Recurrent Neural Network)]() 

From 44ecd638869951bf4de1a0464476130dd7213605 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 23:00:00 +0800
Subject: [PATCH 0831/1406] Update ANN.0.1.md

---
 assets/src/ANN/ANN.0.1.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/assets/src/ANN/ANN.0.1.md b/assets/src/ANN/ANN.0.1.md
index 1c67e1d7..de6fd003 100644
--- a/assets/src/ANN/ANN.0.1.md
+++ b/assets/src/ANN/ANN.0.1.md
@@ -12,3 +12,14 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 人工神经网络(Artificial Neural Network)
+
+人工神经网络 （Artificial Neural Network，ANN）简称神经网络(NN)，是基于生物学中神经网络的基本原理，在理解和抽象了人脑结构和外界刺激响应机制后，以网络拓扑知识为理论基础，模拟人脑的神经系统对复杂信息的处理机制的一种数学模型，根植于神经科学、数学、思维科学、人工智能、统计学、物理学、计算机科学以及工程科学的一门技术，通常用于解决分类和回归问题。具有并行分布的处理能力、高容错性、智能化和自学习等能力的特征，本质上是一个有大量简单元件相互连接而成的复杂网络，具有高度的非线性，能够进行复杂的逻辑操作和非线性关系实现的系统。
+
+神经网络由大量的节点（或称神经元）之间相互联接构成，每个节点代表一种特定的输出函数，称为激活函数（activation function）；每两个节点间的连接都代表一个对于通过该连接信号的加权值，称之为权重（weight），神经网络就是通过这种方式来模拟人类的记忆。网络的输出则取决于网络的结构、网络的连接方式、权重和激活函数。而网络自身通常都是对自然界某种算法或者函数的逼近，也可能是对一种逻辑策略的表达，是对传统逻辑学演算的进一步延伸。
+
+<p align="center">
+<img width="300" align="center" src="../../images/1.jpg" />
+</p>
+
+
+人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。

From cb55538d461d6dfc37bfae838185e4aff31740af Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 23:00:47 +0800
Subject: [PATCH 0832/1406] Update ANN.0.1.md

---
 assets/src/ANN/ANN.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ANN/ANN.0.1.md b/assets/src/ANN/ANN.0.1.md
index de6fd003..d41a2d34 100644
--- a/assets/src/ANN/ANN.0.1.md
+++ b/assets/src/ANN/ANN.0.1.md
@@ -23,3 +23,5 @@
 
 
 人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。
+
+应用领域：神经网络克服了传统人工智能方法对于直觉的缺陷，因而在神经专家系统、模式识别、智能控制、组合优化、预测等领域有成功的应用。

From 7fa2ef5ac017e1647290ca6066e9da5b9b3f7983 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 20 Apr 2018 23:02:35 +0800
Subject: [PATCH 0833/1406] Update ANN.0.1.md

---
 assets/src/ANN/ANN.0.1.md | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/assets/src/ANN/ANN.0.1.md b/assets/src/ANN/ANN.0.1.md
index d41a2d34..a653ef5f 100644
--- a/assets/src/ANN/ANN.0.1.md
+++ b/assets/src/ANN/ANN.0.1.md
@@ -25,3 +25,16 @@
 人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。
 
 应用领域：神经网络克服了传统人工智能方法对于直觉的缺陷，因而在神经专家系统、模式识别、智能控制、组合优化、预测等领域有成功的应用。
+
+人工神经网络(Artificial Neural Network)算法应用： 
+ * 自动编码器(Autoencoder) 
+ * 反向传播(Backpropagation)
+ * 回归神经网络(Recurrent Neural Network)
+ * 多层感知器(Multilayer Perceptron)
+ * 玻尔兹曼机(Boltzmann Machine)
+ * 卷积神经网络(Convolutional Neural Network)
+ * Hopfield网络(Hopfield Network)]() 
+ * 径向基函数网络(Radial Basis Function Network)
+ * 受限玻尔兹曼机(Restricted Boltzmann Machine)
+ * 自组织映射(Self-Organizing Map)
+ * 尖峰神经网络(Spiking Neural Network)

From 35a8f1a3da7494ef0420a9fcb6b091d45048f175 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 23:03:30 +0800
Subject: [PATCH 0834/1406] add Autoencoder

---
 assets/src/ANN/ANN.0.2.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)
 create mode 100644 assets/src/ANN/ANN.0.2.md

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
new file mode 100644
index 00000000..0487b1cb
--- /dev/null
+++ b/assets/src/ANN/ANN.0.2.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 自动编码器(Autoencoder)

From ce026b5adf5f39651695aa6ccb34b8452f21dca3 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 20 Apr 2018 23:04:29 +0800
Subject: [PATCH 0835/1406] change page of ANN

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 538dcec5..b435d102 100644
--- a/README.md
+++ b/README.md
@@ -121,7 +121,7 @@
      * [Eclat算法(Eclat Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.3.md) 
      * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
  * [人工神经网络(Artificial Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.1.md)      
-     * [自动编码器(Autoencoder)]() 
+     * [自动编码器(Autoencoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.2.md) 
      * [反向传播(Backpropagation)]() 
      * [回归神经网络(Recurrent Neural Network)]() 
      * [多层感知器(Multilayer Perceptron)]() 

From d9b46242b2e7a5e81748c4c06c19d08041e57ded Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 21 Apr 2018 09:04:06 +0800
Subject: [PATCH 0836/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index 0487b1cb..a7b38806 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -12,3 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 自动编码器(Autoencoder)
+自动编码器(Autoencoder)是一种无监督的学习算法，主要用于数据的降维或者特征的抽取，在深度学习中，autoencoder可用于在训练阶段开始前，确定权重矩阵的初始值。
+
+神经网络中的权重矩阵可看作是对输入的数据进行特征转换，即先将数据编码为另一种形式，然后在此基础上进行一系列学习。然而，在对权重初始化时，我们并不知道初始的权重值在训练时会起到怎样的作用，也不知道在训练过程中权重会怎样的变化。因此一种较好的思路是，利用初始化生成的权重矩阵进行编码时，我们希望编码后的数据能够较好的保留原始数据的主要特征。那么，如何衡量码后的数据是否保留了较完整的信息呢？答案是：如果编码后的数据能够较为容易地通过解码恢复成原始数据，我们则认为较好的保留了数据信息。

From c17d189b2fe18a9c4b0f9b076940e2b387cb6f1d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 21 Apr 2018 09:13:07 +0800
Subject: [PATCH 0837/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index a7b38806..1ee7f06d 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -12,6 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 自动编码器(Autoencoder)
-自动编码器(Autoencoder)是一种无监督的学习算法，主要用于数据的降维或者特征的抽取，在深度学习中，autoencoder可用于在训练阶段开始前，确定权重矩阵的初始值。
+自动编码器(Autoencoder)是一种无监督的学习算法，主要用于数据的降维或者特征的抽取，在深度学习中，自动编码器(Autoencoder)可用于在训练阶段开始前，确定权重矩阵的初始值。
 
 神经网络中的权重矩阵可看作是对输入的数据进行特征转换，即先将数据编码为另一种形式，然后在此基础上进行一系列学习。然而，在对权重初始化时，我们并不知道初始的权重值在训练时会起到怎样的作用，也不知道在训练过程中权重会怎样的变化。因此一种较好的思路是，利用初始化生成的权重矩阵进行编码时，我们希望编码后的数据能够较好的保留原始数据的主要特征。那么，如何衡量码后的数据是否保留了较完整的信息呢？答案是：如果编码后的数据能够较为容易地通过解码恢复成原始数据，我们则认为较好的保留了数据信息。

From 64eb59acdc8ebce880aff0cd757a1ff3c054b8ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 21 Apr 2018 22:31:01 +0800
Subject: [PATCH 0838/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index 1ee7f06d..fad4a576 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -15,3 +15,9 @@
 自动编码器(Autoencoder)是一种无监督的学习算法，主要用于数据的降维或者特征的抽取，在深度学习中，自动编码器(Autoencoder)可用于在训练阶段开始前，确定权重矩阵的初始值。
 
 神经网络中的权重矩阵可看作是对输入的数据进行特征转换，即先将数据编码为另一种形式，然后在此基础上进行一系列学习。然而，在对权重初始化时，我们并不知道初始的权重值在训练时会起到怎样的作用，也不知道在训练过程中权重会怎样的变化。因此一种较好的思路是，利用初始化生成的权重矩阵进行编码时，我们希望编码后的数据能够较好的保留原始数据的主要特征。那么，如何衡量码后的数据是否保留了较完整的信息呢？答案是：如果编码后的数据能够较为容易地通过解码恢复成原始数据，我们则认为较好的保留了数据信息。
+
+自动编码器(Autoencoder)中：原始input（设为x）经过加权（W、b)、映射（Sigmoid）之后得到y，再对y反向加权映射回来成为z。
+
+通过反复迭代训练两组（W、b），使得误差函数最小，即尽可能保证z近似于x，即完美重构了x。
+
+那么可以说正向第一组权（W、b）是成功的，很好的学习了input中的关键特征，不然也不会重构得如此完美.

From 7c23b3cfbdae7cf72e9c2e39ab0f8dcf2d86d448 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 21 Apr 2018 22:32:21 +0800
Subject: [PATCH 0839/1406] change ANN

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
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From 7ecbc2cb5f09695d6bb640f7df76985dc84226c6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 21 Apr 2018 22:35:25 +0800
Subject: [PATCH 0840/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index fad4a576..b54f7fe6 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -21,3 +21,6 @@
 通过反复迭代训练两组（W、b），使得误差函数最小，即尽可能保证z近似于x，即完美重构了x。
 
 那么可以说正向第一组权（W、b）是成功的，很好的学习了input中的关键特征，不然也不会重构得如此完美.
+<p align="center">
+<img width="300" align="center" src="../../images/252.jpg" />
+</p>

From f3c0db55c8df20811d0fd8ba80c11a174f3a9c02 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 09:47:46 +0800
Subject: [PATCH 0841/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index b54f7fe6..5bf5f8f5 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -24,3 +24,15 @@
 <p align="center">
 <img width="300" align="center" src="../../images/252.jpg" />
 </p>
+
+这个过程很有趣，首先，它没有使用数据标签来计算误差update参数，所以是无监督学习。
+
+其次，利用类似神经网络的双隐层的方式，简单粗暴地提取了样本的特征。 
+
+这个双隐层是有争议的，最初的编码器确实使用了两组（W，b），但是Vincent在2010年的论文中做了研究，发现只要单组W就可以了。
+
+即W'=W^T, W和W'称为Tied Weights。实验证明，W'真的只是在打酱油，完全没有必要去做训练。
+
+逆向重构矩阵让人想起了逆矩阵，若W^-1=W^T的话，W就是个正交矩阵了，即W是可以训成近似正交阵的。
+
+由于W'就是个酱油，训练完之后就没它事了。正向传播用W即可，相当于为input预先编个码，再导入到下一layer去。所以叫自动编码器，而不叫自动编码解码器。

From 1142d511aa33a78426d3892584ed7af4717e6a2e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 09:49:52 +0800
Subject: [PATCH 0842/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index 5bf5f8f5..daa04563 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -36,3 +36,12 @@
 逆向重构矩阵让人想起了逆矩阵，若W^-1=W^T的话，W就是个正交矩阵了，即W是可以训成近似正交阵的。
 
 由于W'就是个酱油，训练完之后就没它事了。正向传播用W即可，相当于为input预先编个码，再导入到下一layer去。所以叫自动编码器，而不叫自动编码解码器。
+
+自动编码器相当于创建了一个隐层，一个简单想法就是加在深度网络的开头，作为原始信号的初级filter，起到降维、提取特征的效果。
+当然，这种做法就有一个问题，AutoEncoder可以看作是PCA的非线性补丁加强版，PCA的取得的效果是建立在降维基础上的。
+
+仔细想想CNN这种结构，随着layer的推进，每层的神经元个数在递增，如果用了AutoEncoder去预训练，岂不是增维了？真的没问题？
+
+相关论文中给出的实验结果认为AutoEncoder的增维效果还不赖，原因可能是非线性网络能力很强，尽管神经元个数增多，但是每个神经元的效果在衰减。
+
+同时，随机梯度算法给了后续监督学习一个良好的开端。整体上，增维是利大于弊的。

From 7950e23d2f7347ef8baf0b5e53873a39adbeddb0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 09:52:08 +0800
Subject: [PATCH 0843/1406] Update ANN.0.2.md

---
 assets/src/ANN/ANN.0.2.md | 426 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 426 insertions(+)

diff --git a/assets/src/ANN/ANN.0.2.md b/assets/src/ANN/ANN.0.2.md
index daa04563..d96220c3 100644
--- a/assets/src/ANN/ANN.0.2.md
+++ b/assets/src/ANN/ANN.0.2.md
@@ -45,3 +45,429 @@
 相关论文中给出的实验结果认为AutoEncoder的增维效果还不赖，原因可能是非线性网络能力很强，尽管神经元个数增多，但是每个神经元的效果在衰减。
 
 同时，随机梯度算法给了后续监督学习一个良好的开端。整体上，增维是利大于弊的。
+
+#### 应用示例
+```python
+from __future__ import division
+
+import tensorflow as tf
+import numpy as np
+import logging
+import json
+import os
+
+
+class TextAutoencoder(object):
+    """
+    Class that encapsulates the encoder-decoder architecture to
+    reconstruct pieces of text.
+    """
+
+    def __init__(self, lstm_units, embeddings, go, train=True,
+                 train_embeddings=False, bidirectional=True):
+        """
+        Initialize the encoder/decoder and creates Tensor objects
+        :param lstm_units: number of LSTM units
+        :param embeddings: numpy array with initial embeddings
+        :param go: index of the GO symbol in the embedding matrix
+        :param train_embeddings: whether to adjust embeddings during training
+        :param bidirectional: whether to create a bidirectional autoencoder
+            (if False, a simple linear LSTM is used)
+        """
+        # EOS and GO share the same symbol. Only GO needs to be embedded, and
+        # only EOS exists as a possible network output
+        self.go = go
+        self.eos = go
+
+        self.bidirectional = bidirectional
+        self.vocab_size = embeddings.shape[0]
+        self.embedding_size = embeddings.shape[1]
+        self.global_step = tf.Variable(0, name='global_step', trainable=False)
+
+        # the sentence is the object to be memorized
+        self.sentence = tf.placeholder(tf.int32, [None, None], 'sentence')
+        self.sentence_size = tf.placeholder(tf.int32, [None],
+                                            'sentence_size')
+        self.l2_constant = tf.placeholder(tf.float32, name='l2_constant')
+        self.clip_value = tf.placeholder(tf.float32, name='clip')
+        self.learning_rate = tf.placeholder(tf.float32, name='learning_rate')
+        self.dropout_keep = tf.placeholder(tf.float32, name='dropout_keep')
+
+        self.decoder_step_input = tf.placeholder(tf.int32,
+                                                 [None],
+                                                 'prediction_step')
+
+        name = 'decoder_fw_step_state_c'
+        self.decoder_fw_step_c = tf.placeholder(tf.float32,
+                                                [None, lstm_units], name)
+        name = 'decoder_fw_step_state_h'
+        self.decoder_fw_step_h = tf.placeholder(tf.float32,
+                                                [None, lstm_units], name)
+        self.decoder_bw_step_c = tf.placeholder(tf.float32,
+                                                [None, lstm_units],
+                                                'decoder_bw_step_state_c')
+        self.decoder_bw_step_h = tf.placeholder(tf.float32,
+                                                [None, lstm_units],
+                                                'decoder_bw_step_state_h')
+
+        with tf.variable_scope('autoencoder') as self.scope:
+            self.embeddings = tf.Variable(embeddings, name='embeddings',
+                                          trainable=train_embeddings)
+
+            initializer = tf.glorot_normal_initializer()
+            self.lstm_fw = tf.nn.rnn_cell.LSTMCell(lstm_units,
+                                                   initializer=initializer)
+            self.lstm_bw = tf.nn.rnn_cell.LSTMCell(lstm_units,
+                                                   initializer=initializer)
+
+            embedded = tf.nn.embedding_lookup(self.embeddings, self.sentence)
+            embedded = tf.nn.dropout(embedded, self.dropout_keep)
+
+            # encoding step
+            if bidirectional:
+                bdr = tf.nn.bidirectional_dynamic_rnn
+                ret = bdr(self.lstm_fw, self.lstm_bw,
+                          embedded, dtype=tf.float32,
+                          sequence_length=self.sentence_size,
+                          scope=self.scope)
+            else:
+                ret = tf.nn.dynamic_rnn(self.lstm_fw, embedded,
+                                        dtype=tf.float32,
+                                        sequence_length=self.sentence_size,
+                                        scope=self.scope)
+            _, self.encoded_state = ret
+            if bidirectional:
+                encoded_state_fw, encoded_state_bw = self.encoded_state
+
+                # set the scope name used inside the decoder.
+                # maybe there's a more elegant way to do it?
+                fw_scope_name = self.scope.name + '/fw'
+                bw_scope_name = self.scope.name + '/bw'
+            else:
+                encoded_state_fw = self.encoded_state
+                fw_scope_name = self.scope
+
+            self.scope.reuse_variables()
+
+            # generate a batch of embedded GO
+            # sentence_size has the batch dimension
+            go_batch = self._generate_batch_go(self.sentence_size)
+            embedded_eos = tf.nn.embedding_lookup(self.embeddings,
+                                                  go_batch)
+            embedded_eos = tf.reshape(embedded_eos,
+                                      [-1, 1, self.embedding_size])
+            decoder_input = tf.concat([embedded_eos, embedded], axis=1)
+
+            # decoding step
+
+            # We give the same inputs to the forward and backward LSTMs,
+            # but each one has its own hidden state
+            # their outputs are concatenated and fed to the softmax layer
+            if bidirectional:
+                outputs, _ = tf.nn.bidirectional_dynamic_rnn(
+                    self.lstm_fw, self.lstm_bw, decoder_input,
+                    self.sentence_size, encoded_state_fw, encoded_state_bw)
+
+                # concat fw and bw outputs
+                outputs = tf.concat(outputs, -1)
+            else:
+                outputs, _ = tf.nn.dynamic_rnn(
+                    self.lstm_fw, decoder_input, self.sentence_size,
+                    encoded_state_fw)
+
+            self.decoder_outputs = outputs
+
+        # now project the outputs to the vocabulary
+        with tf.variable_scope('projection') as self.projection_scope:
+            # decoder_outputs has shape (batch, max_sentence_size, vocab_size)
+            self.logits = tf.layers.dense(outputs, self.vocab_size)
+
+        # tensors for running a model
+        embedded_step = tf.nn.embedding_lookup(self.embeddings,
+                                               self.decoder_step_input)
+        state_fw = tf.nn.rnn_cell.LSTMStateTuple(self.decoder_fw_step_c,
+                                                 self.decoder_fw_step_h)
+        state_bw = tf.nn.rnn_cell.LSTMStateTuple(self.decoder_bw_step_c,
+                                                 self.decoder_bw_step_h)
+        with tf.variable_scope(fw_scope_name, reuse=True):
+            ret_fw = self.lstm_fw(embedded_step, state_fw)
+        step_output_fw, self.decoder_fw_step_state = ret_fw
+
+        if bidirectional:
+            with tf.variable_scope(bw_scope_name, reuse=True):
+                ret_bw = self.lstm_bw(embedded_step, state_bw)
+                step_output_bw, self.decoder_bw_step_state = ret_bw
+                step_output = tf.concat(axis=1, values=[step_output_fw,
+                                                        step_output_bw])
+        else:
+            step_output = step_output_fw
+
+        with tf.variable_scope(self.projection_scope, reuse=True):
+            self.projected_step_output = tf.layers.dense(step_output,
+                                                         self.vocab_size)
+
+        if train:
+            self._create_training_tensors()
+
+    def _create_training_tensors(self):
+        """
+        Create member variables related to training.
+        """
+        eos_batch = self._generate_batch_go(self.sentence_size)
+        eos_batch = tf.reshape(eos_batch, [-1, 1])
+        decoder_labels = tf.concat([self.sentence, eos_batch], -1)
+
+        projection_vars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,
+                                            scope=self.projection_scope.name)
+        # a bit ugly, maybe we should improve this?
+        projection_w = [var for var in projection_vars
+                        if 'kernel' in var.name][0]
+        projection_b = [var for var in projection_vars
+                        if 'bias' in var.name][0]
+
+        # set the importance of each time step
+        # 1 if before sentence end or EOS itself; 0 otherwise
+        max_len = tf.shape(self.sentence)[1]
+        mask = tf.sequence_mask(self.sentence_size + 1, max_len + 1, tf.float32)
+        num_actual_labels = tf.reduce_sum(mask)
+        projection_w_t = tf.transpose(projection_w)
+
+        # reshape to have batch and time steps in the same dimension
+        decoder_outputs2d = tf.reshape(self.decoder_outputs,
+                                       [-1, tf.shape(self.decoder_outputs)[-1]])
+        labels = tf.reshape(decoder_labels, [-1, 1])
+        sampled_loss = tf.nn.sampled_softmax_loss(
+            projection_w_t, projection_b, labels, decoder_outputs2d, 100,
+            self.vocab_size)
+
+        masked_loss = tf.reshape(mask, [-1]) * sampled_loss
+        self.loss = tf.reduce_sum(masked_loss) / num_actual_labels
+
+        optimizer = tf.train.AdamOptimizer(self.learning_rate)
+        gradients, v = zip(*optimizer.compute_gradients(self.loss))
+        gradients, _ = tf.clip_by_global_norm(gradients, self.clip_value)
+
+        self.train_op = optimizer.apply_gradients(zip(gradients, v),
+                                                  global_step=self.global_step)
+
+    def get_trainable_variables(self):
+        """
+        Return all trainable variables inside the model
+        """
+        return tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES)
+
+    def train(self, session, save_path, train_data, valid_data,
+              batch_size, epochs, learning_rate, dropout_keep,
+              clip_value, report_interval):
+        """
+        Train the model
+        :param session: tensorflow session
+        :param train_data: Dataset object with training data
+        :param valid_data: Dataset object with validation data
+        :param batch_size: batch size
+        :param learning_rate: initial learning rate
+        :param dropout_keep: the probability that each LSTM input/output is kept
+        :param epochs: how many epochs to train for
+        :param clip_value: value to clip tensor norm during training
+        :param save_path: folder to save the model
+        :param report_interval: report after that many batches
+        """
+        saver = tf.train.Saver(self.get_trainable_variables(),
+                               max_to_keep=1)
+
+        best_loss = 10000
+        accumulated_loss = 0
+        batch_counter = 0
+        num_sents = 0
+
+        # get all data at once. we need all matrices with the same size,
+        # or else they don't fit the placeholders
+        # train_sents, train_sizes = train_data.join_all(self.go,
+        #                                                self.num_time_steps,
+        #                                                shuffle=True)
+
+        # del train_data  # save memory...
+        valid_sents, valid_sizes = valid_data.join_all(self.go,
+                                                       shuffle=True)
+        train_data.reset_epoch_counter()
+        feeds = {self.clip_value: clip_value,
+                 self.dropout_keep: dropout_keep,
+                 self.learning_rate: learning_rate}
+
+        while train_data.epoch_counter < epochs:
+            batch_counter += 1
+            train_sents, train_sizes = train_data.next_batch(batch_size)
+            feeds[self.sentence] = train_sents
+            feeds[self.sentence_size] = train_sizes
+
+            _, loss = session.run([self.train_op, self.loss], feeds)
+
+            # multiply by len because some batches may be smaller
+            # (due to bucketing), then take the average
+            accumulated_loss += loss * len(train_sents)
+            num_sents += len(train_sents)
+
+            if batch_counter % report_interval == 0:
+                avg_loss = accumulated_loss / num_sents
+                accumulated_loss = 0
+                num_sents = 0
+
+                # we can't use all the validation at once, since it would
+                # take too much memory. running many small batches would
+                # instead take too much time. So let's just sample it.
+                sample_indices = np.random.randint(0, len(valid_data),
+                                                   5000)
+                validation_feeds = {
+                    self.sentence: valid_sents[sample_indices],
+                    self.sentence_size: valid_sizes[sample_indices],
+                    self.dropout_keep: 1}
+
+                loss = session.run(self.loss, validation_feeds)
+                msg = '%d epochs, %d batches\t' % (train_data.epoch_counter,
+                                                   batch_counter)
+                msg += 'Avg batch loss: %f\t' % avg_loss
+                msg += 'Validation loss: %f' % loss
+                if loss < best_loss:
+                    best_loss = loss
+                    self.save(saver, session, save_path)
+                    msg += '\t(saved model)'
+
+                logging.info(msg)
+
+    def save(self, saver, session, directory):
+        """
+        Save the autoencoder model and metadata to the specified
+        directory.
+        """
+        model_path = os.path.join(directory, 'model')
+        saver.save(session, model_path)
+        metadata = {'vocab_size': self.vocab_size,
+                    'embedding_size': self.embedding_size,
+                    'num_units': self.lstm_fw.output_size,
+                    'go': self.go,
+                    'bidirectional': self.bidirectional
+                    }
+        metadata_path = os.path.join(directory, 'metadata.json')
+        with open(metadata_path, 'wb') as f:
+            json.dump(metadata, f)
+
+    @classmethod
+    def load(cls, directory, session, train=False):
+        """
+        Load an instance of this class from a previously saved one.
+        :param directory: directory with the model files
+        :param session: tensorflow session
+        :param train: if True, also create training tensors
+        :return: a TextAutoencoder instance
+        """
+        model_path = os.path.join(directory, 'model')
+        metadata_path = os.path.join(directory, 'metadata.json')
+        with open(metadata_path, 'rb') as f:
+            metadata = json.load(f)
+        dummy_embeddings = np.empty((metadata['vocab_size'],
+                                     metadata['embedding_size'],),
+                                    dtype=np.float32)
+
+        ae = TextAutoencoder(metadata['num_units'], dummy_embeddings,
+                             metadata['go'], train=train,
+                             bidirectional=metadata['bidirectional'])
+        vars_to_load = ae.get_trainable_variables()
+        if not train:
+            # if not flagged for training, the embeddings won't be in
+            # the list
+            vars_to_load.append(ae.embeddings)
+
+        saver = tf.train.Saver(vars_to_load)
+        saver.restore(session, model_path)
+        return ae
+
+    def encode(self, session, inputs, sizes):
+        """
+        Run the encoder to obtain the encoded hidden state
+        :param session: tensorflow session
+        :param inputs: 2-d array with the word indices
+        :param sizes: 1-d array with size of each sentence
+        :return: a 2-d numpy array with the hidden state
+        """
+        feeds = {self.sentence: inputs,
+                 self.sentence_size: sizes,
+                 self.dropout_keep: 1}
+        state = session.run(self.encoded_state, feeds)
+        if self.bidirectional:
+            state_fw, state_bw = state
+            return np.hstack((state_fw.c, state_bw.c))
+        return state.c
+
+    def run(self, session, inputs, sizes):
+        """
+        Run the autoencoder with the given data
+        :param session: tensorflow session
+        :param inputs: 2-d array with the word indices
+        :param sizes: 1-d array with size of each sentence
+        :return: a 2-d array (batch, output_length) with the answer
+            produced by the autoencoder. The output length is not
+            fixed; it stops after producing EOS for all items in the
+            batch or reaching two times the maximum number of time
+            steps in the inputs.
+        """
+        feeds = {self.sentence: inputs,
+                 self.sentence_size: sizes,
+                 self.dropout_keep: 1}
+        state = session.run(self.encoded_state, feeds)
+        if self.bidirectional:
+            state_fw, state_bw = state
+        else:
+            state_fw = state
+
+        time_steps = 0
+        max_time_steps = 2 * len(inputs[0])
+        answer = []
+        input_symbol = self.go * np.ones_like(sizes, dtype=np.int32)
+
+        # this array control which sequences have already been finished by the
+        # decoder, i.e., for which ones it already produced the END symbol
+        sequences_done = np.zeros_like(sizes, dtype=np.bool)
+
+        while True:
+            # we could use tensorflow's rnn_decoder, but this gives us
+            # finer control
+
+            feeds = {self.decoder_fw_step_c: state_fw.c,
+                     self.decoder_fw_step_h: state_fw.h,
+                     self.decoder_step_input: input_symbol,
+                     self.dropout_keep: 1}
+            if self.bidirectional:
+                feeds[self.decoder_bw_step_c] = state_bw.c
+                feeds[self.decoder_bw_step_h] = state_bw.h
+
+                ops = [self.projected_step_output,
+                       self.decoder_fw_step_state,
+                       self.decoder_bw_step_state]
+                outputs, state_fw, state_bw = session.run(ops, feeds)
+            else:
+                ops = [self.projected_step_output,
+                       self.decoder_fw_step_state]
+                outputs, state_fw = session.run(ops, feeds)
+
+            input_symbol = outputs.argmax(1)
+            answer.append(input_symbol)
+
+            # use an "additive" or in order to avoid infinite loops
+            sequences_done |= (input_symbol == self.eos)
+
+            if sequences_done.all() or time_steps > max_time_steps:
+                break
+            else:
+                time_steps += 1
+
+        return np.hstack(answer)
+
+    def _generate_batch_go(self, like):
+        """
+        Generate a 1-d tensor with copies of EOS as big as the batch size,
+        :param like: a tensor whose shape the returned embeddings should match
+        :return: a tensor with shape as `like`
+        """
+        ones = tf.ones_like(like)
+        return ones * self.go
+```

From c8261758a5a652cecdc7142b9bcd0d006ab7a5f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 22 Apr 2018 11:01:55 +0800
Subject: [PATCH 0844/1406] change page

---
 assets/src/ANN/ANN.0.3.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)
 create mode 100644 assets/src/ANN/ANN.0.3.md

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
new file mode 100644
index 00000000..f394730e
--- /dev/null
+++ b/assets/src/ANN/ANN.0.3.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 反向传播(Backpropagation

From 8854ee059284440ffe88d2cffb60145f0f539e2f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 11:16:23 +0800
Subject: [PATCH 0845/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b435d102..3049fd3a 100644
--- a/README.md
+++ b/README.md
@@ -122,7 +122,7 @@
      * [FP-growth算法(FP-Growth Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARL/ARL.0.4.md) 
  * [人工神经网络(Artificial Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.1.md)      
      * [自动编码器(Autoencoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.2.md) 
-     * [反向传播(Backpropagation)]() 
+     * [反向传播(Backpropagation)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.3.md) 
      * [回归神经网络(Recurrent Neural Network)]() 
      * [多层感知器(Multilayer Perceptron)]() 
      * [玻尔兹曼机(Boltzmann Machine)]() 

From b0ab07a7b89b7e5edb18d1e801710371ed78b4be Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 11:17:13 +0800
Subject: [PATCH 0846/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index f394730e..cab7a6ce 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -11,4 +11,4 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
-#### 反向传播(Backpropagation
+#### 反向传播(Backpropagation)

From 0b264a589fff98692cc2d5a61c92556c2586d8eb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 22 Apr 2018 11:17:58 +0800
Subject: [PATCH 0847/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index cab7a6ce..e3d3796f 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,3 +12,8 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
+反向传播模型也称B-P模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
+
+B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
+
+BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先不知道输入输出具体数学表达式的情况下，通过学习来存储这种复杂的映射关系．其网络中参数的学习通常采用反向传播的策略，借助最速梯度信息来寻找使网络误差最小化的参数组合．常见的3层BP网络模型如图所示

From 7feccbd54959ad2636e2a2a73b285b79556cac89 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 23 Apr 2018 09:07:24 +0800
Subject: [PATCH 0848/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index e3d3796f..eb6ec0d0 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
+
 反向传播模型也称B-P模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
 
 B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。

From 3d34133c21e5a5c664cbe86dfcdf866bca5d1edb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 09:06:53 +0800
Subject: [PATCH 0849/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index eb6ec0d0..e3d3796f 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,7 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
-
 反向传播模型也称B-P模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
 
 B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。

From 37ee5b5a089d0b8415a3a149a82022b2ac1f94eb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 20:52:07 +0800
Subject: [PATCH 0850/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index e3d3796f..0497ecf2 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -17,3 +17,7 @@
 B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
 
 BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先不知道输入输出具体数学表达式的情况下，通过学习来存储这种复杂的映射关系．其网络中参数的学习通常采用反向传播的策略，借助最速梯度信息来寻找使网络误差最小化的参数组合．常见的3层BP网络模型如图所示
+
+<p align="center">
+<img width="300" align="center" src="../../images/2.jpg" />
+</p>

From e4572055cf94852d023037e6a153f1602985e8cc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 21:23:05 +0800
Subject: [PATCH 0851/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 209 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 209 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 0497ecf2..adda284a 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,6 +12,9 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
+反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
+反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
+
 反向传播模型也称B-P模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
 
 B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
@@ -21,3 +24,209 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 <p align="center">
 <img width="300" align="center" src="../../images/2.jpg" />
 </p>
+
+
+#### 应用示例
+```python
+
+import random
+import math
+
+#   参数解释：
+#   "pd_" ：偏导的前缀
+#   "d_" ：导数的前缀
+#   "w_ho" ：隐含层到输出层的权重系数索引
+#   "w_ih" ：输入层到隐含层的权重系数的索引
+
+class NeuralNetwork:
+    LEARNING_RATE = 0.5
+
+    def __init__(self, num_inputs, num_hidden, num_outputs, hidden_layer_weights = None, hidden_layer_bias = None, output_layer_weights = None, output_layer_bias = None):
+        self.num_inputs = num_inputs
+
+        self.hidden_layer = NeuronLayer(num_hidden, hidden_layer_bias)
+        self.output_layer = NeuronLayer(num_outputs, output_layer_bias)
+
+        self.init_weights_from_inputs_to_hidden_layer_neurons(hidden_layer_weights)
+        self.init_weights_from_hidden_layer_neurons_to_output_layer_neurons(output_layer_weights)
+
+    def init_weights_from_inputs_to_hidden_layer_neurons(self, hidden_layer_weights):
+        weight_num = 0
+        for h in range(len(self.hidden_layer.neurons)):
+            for i in range(self.num_inputs):
+                if not hidden_layer_weights:
+                    self.hidden_layer.neurons[h].weights.append(random.random())
+                else:
+                    self.hidden_layer.neurons[h].weights.append(hidden_layer_weights[weight_num])
+                weight_num += 1
+
+    def init_weights_from_hidden_layer_neurons_to_output_layer_neurons(self, output_layer_weights):
+        weight_num = 0
+        for o in range(len(self.output_layer.neurons)):
+            for h in range(len(self.hidden_layer.neurons)):
+                if not output_layer_weights:
+                    self.output_layer.neurons[o].weights.append(random.random())
+                else:
+                    self.output_layer.neurons[o].weights.append(output_layer_weights[weight_num])
+                weight_num += 1
+
+    def inspect(self):
+        print('------')
+        print('* Inputs: {}'.format(self.num_inputs))
+        print('------')
+        print('Hidden Layer')
+        self.hidden_layer.inspect()
+        print('------')
+        print('* Output Layer')
+        self.output_layer.inspect()
+        print('------')
+
+    def feed_forward(self, inputs):
+        hidden_layer_outputs = self.hidden_layer.feed_forward(inputs)
+        return self.output_layer.feed_forward(hidden_layer_outputs)
+
+    def train(self, training_inputs, training_outputs):
+        self.feed_forward(training_inputs)
+
+        # 1. 输出神经元的值
+        pd_errors_wrt_output_neuron_total_net_input = [0] * len(self.output_layer.neurons)
+        for o in range(len(self.output_layer.neurons)):
+
+            # ∂E/∂zⱼ
+            pd_errors_wrt_output_neuron_total_net_input[o] = self.output_layer.neurons[o].calculate_pd_error_wrt_total_net_input(training_outputs[o])
+
+        # 2. 隐含层神经元的值
+        pd_errors_wrt_hidden_neuron_total_net_input = [0] * len(self.hidden_layer.neurons)
+        for h in range(len(self.hidden_layer.neurons)):
+
+            # dE/dyⱼ = Σ ∂E/∂zⱼ * ∂z/∂yⱼ = Σ ∂E/∂zⱼ * wᵢⱼ
+            d_error_wrt_hidden_neuron_output = 0
+            for o in range(len(self.output_layer.neurons)):
+                d_error_wrt_hidden_neuron_output += pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].weights[h]
+
+            # ∂E/∂zⱼ = dE/dyⱼ * ∂zⱼ/∂
+            pd_errors_wrt_hidden_neuron_total_net_input[h] = d_error_wrt_hidden_neuron_output * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_input()
+
+        # 3. 更新输出层权重系数
+        for o in range(len(self.output_layer.neurons)):
+            for w_ho in range(len(self.output_layer.neurons[o].weights)):
+
+                # ∂Eⱼ/∂wᵢⱼ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢⱼ
+                pd_error_wrt_weight = pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].calculate_pd_total_net_input_wrt_weight(w_ho)
+
+                # Δw = α * ∂Eⱼ/∂wᵢ
+                self.output_layer.neurons[o].weights[w_ho] -= self.LEARNING_RATE * pd_error_wrt_weight
+
+        # 4. 更新隐含层的权重系数
+        for h in range(len(self.hidden_layer.neurons)):
+            for w_ih in range(len(self.hidden_layer.neurons[h].weights)):
+
+                # ∂Eⱼ/∂wᵢ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢ
+                pd_error_wrt_weight = pd_errors_wrt_hidden_neuron_total_net_input[h] * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_weight(w_ih)
+
+                # Δw = α * ∂Eⱼ/∂wᵢ
+                self.hidden_layer.neurons[h].weights[w_ih] -= self.LEARNING_RATE * pd_error_wrt_weight
+
+    def calculate_total_error(self, training_sets):
+        total_error = 0
+        for t in range(len(training_sets)):
+            training_inputs, training_outputs = training_sets[t]
+            self.feed_forward(training_inputs)
+            for o in range(len(training_outputs)):
+                total_error += self.output_layer.neurons[o].calculate_error(training_outputs[o])
+        return total_error
+
+class NeuronLayer:
+    def __init__(self, num_neurons, bias):
+
+        # 同一层的神经元共享一个截距项b
+        self.bias = bias if bias else random.random()
+
+        self.neurons = []
+        for i in range(num_neurons):
+            self.neurons.append(Neuron(self.bias))
+
+    def inspect(self):
+        print('Neurons:', len(self.neurons))
+        for n in range(len(self.neurons)):
+            print(' Neuron', n)
+            for w in range(len(self.neurons[n].weights)):
+                print('  Weight:', self.neurons[n].weights[w])
+            print('  Bias:', self.bias)
+
+    def feed_forward(self, inputs):
+        outputs = []
+        for neuron in self.neurons:
+            outputs.append(neuron.calculate_output(inputs))
+        return outputs
+
+    def get_outputs(self):
+        outputs = []
+        for neuron in self.neurons:
+            outputs.append(neuron.output)
+        return outputs
+
+class Neuron:
+    def __init__(self, bias):
+        self.bias = bias
+        self.weights = []
+
+    def calculate_output(self, inputs):
+        self.inputs = inputs
+        self.output = self.squash(self.calculate_total_net_input())
+        return self.output
+
+    def calculate_total_net_input(self):
+        total = 0
+        for i in range(len(self.inputs)):
+            total += self.inputs[i] * self.weights[i]
+        return total + self.bias
+
+    # 激活函数sigmoid
+    def squash(self, total_net_input):
+        return 1 / (1 + math.exp(-total_net_input))
+
+
+    def calculate_pd_error_wrt_total_net_input(self, target_output):
+        return self.calculate_pd_error_wrt_output(target_output) * self.calculate_pd_total_net_input_wrt_input();
+
+    # 每一个神经元的误差是由平方差公式计算的
+    def calculate_error(self, target_output):
+        return 0.5 * (target_output - self.output) ** 2
+
+    
+    def calculate_pd_error_wrt_output(self, target_output):
+        return -(target_output - self.output)
+
+    
+    def calculate_pd_total_net_input_wrt_input(self):
+        return self.output * (1 - self.output)
+
+
+    def calculate_pd_total_net_input_wrt_weight(self, index):
+        return self.inputs[index]
+
+
+# 示例:
+
+nn = NeuralNetwork(2, 2, 2, hidden_layer_weights=[0.15, 0.2, 0.25, 0.3], hidden_layer_bias=0.35, output_layer_weights=[0.4, 0.45, 0.5, 0.55], output_layer_bias=0.6)
+for i in range(10000):
+    nn.train([0.05, 0.1], [0.01, 0.09])
+    print(i, round(nn.calculate_total_error([[[0.05, 0.1], [0.01, 0.09]]]), 9))
+
+
+#另外一个例子，可以把上面的例子注释掉再运行一下:
+
+# training_sets = [
+#     [[0, 0], [0]],
+#     [[0, 1], [1]],
+#     [[1, 0], [1]],
+#     [[1, 1], [0]]
+# ]
+
+# nn = NeuralNetwork(len(training_sets[0][0]), 5, len(training_sets[0][1]))
+# for i in range(10000):
+#     training_inputs, training_outputs = random.choice(training_sets)
+#     nn.train(training_inputs, training_outputs)
+#     print(i, nn.calculate_total_error(training_sets))
+```

From edfc84ef8961f5bdafba086972c1d2446bc6b8aa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 21:24:02 +0800
Subject: [PATCH 0852/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index adda284a..78dee484 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -15,7 +15,7 @@
 反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
 反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
 
-反向传播模型也称B-P模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
+反向传播模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
 
 B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
 

From f941548fcdca85419a256be2e26815ffb9c5f0fd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 21:31:42 +0800
Subject: [PATCH 0853/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 78dee484..fe3bebbb 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -25,6 +25,28 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 <img width="300" align="center" src="../../images/2.jpg" />
 </p>
 
+任何监督式学习算法的目标是找到一个能把一组输入最好地映射到其正确的输出的函数。例如一个简单的分类任务，其中输入是动物的图像，正确的输出将是动物的名称。一些输入和输出模式可以很容易地通过单层神经网络（如感知器）学习。但是这些单层的感知机不能学习一些比较简单的模式，例如那些非线性可分的模式。例如，人可以通过识别动物的图像的某些特征进行分类，例如肢的数目，皮肤的纹理（无论是毛皮，羽毛，鳞片等），该动物的体型，以及种种其他特征。但是，单层神经网络必须仅仅使用图像中的像素的强度来学习一个输出一个标签函数。因为它被限制为仅具有一个层，所以没有办法从输入中学习到任何抽象特征。多层的网络克服了这一限制，因为它可以创建内部表示，并在每一层学习不同的特征。第一层可能负责从图像的单个像素的输入学习线条的走向。第二层可能就会结合第一层所学并学习识别简单形状（如圆形）。每升高一层就学习越来越多的抽象特征，如上文提到的用来图像分类。每一层都是从它下方的层中找到模式，就是这种能力创建了独立于为多层网络提供能量的外界输入的内部表达形式。 反向传播算法的发展的目标和动机是找到一种训练的多层神经网络的方法，于是它可以学习合适的内部表达来让它学习任意的输入到输出的映射。
+
+
+反向传播算法（BP算法）主要由两个阶段:激励传播与权重更新.
+
+* 第1阶段：激励传播
+
+每次迭代中的传播环节包含两步：
+* 1.（前向传播阶段）将训练输入送入网络以获得激励响应；
+* 2.（反向传播阶段）将激励响应同训练输入对应的目标输出求差，从而获得隐层和输出层的响应误差。
+
+* 第2阶段：权重更新
+
+对于每个突触上的权重，按照以下步骤进行更新：
+
+* 1.将输入激励和响应误差相乘，从而获得权重的梯度；
+* 2.将这个梯度乘上一个比例并取反后加到权重上。
+这个比例（百分比）将会影响到训练过程的速度和效果，因此称为“训练因子”。梯度的方向指明了误差扩大的方向，因此在更新权重的时候需要对其取反，从而减小权重引起的误差。
+
+第1和第2阶段可以反复循环迭代，直到网络的对输入的响应达到满意的预定的目标范围为止。
+
+
 
 #### 应用示例
 ```python

From 98ebe0e20325b088299a7882fe272956adcba75f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 21:48:52 +0800
Subject: [PATCH 0854/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index fe3bebbb..7d36cb92 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -46,6 +46,8 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 
 第1和第2阶段可以反复循环迭代，直到网络的对输入的响应达到满意的预定的目标范围为止。
 
+三层网络算法（只有一个隐藏层）：
+
 
 
 #### 应用示例

From 395e98b4bdbbe7d76f44e115d4945ef5b7a7df6f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 24 Apr 2018 21:53:08 +0800
Subject: [PATCH 0855/1406] add ANN0.3

---
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 assets/images/256.jpg     | Bin 0 -> 3116 bytes
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 assets/images/259.jpg     | Bin 0 -> 4394 bytes
 assets/images/260.jpg     | Bin 0 -> 1807 bytes
 assets/images/261.jpg     | Bin 0 -> 2337 bytes
 assets/images/262.jpg     | Bin 0 -> 6140 bytes
 assets/images/263.jpg     | Bin 0 -> 3981 bytes
 assets/images/264.jpg     | Bin 0 -> 2985 bytes
 assets/src/ANN/ANN.0.3.md |  13 +++----------
 12 files changed, 3 insertions(+), 10 deletions(-)
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diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 7d36cb92..7cfe273a 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -165,7 +165,6 @@ class NeuronLayer:
 
         # 同一层的神经元共享一个截距项b
         self.bias = bias if bias else random.random()
-
         self.neurons = []
         for i in range(num_neurons):
             self.neurons.append(Neuron(self.bias))
@@ -189,7 +188,7 @@ class NeuronLayer:
         for neuron in self.neurons:
             outputs.append(neuron.output)
         return outputs
-
+        
 class Neuron:
     def __init__(self, bias):
         self.bias = bias
@@ -210,27 +209,21 @@ class Neuron:
     def squash(self, total_net_input):
         return 1 / (1 + math.exp(-total_net_input))
 
-
     def calculate_pd_error_wrt_total_net_input(self, target_output):
         return self.calculate_pd_error_wrt_output(target_output) * self.calculate_pd_total_net_input_wrt_input();
 
     # 每一个神经元的误差是由平方差公式计算的
     def calculate_error(self, target_output):
         return 0.5 * (target_output - self.output) ** 2
-
-    
+        
     def calculate_pd_error_wrt_output(self, target_output):
         return -(target_output - self.output)
-
-    
+        
     def calculate_pd_total_net_input_wrt_input(self):
         return self.output * (1 - self.output)
 
-
     def calculate_pd_total_net_input_wrt_weight(self, index):
         return self.inputs[index]
-
-
 # 示例:
 
 nn = NeuralNetwork(2, 2, 2, hidden_layer_weights=[0.15, 0.2, 0.25, 0.3], hidden_layer_bias=0.35, output_layer_weights=[0.4, 0.45, 0.5, 0.55], output_layer_bias=0.6)

From 18c9bbc49f787654b1597823f2c0e31909ca7121 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 21:58:30 +0800
Subject: [PATCH 0856/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 7cfe273a..6a188912 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -48,7 +48,16 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 
 三层网络算法（只有一个隐藏层）：
 
-
+输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
+正向传播：对每个<img width="30" align="center" src="../../images/255.jpg" />计算<img width="30" align="center" src="../../images/256.jpg" />和<img width="30" align="center" src="../../images/257.jpg" />。
+输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="30" align="center" src="../../images/259.jpg" />。
+将误差反向传播：对每个<img width="30" align="center" src="../../images/260.jpg" />,<img width="30" align="center" src="../../images/261.jpg" /> 计算<img width="30" align="center" src="../../images/262.jpg" />
+输出：代价函数的梯度为<img width="30" align="center" src="../../images/263.jpg" />和<img width="30" align="center" src="../../images/264.jpg" /> 
+
+这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。
+BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层及一个输出层）。为了使隐藏层能够适合所有有用的函数，多层网络必须具有用于多个层的非线性激活函数：仅用线性激活函数的多层网络会与相当于单层线性网络。常用的非线性激活函数有逻辑函数、柔性最大函数和高斯函数。
+用反向传播算法求梯度已被重新发现多次，是更加一般的自动微分技术在反向积累模式的特例。
+它也与高斯-牛顿算法密切相关，也是继续研究神经反向传播的一部分。
 
 #### 应用示例
 ```python

From 01d71567affc5d6e8862b60fe4b80235deb0b390 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 22:00:20 +0800
Subject: [PATCH 0857/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 6a188912..b0fca443 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -48,11 +48,11 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 
 三层网络算法（只有一个隐藏层）：
 
-输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
-正向传播：对每个<img width="30" align="center" src="../../images/255.jpg" />计算<img width="30" align="center" src="../../images/256.jpg" />和<img width="30" align="center" src="../../images/257.jpg" />。
-输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="30" align="center" src="../../images/259.jpg" />。
-将误差反向传播：对每个<img width="30" align="center" src="../../images/260.jpg" />,<img width="30" align="center" src="../../images/261.jpg" /> 计算<img width="30" align="center" src="../../images/262.jpg" />
-输出：代价函数的梯度为<img width="30" align="center" src="../../images/263.jpg" />和<img width="30" align="center" src="../../images/264.jpg" /> 
+* 输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
+* 正向传播：对每个<img width="100" align="center" src="../../images/255.jpg" />计算<img width="100" align="center" src="../../images/256.jpg" />和<img width="100" align="center" src="../../images/257.jpg" />。
+* 输出误差<img width="100" align="center" src="../../images/258.jpg" /> ：计算向量<img width="100" align="center" src="../../images/259.jpg" />。
+* 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="100" align="center" src="../../images/262.jpg" />
+* 输出：代价函数的梯度为<img width="100" align="center" src="../../images/263.jpg" />和<img width="100" align="center" src="../../images/264.jpg" /> 
 
 这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。
 BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层及一个输出层）。为了使隐藏层能够适合所有有用的函数，多层网络必须具有用于多个层的非线性激活函数：仅用线性激活函数的多层网络会与相当于单层线性网络。常用的非线性激活函数有逻辑函数、柔性最大函数和高斯函数。

From 1ec2f3aa6f6edcc767ee00a3b1bc36e57192e1a4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 22:02:12 +0800
Subject: [PATCH 0858/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index b0fca443..9ca355af 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -50,9 +50,9 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 
 * 输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
 * 正向传播：对每个<img width="100" align="center" src="../../images/255.jpg" />计算<img width="100" align="center" src="../../images/256.jpg" />和<img width="100" align="center" src="../../images/257.jpg" />。
-* 输出误差<img width="100" align="center" src="../../images/258.jpg" /> ：计算向量<img width="100" align="center" src="../../images/259.jpg" />。
+* 输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="150" align="center" src="../../images/259.jpg" />。
 * 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="100" align="center" src="../../images/262.jpg" />
-* 输出：代价函数的梯度为<img width="100" align="center" src="../../images/263.jpg" />和<img width="100" align="center" src="../../images/264.jpg" /> 
+* 输出：代价函数的梯度为<img width="130" align="center" src="../../images/263.jpg" />和<img width="130" align="center" src="../../images/264.jpg" /> 
 
 这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。
 BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层及一个输出层）。为了使隐藏层能够适合所有有用的函数，多层网络必须具有用于多个层的非线性激活函数：仅用线性激活函数的多层网络会与相当于单层线性网络。常用的非线性激活函数有逻辑函数、柔性最大函数和高斯函数。

From 754f287f40531921fb7bb60280899d34a68f1391 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 22:02:46 +0800
Subject: [PATCH 0859/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 9ca355af..2e9fe131 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -51,7 +51,7 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 * 输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
 * 正向传播：对每个<img width="100" align="center" src="../../images/255.jpg" />计算<img width="100" align="center" src="../../images/256.jpg" />和<img width="100" align="center" src="../../images/257.jpg" />。
 * 输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="150" align="center" src="../../images/259.jpg" />。
-* 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="100" align="center" src="../../images/262.jpg" />
+* 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="180" align="center" src="../../images/262.jpg" />
 * 输出：代价函数的梯度为<img width="130" align="center" src="../../images/263.jpg" />和<img width="130" align="center" src="../../images/264.jpg" /> 
 
 这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。

From 72af06c7de125eeaf9ef664e329d18c66944ca19 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 24 Apr 2018 22:05:16 +0800
Subject: [PATCH 0860/1406] change page of ANN

---
 assets/images/265.jpg     | Bin 0 -> 19539 bytes
 assets/src/ANN/ANN.0.3.md |   4 ++++
 2 files changed, 4 insertions(+)
 create mode 100644 assets/images/265.jpg

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diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 2e9fe131..991b17e5 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -59,6 +59,10 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 用反向传播算法求梯度已被重新发现多次，是更加一般的自动微分技术在反向积累模式的特例。
 它也与高斯-牛顿算法密切相关，也是继续研究神经反向传播的一部分。
 
+<p align="center">
+<img width="300" align="center" src="../../images/265.jpg" />
+</p>
+
 #### 应用示例
 ```python
 

From f96d51aca753bcdfd0e703bcfe98f8c1f1ae12f2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 24 Apr 2018 22:36:50 +0800
Subject: [PATCH 0861/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 991b17e5..bdb38b95 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -63,6 +63,12 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/265.jpg" />
 </p>
 
+由于反向传播使用梯度下降法，需要计算平方误差函数对网络权重的导数。假设对于一个输出神经元，[note 2] 平方误差函数为：
+<p align="center">
+<img width="150" align="center" src="../../images/267.jpg" />
+</p>
+其中E 为平方误差,t 为训练样本的目标输出，y 为输出神经元的实际输出。
+
 #### 应用示例
 ```python
 

From 9bd88763a3ef0c8d221da0e32704d269be48775f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 14:04:36 +0800
Subject: [PATCH 0862/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index bdb38b95..8929df90 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
+
 反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
 反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
 

From 58358d495a56b10ae51ed83165bd81ab79e8ca33 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 25 Apr 2018 21:14:39 +0800
Subject: [PATCH 0863/1406] add page

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From ae3e752bfa6b36c5651fea20bd7d92276d3962cf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:29:24 +0800
Subject: [PATCH 0864/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 8929df90..657094ed 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -70,6 +70,24 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 </p>
 其中E 为平方误差,t 为训练样本的目标输出，y 为输出神经元的实际输出。
 
+加入系数<img width="50" align="center" src="../../images/266.jpg" />是为了抵消微分出来的指数。之后，该表达式会乘以一个任意的学习速率，因此在这里乘上一个常系数是没有关系的。 对每个神经元j，它的输出<img width="100" align="center" src="../../images/268.jpg" /> 定义为
+<p align="center">
+<img width="150" align="center" src="../../images/269.jpg" />
+</p>
+
+通向一个神经元的输入<img width="150" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="150" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="150" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="150" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="150" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
+
+激活函数<img width="150" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
+<p align="center">
+<img width="150" align="center" src="../../images/275.jpg" />
+</p>
+
+其导数的形式很好：
+<p align="center">
+<img width="150" align="center" src="../../images/276.jpg" />
+</p>
+
+
 #### 应用示例
 ```python
 

From bb004fbe8e70b411b985a1052938b0363896c5ae Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:30:52 +0800
Subject: [PATCH 0865/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 657094ed..d62ac903 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -64,7 +64,7 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/265.jpg" />
 </p>
 
-由于反向传播使用梯度下降法，需要计算平方误差函数对网络权重的导数。假设对于一个输出神经元，[note 2] 平方误差函数为：
+由于反向传播使用梯度下降法，需要计算平方误差函数对网络权重的导数。假设对于一个输出神经元，平方误差函数为：
 <p align="center">
 <img width="150" align="center" src="../../images/267.jpg" />
 </p>
@@ -75,16 +75,16 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="150" align="center" src="../../images/269.jpg" />
 </p>
 
-通向一个神经元的输入<img width="150" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="150" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="150" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="150" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="150" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
+通向一个神经元的输入<img width="70" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="70" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="70" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="70" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="70" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
 
-激活函数<img width="150" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
+激活函数<img width="70" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
 <p align="center">
-<img width="150" align="center" src="../../images/275.jpg" />
+<img width="300" align="center" src="../../images/275.jpg" />
 </p>
 
 其导数的形式很好：
 <p align="center">
-<img width="150" align="center" src="../../images/276.jpg" />
+<img width="300" align="center" src="../../images/276.jpg" />
 </p>
 
 

From 3b88a462149cd94be7661b9ea3907034819e14cd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:33:12 +0800
Subject: [PATCH 0866/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index d62ac903..19211ff9 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -70,14 +70,14 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 </p>
 其中E 为平方误差,t 为训练样本的目标输出，y 为输出神经元的实际输出。
 
-加入系数<img width="50" align="center" src="../../images/266.jpg" />是为了抵消微分出来的指数。之后，该表达式会乘以一个任意的学习速率，因此在这里乘上一个常系数是没有关系的。 对每个神经元j，它的输出<img width="100" align="center" src="../../images/268.jpg" /> 定义为
+加入系数<img width="30" align="center" src="../../images/266.jpg" />是为了抵消微分出来的指数。之后，该表达式会乘以一个任意的学习速率，因此在这里乘上一个常系数是没有关系的。 对每个神经元j，它的输出<img width="30" align="center" src="../../images/268.jpg" /> 定义为
 <p align="center">
-<img width="150" align="center" src="../../images/269.jpg" />
+<img width="300" align="center" src="../../images/269.jpg" />
 </p>
 
-通向一个神经元的输入<img width="70" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="70" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="70" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="70" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="70" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
+通向一个神经元的输入<img width="70" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="30" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="30" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="30" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="30" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
 
-激活函数<img width="70" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
+激活函数<img width="30" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
 <p align="center">
 <img width="300" align="center" src="../../images/275.jpg" />
 </p>

From f9e750e8806b1753daf7431846dfe9eaaa52f479 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:36:48 +0800
Subject: [PATCH 0867/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 19211ff9..6b33b182 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -29,7 +29,7 @@ BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先
 任何监督式学习算法的目标是找到一个能把一组输入最好地映射到其正确的输出的函数。例如一个简单的分类任务，其中输入是动物的图像，正确的输出将是动物的名称。一些输入和输出模式可以很容易地通过单层神经网络（如感知器）学习。但是这些单层的感知机不能学习一些比较简单的模式，例如那些非线性可分的模式。例如，人可以通过识别动物的图像的某些特征进行分类，例如肢的数目，皮肤的纹理（无论是毛皮，羽毛，鳞片等），该动物的体型，以及种种其他特征。但是，单层神经网络必须仅仅使用图像中的像素的强度来学习一个输出一个标签函数。因为它被限制为仅具有一个层，所以没有办法从输入中学习到任何抽象特征。多层的网络克服了这一限制，因为它可以创建内部表示，并在每一层学习不同的特征。第一层可能负责从图像的单个像素的输入学习线条的走向。第二层可能就会结合第一层所学并学习识别简单形状（如圆形）。每升高一层就学习越来越多的抽象特征，如上文提到的用来图像分类。每一层都是从它下方的层中找到模式，就是这种能力创建了独立于为多层网络提供能量的外界输入的内部表达形式。 反向传播算法的发展的目标和动机是找到一种训练的多层神经网络的方法，于是它可以学习合适的内部表达来让它学习任意的输入到输出的映射。
 
 
-反向传播算法（BP算法）主要由两个阶段:激励传播与权重更新.
+#### 反向传播算法（BP算法）主要由两个阶段:激励传播与权重更新.
 
 * 第1阶段：激励传播
 
@@ -87,6 +87,19 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/276.jpg" />
 </p>
 
+#### 求误差的导数
+
+计算误差对权重<img width="30" align="center" src="../../images/273.jpg" />的偏导数是两次使用链式法则得到的：
+<p align="center">
+<img width="300" align="center" src="../../images/277.jpg" />
+</p>
+
+在右边的最后一项中，只有加权和<img width="30" align="center" src="../../images/270.jpg" />取决于<img width="30" align="center" src="../../images/273.jpg" />，因此:
+
+<p align="center">
+<img width="300" align="center" src="../../images/278.jpg" />
+</p>
+
 
 #### 应用示例
 ```python

From 779337dd7e8b7812e7db5485c0e6a618462719b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:47:20 +0800
Subject: [PATCH 0868/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 6b33b182..8345e5fe 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -100,6 +100,44 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/278.jpg" />
 </p>
 
+神经元j 的输出对其输入的导数就是激活函数的偏导数（这里假定使用逻辑函数）：
+
+<p align="center">
+<img width="300" align="center" src="../../images/279.jpg" />
+</p>
+
+这就是为什么反向传播需要的激活函数是可微的。
+如果神经元在输出层中，因为此时<img width="30" align="center" src="../../images/280.jpg" />以及
+<p align="center">
+<img width="300" align="center" src="../../images/281.jpg" />
+</p>
+所以第一项可以直接算出。
+但如果j 是网络中任一内层，求E 关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数就不太简单了。
+
+考虑E为接受来自神经元j的输入的所有神经元<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/282.jpg">的输入的函数，
+<p align="center">
+<img width="300" align="center" src="../../images/283.jpg" />
+</p>
+
+并关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">取全微分，可以得到该导数的一个递归表达式：
+<p align="center">
+<img width="300" align="center" src="../../images/284.jpg" />
+</p>
+因此，若已知所有关于下一层（更接近输出神经元的一层）的输出 {\displaystyle o_{l}} o_{l} 的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
+
+把它们放在一起：
+<p align="center">
+<img width="300" align="center" src="../../images/285.jpg" />
+</p>
+
+其中:
+<p align="center">
+<img width="300" align="center" src="../../images/286.jpg" />
+</p>
+
+要使用梯度下降法更新<img width="30" align="center" src="../../images/273.jpg" />，必须选择一个学习速率a。要加在原本的权重上的权重的变化，等于学习速率与梯度的乘积，乘以-1：
+
+之所以要乘以-1 是因为要更新误差函数极小值而不是极大值的方向。对于单层网络，这个表达式变为Delta规则。
 
 #### 应用示例
 ```python

From a1de38ecdba5998a29b8a70fb568038c699a2027 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 25 Apr 2018 21:53:46 +0800
Subject: [PATCH 0869/1406] change page of ANN"

---
 assets/images/288.jpg     | Bin 0 -> 979 bytes
 assets/src/ANN/ANN.0.3.md |  11 +++++++----
 2 files changed, 7 insertions(+), 4 deletions(-)
 create mode 100644 assets/images/288.jpg

diff --git a/assets/images/288.jpg b/assets/images/288.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..dde37259aa1e8baf60c3c4ade56d227f051dccf5
GIT binary patch
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diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 8345e5fe..57952539 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -121,21 +121,24 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 
 并关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">取全微分，可以得到该导数的一个递归表达式：
 <p align="center">
-<img width="300" align="center" src="../../images/284.jpg" />
+<img width="500" align="center" src="../../images/284.jpg" />
 </p>
-因此，若已知所有关于下一层（更接近输出神经元的一层）的输出 {\displaystyle o_{l}} o_{l} 的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
+因此，若已知所有关于下一层（更接近输出神经元的一层）的输出<img width="30" align="center" src="../../images/288.jpg" />的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
 
 把它们放在一起：
 <p align="center">
-<img width="300" align="center" src="../../images/285.jpg" />
+<img width="200" align="center" src="../../images/285.jpg" />
 </p>
 
 其中:
 <p align="center">
-<img width="300" align="center" src="../../images/286.jpg" />
+<img width="500" align="center" src="../../images/286.jpg" />
 </p>
 
 要使用梯度下降法更新<img width="30" align="center" src="../../images/273.jpg" />，必须选择一个学习速率a。要加在原本的权重上的权重的变化，等于学习速率与梯度的乘积，乘以-1：
+<p align="center">
+<img width="300" align="center" src="../../images/287.jpg" />
+</p>
 
 之所以要乘以-1 是因为要更新误差函数极小值而不是极大值的方向。对于单层网络，这个表达式变为Delta规则。
 

From e391700b45761b87797a6942d917943fad60f33c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:57:07 +0800
Subject: [PATCH 0870/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 8345e5fe..c92f8e44 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -112,7 +112,8 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/281.jpg" />
 </p>
 所以第一项可以直接算出。
-但如果j 是网络中任一内层，求E 关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数就不太简单了。
+
+但如果j 是网络中任一内层，求E关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数就不太简单了。
 
 考虑E为接受来自神经元j的输入的所有神经元<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/282.jpg">的输入的函数，
 <p align="center">

From 771ba194b5095c13a3f6859342bcd61f7276ccb8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:58:36 +0800
Subject: [PATCH 0871/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index c92f8e44..f5191b15 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -122,18 +122,18 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 
 并关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">取全微分，可以得到该导数的一个递归表达式：
 <p align="center">
-<img width="300" align="center" src="../../images/284.jpg" />
+<img width="500" align="center" src="../../images/284.jpg" />
 </p>
 因此，若已知所有关于下一层（更接近输出神经元的一层）的输出 {\displaystyle o_{l}} o_{l} 的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
 
 把它们放在一起：
 <p align="center">
-<img width="300" align="center" src="../../images/285.jpg" />
+<img width="100" align="center" src="../../images/285.jpg" />
 </p>
 
 其中:
 <p align="center">
-<img width="300" align="center" src="../../images/286.jpg" />
+<img width="500" align="center" src="../../images/286.jpg" />
 </p>
 
 要使用梯度下降法更新<img width="30" align="center" src="../../images/273.jpg" />，必须选择一个学习速率a。要加在原本的权重上的权重的变化，等于学习速率与梯度的乘积，乘以-1：

From a953e230b13cef31f6b57382168af04e71698f82 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 21:59:24 +0800
Subject: [PATCH 0872/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index f5191b15..4401fb88 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -128,7 +128,7 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 
 把它们放在一起：
 <p align="center">
-<img width="100" align="center" src="../../images/285.jpg" />
+<img width="200" align="center" src="../../images/285.jpg" />
 </p>
 
 其中:

From fedba356510fc6ad99831d61b62dbcd9f02c458b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 25 Apr 2018 22:00:10 +0800
Subject: [PATCH 0873/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 4401fb88..6c8e7f88 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -79,12 +79,12 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 
 激活函数<img width="30" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
 <p align="center">
-<img width="300" align="center" src="../../images/275.jpg" />
+<img width="200" align="center" src="../../images/275.jpg" />
 </p>
 
 其导数的形式很好：
 <p align="center">
-<img width="300" align="center" src="../../images/276.jpg" />
+<img width="200" align="center" src="../../images/276.jpg" />
 </p>
 
 #### 求误差的导数

From 6f84f46a2a181cbe840530bb01166c62852102ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Apr 2018 08:40:33 +0800
Subject: [PATCH 0874/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 6c8e7f88..0d8c58f2 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,7 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
-
 反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
 反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
 

From 8fb836400060402b189888a7c1649d23d57fcecf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Apr 2018 08:41:06 +0800
Subject: [PATCH 0875/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index 0d8c58f2..f1df0ab1 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -74,7 +74,7 @@ BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层
 <img width="300" align="center" src="../../images/269.jpg" />
 </p>
 
-通向一个神经元的输入<img width="70" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="30" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="30" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="30" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="30" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
+通向一个神经元的输入<img width="50" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="30" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="30" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="30" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="30" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
 
 激活函数<img width="30" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
 <p align="center">

From f6ab124273ab05bbe0447ead516b71778ecb70bd Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 27 Apr 2018 08:48:31 +0800
Subject: [PATCH 0876/1406] add ANN.0.4

---
 assets/src/ANN/ANN.0.4.md | 341 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 341 insertions(+)
 create mode 100644 assets/src/ANN/ANN.0.4.md

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
new file mode 100644
index 00000000..e4ec1e9c
--- /dev/null
+++ b/assets/src/ANN/ANN.0.4.md
@@ -0,0 +1,341 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 反向传播(Backpropagation)
+反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
+反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
+
+反向传播模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
+
+B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
+
+BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先不知道输入输出具体数学表达式的情况下，通过学习来存储这种复杂的映射关系．其网络中参数的学习通常采用反向传播的策略，借助最速梯度信息来寻找使网络误差最小化的参数组合．常见的3层BP网络模型如图所示
+
+<p align="center">
+<img width="300" align="center" src="../../images/2.jpg" />
+</p>
+
+任何监督式学习算法的目标是找到一个能把一组输入最好地映射到其正确的输出的函数。例如一个简单的分类任务，其中输入是动物的图像，正确的输出将是动物的名称。一些输入和输出模式可以很容易地通过单层神经网络（如感知器）学习。但是这些单层的感知机不能学习一些比较简单的模式，例如那些非线性可分的模式。例如，人可以通过识别动物的图像的某些特征进行分类，例如肢的数目，皮肤的纹理（无论是毛皮，羽毛，鳞片等），该动物的体型，以及种种其他特征。但是，单层神经网络必须仅仅使用图像中的像素的强度来学习一个输出一个标签函数。因为它被限制为仅具有一个层，所以没有办法从输入中学习到任何抽象特征。多层的网络克服了这一限制，因为它可以创建内部表示，并在每一层学习不同的特征。第一层可能负责从图像的单个像素的输入学习线条的走向。第二层可能就会结合第一层所学并学习识别简单形状（如圆形）。每升高一层就学习越来越多的抽象特征，如上文提到的用来图像分类。每一层都是从它下方的层中找到模式，就是这种能力创建了独立于为多层网络提供能量的外界输入的内部表达形式。 反向传播算法的发展的目标和动机是找到一种训练的多层神经网络的方法，于是它可以学习合适的内部表达来让它学习任意的输入到输出的映射。
+
+
+#### 反向传播算法（BP算法）主要由两个阶段:激励传播与权重更新.
+
+* 第1阶段：激励传播
+
+每次迭代中的传播环节包含两步：
+* 1.（前向传播阶段）将训练输入送入网络以获得激励响应；
+* 2.（反向传播阶段）将激励响应同训练输入对应的目标输出求差，从而获得隐层和输出层的响应误差。
+
+* 第2阶段：权重更新
+
+对于每个突触上的权重，按照以下步骤进行更新：
+
+* 1.将输入激励和响应误差相乘，从而获得权重的梯度；
+* 2.将这个梯度乘上一个比例并取反后加到权重上。
+这个比例（百分比）将会影响到训练过程的速度和效果，因此称为“训练因子”。梯度的方向指明了误差扩大的方向，因此在更新权重的时候需要对其取反，从而减小权重引起的误差。
+
+第1和第2阶段可以反复循环迭代，直到网络的对输入的响应达到满意的预定的目标范围为止。
+
+三层网络算法（只有一个隐藏层）：
+
+* 输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
+* 正向传播：对每个<img width="100" align="center" src="../../images/255.jpg" />计算<img width="100" align="center" src="../../images/256.jpg" />和<img width="100" align="center" src="../../images/257.jpg" />。
+* 输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="150" align="center" src="../../images/259.jpg" />。
+* 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="180" align="center" src="../../images/262.jpg" />
+* 输出：代价函数的梯度为<img width="130" align="center" src="../../images/263.jpg" />和<img width="130" align="center" src="../../images/264.jpg" /> 
+
+这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。
+BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层及一个输出层）。为了使隐藏层能够适合所有有用的函数，多层网络必须具有用于多个层的非线性激活函数：仅用线性激活函数的多层网络会与相当于单层线性网络。常用的非线性激活函数有逻辑函数、柔性最大函数和高斯函数。
+用反向传播算法求梯度已被重新发现多次，是更加一般的自动微分技术在反向积累模式的特例。
+它也与高斯-牛顿算法密切相关，也是继续研究神经反向传播的一部分。
+
+<p align="center">
+<img width="300" align="center" src="../../images/265.jpg" />
+</p>
+
+由于反向传播使用梯度下降法，需要计算平方误差函数对网络权重的导数。假设对于一个输出神经元，平方误差函数为：
+<p align="center">
+<img width="150" align="center" src="../../images/267.jpg" />
+</p>
+其中E 为平方误差,t 为训练样本的目标输出，y 为输出神经元的实际输出。
+
+加入系数<img width="30" align="center" src="../../images/266.jpg" />是为了抵消微分出来的指数。之后，该表达式会乘以一个任意的学习速率，因此在这里乘上一个常系数是没有关系的。 对每个神经元j，它的输出<img width="30" align="center" src="../../images/268.jpg" /> 定义为
+<p align="center">
+<img width="300" align="center" src="../../images/269.jpg" />
+</p>
+
+通向一个神经元的输入<img width="50" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="30" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="30" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="30" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="30" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
+
+激活函数<img width="30" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
+<p align="center">
+<img width="200" align="center" src="../../images/275.jpg" />
+</p>
+
+其导数的形式很好：
+<p align="center">
+<img width="200" align="center" src="../../images/276.jpg" />
+</p>
+
+#### 求误差的导数
+
+计算误差对权重<img width="30" align="center" src="../../images/273.jpg" />的偏导数是两次使用链式法则得到的：
+<p align="center">
+<img width="300" align="center" src="../../images/277.jpg" />
+</p>
+
+在右边的最后一项中，只有加权和<img width="30" align="center" src="../../images/270.jpg" />取决于<img width="30" align="center" src="../../images/273.jpg" />，因此:
+
+<p align="center">
+<img width="300" align="center" src="../../images/278.jpg" />
+</p>
+
+神经元j 的输出对其输入的导数就是激活函数的偏导数（这里假定使用逻辑函数）：
+
+<p align="center">
+<img width="300" align="center" src="../../images/279.jpg" />
+</p>
+
+这就是为什么反向传播需要的激活函数是可微的。
+如果神经元在输出层中，因为此时<img width="30" align="center" src="../../images/280.jpg" />以及
+<p align="center">
+<img width="300" align="center" src="../../images/281.jpg" />
+</p>
+所以第一项可以直接算出。
+
+但如果j 是网络中任一内层，求E关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数就不太简单了。
+
+考虑E为接受来自神经元j的输入的所有神经元<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/282.jpg">的输入的函数，
+<p align="center">
+<img width="300" align="center" src="../../images/283.jpg" />
+</p>
+
+并关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">取全微分，可以得到该导数的一个递归表达式：
+<p align="center">
+<img width="500" align="center" src="../../images/284.jpg" />
+</p>
+因此，若已知所有关于下一层（更接近输出神经元的一层）的输出<img width="30" align="center" src="../../images/288.jpg" />的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
+
+把它们放在一起：
+<p align="center">
+<img width="200" align="center" src="../../images/285.jpg" />
+</p>
+
+其中:
+<p align="center">
+<img width="500" align="center" src="../../images/286.jpg" />
+</p>
+
+要使用梯度下降法更新<img width="30" align="center" src="../../images/273.jpg" />，必须选择一个学习速率a。要加在原本的权重上的权重的变化，等于学习速率与梯度的乘积，乘以-1：
+<p align="center">
+<img width="300" align="center" src="../../images/287.jpg" />
+</p>
+
+之所以要乘以-1 是因为要更新误差函数极小值而不是极大值的方向。对于单层网络，这个表达式变为Delta规则。
+
+#### 应用示例
+```python
+
+import random
+import math
+
+#   参数解释：
+#   "pd_" ：偏导的前缀
+#   "d_" ：导数的前缀
+#   "w_ho" ：隐含层到输出层的权重系数索引
+#   "w_ih" ：输入层到隐含层的权重系数的索引
+
+class NeuralNetwork:
+    LEARNING_RATE = 0.5
+
+    def __init__(self, num_inputs, num_hidden, num_outputs, hidden_layer_weights = None, hidden_layer_bias = None, output_layer_weights = None, output_layer_bias = None):
+        self.num_inputs = num_inputs
+
+        self.hidden_layer = NeuronLayer(num_hidden, hidden_layer_bias)
+        self.output_layer = NeuronLayer(num_outputs, output_layer_bias)
+
+        self.init_weights_from_inputs_to_hidden_layer_neurons(hidden_layer_weights)
+        self.init_weights_from_hidden_layer_neurons_to_output_layer_neurons(output_layer_weights)
+
+    def init_weights_from_inputs_to_hidden_layer_neurons(self, hidden_layer_weights):
+        weight_num = 0
+        for h in range(len(self.hidden_layer.neurons)):
+            for i in range(self.num_inputs):
+                if not hidden_layer_weights:
+                    self.hidden_layer.neurons[h].weights.append(random.random())
+                else:
+                    self.hidden_layer.neurons[h].weights.append(hidden_layer_weights[weight_num])
+                weight_num += 1
+
+    def init_weights_from_hidden_layer_neurons_to_output_layer_neurons(self, output_layer_weights):
+        weight_num = 0
+        for o in range(len(self.output_layer.neurons)):
+            for h in range(len(self.hidden_layer.neurons)):
+                if not output_layer_weights:
+                    self.output_layer.neurons[o].weights.append(random.random())
+                else:
+                    self.output_layer.neurons[o].weights.append(output_layer_weights[weight_num])
+                weight_num += 1
+
+    def inspect(self):
+        print('------')
+        print('* Inputs: {}'.format(self.num_inputs))
+        print('------')
+        print('Hidden Layer')
+        self.hidden_layer.inspect()
+        print('------')
+        print('* Output Layer')
+        self.output_layer.inspect()
+        print('------')
+
+    def feed_forward(self, inputs):
+        hidden_layer_outputs = self.hidden_layer.feed_forward(inputs)
+        return self.output_layer.feed_forward(hidden_layer_outputs)
+
+    def train(self, training_inputs, training_outputs):
+        self.feed_forward(training_inputs)
+
+        # 1. 输出神经元的值
+        pd_errors_wrt_output_neuron_total_net_input = [0] * len(self.output_layer.neurons)
+        for o in range(len(self.output_layer.neurons)):
+
+            # ∂E/∂zⱼ
+            pd_errors_wrt_output_neuron_total_net_input[o] = self.output_layer.neurons[o].calculate_pd_error_wrt_total_net_input(training_outputs[o])
+
+        # 2. 隐含层神经元的值
+        pd_errors_wrt_hidden_neuron_total_net_input = [0] * len(self.hidden_layer.neurons)
+        for h in range(len(self.hidden_layer.neurons)):
+
+            # dE/dyⱼ = Σ ∂E/∂zⱼ * ∂z/∂yⱼ = Σ ∂E/∂zⱼ * wᵢⱼ
+            d_error_wrt_hidden_neuron_output = 0
+            for o in range(len(self.output_layer.neurons)):
+                d_error_wrt_hidden_neuron_output += pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].weights[h]
+
+            # ∂E/∂zⱼ = dE/dyⱼ * ∂zⱼ/∂
+            pd_errors_wrt_hidden_neuron_total_net_input[h] = d_error_wrt_hidden_neuron_output * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_input()
+
+        # 3. 更新输出层权重系数
+        for o in range(len(self.output_layer.neurons)):
+            for w_ho in range(len(self.output_layer.neurons[o].weights)):
+
+                # ∂Eⱼ/∂wᵢⱼ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢⱼ
+                pd_error_wrt_weight = pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].calculate_pd_total_net_input_wrt_weight(w_ho)
+
+                # Δw = α * ∂Eⱼ/∂wᵢ
+                self.output_layer.neurons[o].weights[w_ho] -= self.LEARNING_RATE * pd_error_wrt_weight
+
+        # 4. 更新隐含层的权重系数
+        for h in range(len(self.hidden_layer.neurons)):
+            for w_ih in range(len(self.hidden_layer.neurons[h].weights)):
+
+                # ∂Eⱼ/∂wᵢ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢ
+                pd_error_wrt_weight = pd_errors_wrt_hidden_neuron_total_net_input[h] * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_weight(w_ih)
+
+                # Δw = α * ∂Eⱼ/∂wᵢ
+                self.hidden_layer.neurons[h].weights[w_ih] -= self.LEARNING_RATE * pd_error_wrt_weight
+
+    def calculate_total_error(self, training_sets):
+        total_error = 0
+        for t in range(len(training_sets)):
+            training_inputs, training_outputs = training_sets[t]
+            self.feed_forward(training_inputs)
+            for o in range(len(training_outputs)):
+                total_error += self.output_layer.neurons[o].calculate_error(training_outputs[o])
+        return total_error
+
+class NeuronLayer:
+    def __init__(self, num_neurons, bias):
+
+        # 同一层的神经元共享一个截距项b
+        self.bias = bias if bias else random.random()
+        self.neurons = []
+        for i in range(num_neurons):
+            self.neurons.append(Neuron(self.bias))
+
+    def inspect(self):
+        print('Neurons:', len(self.neurons))
+        for n in range(len(self.neurons)):
+            print(' Neuron', n)
+            for w in range(len(self.neurons[n].weights)):
+                print('  Weight:', self.neurons[n].weights[w])
+            print('  Bias:', self.bias)
+
+    def feed_forward(self, inputs):
+        outputs = []
+        for neuron in self.neurons:
+            outputs.append(neuron.calculate_output(inputs))
+        return outputs
+
+    def get_outputs(self):
+        outputs = []
+        for neuron in self.neurons:
+            outputs.append(neuron.output)
+        return outputs
+        
+class Neuron:
+    def __init__(self, bias):
+        self.bias = bias
+        self.weights = []
+
+    def calculate_output(self, inputs):
+        self.inputs = inputs
+        self.output = self.squash(self.calculate_total_net_input())
+        return self.output
+
+    def calculate_total_net_input(self):
+        total = 0
+        for i in range(len(self.inputs)):
+            total += self.inputs[i] * self.weights[i]
+        return total + self.bias
+
+    # 激活函数sigmoid
+    def squash(self, total_net_input):
+        return 1 / (1 + math.exp(-total_net_input))
+
+    def calculate_pd_error_wrt_total_net_input(self, target_output):
+        return self.calculate_pd_error_wrt_output(target_output) * self.calculate_pd_total_net_input_wrt_input();
+
+    # 每一个神经元的误差是由平方差公式计算的
+    def calculate_error(self, target_output):
+        return 0.5 * (target_output - self.output) ** 2
+        
+    def calculate_pd_error_wrt_output(self, target_output):
+        return -(target_output - self.output)
+        
+    def calculate_pd_total_net_input_wrt_input(self):
+        return self.output * (1 - self.output)
+
+    def calculate_pd_total_net_input_wrt_weight(self, index):
+        return self.inputs[index]
+# 示例:
+
+nn = NeuralNetwork(2, 2, 2, hidden_layer_weights=[0.15, 0.2, 0.25, 0.3], hidden_layer_bias=0.35, output_layer_weights=[0.4, 0.45, 0.5, 0.55], output_layer_bias=0.6)
+for i in range(10000):
+    nn.train([0.05, 0.1], [0.01, 0.09])
+    print(i, round(nn.calculate_total_error([[[0.05, 0.1], [0.01, 0.09]]]), 9))
+
+
+#另外一个例子，可以把上面的例子注释掉再运行一下:
+
+# training_sets = [
+#     [[0, 0], [0]],
+#     [[0, 1], [1]],
+#     [[1, 0], [1]],
+#     [[1, 1], [0]]
+# ]
+
+# nn = NeuralNetwork(len(training_sets[0][0]), 5, len(training_sets[0][1]))
+# for i in range(10000):
+#     training_inputs, training_outputs = random.choice(training_sets)
+#     nn.train(training_inputs, training_outputs)
+#     print(i, nn.calculate_total_error(training_sets))
+```

From e611ed7003f1969b1c65176f80292d8574bfd7c7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Apr 2018 08:49:45 +0800
Subject: [PATCH 0877/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3049fd3a..d7cc59f6 100644
--- a/README.md
+++ b/README.md
@@ -123,7 +123,7 @@
  * [人工神经网络(Artificial Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.1.md)      
      * [自动编码器(Autoencoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.2.md) 
      * [反向传播(Backpropagation)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.3.md) 
-     * [回归神经网络(Recurrent Neural Network)]() 
+     * [回归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
      * [多层感知器(Multilayer Perceptron)]() 
      * [玻尔兹曼机(Boltzmann Machine)]() 
      * [卷积神经网络(Convolutional Neural Network)]() 

From 132eecf2133f13d2efbff1273e3681b3dfb19c1d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Apr 2018 08:50:33 +0800
Subject: [PATCH 0878/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 329 +-------------------------------------
 1 file changed, 1 insertion(+), 328 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index e4ec1e9c..9d262bd3 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -11,331 +11,4 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
-#### 反向传播(Backpropagation)
-反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
-反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
-
-反向传播模型，是一种用于前向多层的反向传播学习算法。之所以称它是一种学习方法，是因为用它可以对组成前向多层网络的各人工神经元之间的连接权值进行不断的修改，从而使该前向多层网络能够将输入它的信息变换成所期望的输出信息。之所以将其称作为反向学习算法，是因为在修改各人工神经元的连接权值时，所依据的是该网络的实际输出与其期望的输出之差，将这一差值反向一层一层的向回传播，来决定连接权值的修改。
-
-B-P算法的网络结构是一个前向多层网络,其基本思想是，学习过程由信号的正向传播与误差的反向传播两个过程组成。正向传播时，输入样本从输入层传入，经隐含层逐层处理后，传向输出层。若输出层的实际输出与期望输出不符，则转向误差的反向传播阶段。误差的反向传播是将输出误差以某种形式通过隐层向输入层逐层反传，并将误差分摊给各层的所有单元，从而获得各层单元的误差信号，此误差信号即作为修正各单元权值的依据。这种信号正向传播与误差反向传播的各层权值调整过程，是周而复始地进行。权值不断调整过程，也就是网络的学习训练过程。此过程一直进行到网络输出的误差减少到可以接受的程度，或进行到预先设定的学习次数为止。
-
-BP网络的拓扑结构包括输入层、隐层和输出层，它能够在事先不知道输入输出具体数学表达式的情况下，通过学习来存储这种复杂的映射关系．其网络中参数的学习通常采用反向传播的策略，借助最速梯度信息来寻找使网络误差最小化的参数组合．常见的3层BP网络模型如图所示
-
-<p align="center">
-<img width="300" align="center" src="../../images/2.jpg" />
-</p>
-
-任何监督式学习算法的目标是找到一个能把一组输入最好地映射到其正确的输出的函数。例如一个简单的分类任务，其中输入是动物的图像，正确的输出将是动物的名称。一些输入和输出模式可以很容易地通过单层神经网络（如感知器）学习。但是这些单层的感知机不能学习一些比较简单的模式，例如那些非线性可分的模式。例如，人可以通过识别动物的图像的某些特征进行分类，例如肢的数目，皮肤的纹理（无论是毛皮，羽毛，鳞片等），该动物的体型，以及种种其他特征。但是，单层神经网络必须仅仅使用图像中的像素的强度来学习一个输出一个标签函数。因为它被限制为仅具有一个层，所以没有办法从输入中学习到任何抽象特征。多层的网络克服了这一限制，因为它可以创建内部表示，并在每一层学习不同的特征。第一层可能负责从图像的单个像素的输入学习线条的走向。第二层可能就会结合第一层所学并学习识别简单形状（如圆形）。每升高一层就学习越来越多的抽象特征，如上文提到的用来图像分类。每一层都是从它下方的层中找到模式，就是这种能力创建了独立于为多层网络提供能量的外界输入的内部表达形式。 反向传播算法的发展的目标和动机是找到一种训练的多层神经网络的方法，于是它可以学习合适的内部表达来让它学习任意的输入到输出的映射。
-
-
-#### 反向传播算法（BP算法）主要由两个阶段:激励传播与权重更新.
-
-* 第1阶段：激励传播
-
-每次迭代中的传播环节包含两步：
-* 1.（前向传播阶段）将训练输入送入网络以获得激励响应；
-* 2.（反向传播阶段）将激励响应同训练输入对应的目标输出求差，从而获得隐层和输出层的响应误差。
-
-* 第2阶段：权重更新
-
-对于每个突触上的权重，按照以下步骤进行更新：
-
-* 1.将输入激励和响应误差相乘，从而获得权重的梯度；
-* 2.将这个梯度乘上一个比例并取反后加到权重上。
-这个比例（百分比）将会影响到训练过程的速度和效果，因此称为“训练因子”。梯度的方向指明了误差扩大的方向，因此在更新权重的时候需要对其取反，从而减小权重引起的误差。
-
-第1和第2阶段可以反复循环迭代，直到网络的对输入的响应达到满意的预定的目标范围为止。
-
-三层网络算法（只有一个隐藏层）：
-
-* 输入x:计算输入层相应的激活函数值<img width="30" align="center" src="../../images/254.jpg" />。
-* 正向传播：对每个<img width="100" align="center" src="../../images/255.jpg" />计算<img width="100" align="center" src="../../images/256.jpg" />和<img width="100" align="center" src="../../images/257.jpg" />。
-* 输出误差<img width="30" align="center" src="../../images/258.jpg" /> ：计算向量<img width="150" align="center" src="../../images/259.jpg" />。
-* 将误差反向传播：对每个<img width="100" align="center" src="../../images/260.jpg" />,<img width="100" align="center" src="../../images/261.jpg" /> 计算<img width="180" align="center" src="../../images/262.jpg" />
-* 输出：代价函数的梯度为<img width="130" align="center" src="../../images/263.jpg" />和<img width="130" align="center" src="../../images/264.jpg" /> 
-
-这个算法的名称意味着误差会从输出结点反向传播到输入结点。严格地讲，反向传播算法对网络的可修改权值计算了网络误差的梯度。[2] 这个梯度会在简单随机梯度下降法中经常用来求最小化误差的权重。通常“反向传播”这个词使用更一般的含义，用来指涵盖了计算梯度以及在随机梯度下降法中使用的整个过程。在适用反向传播算法的网络中，它通常可以快速收敛到令人满意的极小值。
-BP网络都是多层感知机（通常都会有一个输入层、一个隐藏层及一个输出层）。为了使隐藏层能够适合所有有用的函数，多层网络必须具有用于多个层的非线性激活函数：仅用线性激活函数的多层网络会与相当于单层线性网络。常用的非线性激活函数有逻辑函数、柔性最大函数和高斯函数。
-用反向传播算法求梯度已被重新发现多次，是更加一般的自动微分技术在反向积累模式的特例。
-它也与高斯-牛顿算法密切相关，也是继续研究神经反向传播的一部分。
-
-<p align="center">
-<img width="300" align="center" src="../../images/265.jpg" />
-</p>
-
-由于反向传播使用梯度下降法，需要计算平方误差函数对网络权重的导数。假设对于一个输出神经元，平方误差函数为：
-<p align="center">
-<img width="150" align="center" src="../../images/267.jpg" />
-</p>
-其中E 为平方误差,t 为训练样本的目标输出，y 为输出神经元的实际输出。
-
-加入系数<img width="30" align="center" src="../../images/266.jpg" />是为了抵消微分出来的指数。之后，该表达式会乘以一个任意的学习速率，因此在这里乘上一个常系数是没有关系的。 对每个神经元j，它的输出<img width="30" align="center" src="../../images/268.jpg" /> 定义为
-<p align="center">
-<img width="300" align="center" src="../../images/269.jpg" />
-</p>
-
-通向一个神经元的输入<img width="50" align="center" src="../../images/270.jpg" /> 是之前神经元的输出<img width="30" align="center" src="../../images/271.jpg" /> 的加权和。若该神经元输出层后的第一层，输入层的输出<img width="30" align="center" src="../../images/271.jpg" /> 就是网络的输入<img width="30" align="center" src="../../images/272.jpg" />。该神经元的输入数量是n。变<img width="30" align="center" src="../../images/273.jpg" />表示神经元i 与j 之间的权重。
-
-激活函数<img width="30" align="center" src="../../images/274.jpg" />一般是非线性可微函数。常用作激活函数的是逻辑函数：
-<p align="center">
-<img width="200" align="center" src="../../images/275.jpg" />
-</p>
-
-其导数的形式很好：
-<p align="center">
-<img width="200" align="center" src="../../images/276.jpg" />
-</p>
-
-#### 求误差的导数
-
-计算误差对权重<img width="30" align="center" src="../../images/273.jpg" />的偏导数是两次使用链式法则得到的：
-<p align="center">
-<img width="300" align="center" src="../../images/277.jpg" />
-</p>
-
-在右边的最后一项中，只有加权和<img width="30" align="center" src="../../images/270.jpg" />取决于<img width="30" align="center" src="../../images/273.jpg" />，因此:
-
-<p align="center">
-<img width="300" align="center" src="../../images/278.jpg" />
-</p>
-
-神经元j 的输出对其输入的导数就是激活函数的偏导数（这里假定使用逻辑函数）：
-
-<p align="center">
-<img width="300" align="center" src="../../images/279.jpg" />
-</p>
-
-这就是为什么反向传播需要的激活函数是可微的。
-如果神经元在输出层中，因为此时<img width="30" align="center" src="../../images/280.jpg" />以及
-<p align="center">
-<img width="300" align="center" src="../../images/281.jpg" />
-</p>
-所以第一项可以直接算出。
-
-但如果j 是网络中任一内层，求E关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数就不太简单了。
-
-考虑E为接受来自神经元j的输入的所有神经元<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/282.jpg">的输入的函数，
-<p align="center">
-<img width="300" align="center" src="../../images/283.jpg" />
-</p>
-
-并关于<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">取全微分，可以得到该导数的一个递归表达式：
-<p align="center">
-<img width="500" align="center" src="../../images/284.jpg" />
-</p>
-因此，若已知所有关于下一层（更接近输出神经元的一层）的输出<img width="30" align="center" src="../../images/288.jpg" />的导数，则可以计算<img width="30" align="center" src="/KeKe-Li/tutorial/raw/master/assets/images/268.jpg">的导数。
-
-把它们放在一起：
-<p align="center">
-<img width="200" align="center" src="../../images/285.jpg" />
-</p>
-
-其中:
-<p align="center">
-<img width="500" align="center" src="../../images/286.jpg" />
-</p>
-
-要使用梯度下降法更新<img width="30" align="center" src="../../images/273.jpg" />，必须选择一个学习速率a。要加在原本的权重上的权重的变化，等于学习速率与梯度的乘积，乘以-1：
-<p align="center">
-<img width="300" align="center" src="../../images/287.jpg" />
-</p>
-
-之所以要乘以-1 是因为要更新误差函数极小值而不是极大值的方向。对于单层网络，这个表达式变为Delta规则。
-
-#### 应用示例
-```python
-
-import random
-import math
-
-#   参数解释：
-#   "pd_" ：偏导的前缀
-#   "d_" ：导数的前缀
-#   "w_ho" ：隐含层到输出层的权重系数索引
-#   "w_ih" ：输入层到隐含层的权重系数的索引
-
-class NeuralNetwork:
-    LEARNING_RATE = 0.5
-
-    def __init__(self, num_inputs, num_hidden, num_outputs, hidden_layer_weights = None, hidden_layer_bias = None, output_layer_weights = None, output_layer_bias = None):
-        self.num_inputs = num_inputs
-
-        self.hidden_layer = NeuronLayer(num_hidden, hidden_layer_bias)
-        self.output_layer = NeuronLayer(num_outputs, output_layer_bias)
-
-        self.init_weights_from_inputs_to_hidden_layer_neurons(hidden_layer_weights)
-        self.init_weights_from_hidden_layer_neurons_to_output_layer_neurons(output_layer_weights)
-
-    def init_weights_from_inputs_to_hidden_layer_neurons(self, hidden_layer_weights):
-        weight_num = 0
-        for h in range(len(self.hidden_layer.neurons)):
-            for i in range(self.num_inputs):
-                if not hidden_layer_weights:
-                    self.hidden_layer.neurons[h].weights.append(random.random())
-                else:
-                    self.hidden_layer.neurons[h].weights.append(hidden_layer_weights[weight_num])
-                weight_num += 1
-
-    def init_weights_from_hidden_layer_neurons_to_output_layer_neurons(self, output_layer_weights):
-        weight_num = 0
-        for o in range(len(self.output_layer.neurons)):
-            for h in range(len(self.hidden_layer.neurons)):
-                if not output_layer_weights:
-                    self.output_layer.neurons[o].weights.append(random.random())
-                else:
-                    self.output_layer.neurons[o].weights.append(output_layer_weights[weight_num])
-                weight_num += 1
-
-    def inspect(self):
-        print('------')
-        print('* Inputs: {}'.format(self.num_inputs))
-        print('------')
-        print('Hidden Layer')
-        self.hidden_layer.inspect()
-        print('------')
-        print('* Output Layer')
-        self.output_layer.inspect()
-        print('------')
-
-    def feed_forward(self, inputs):
-        hidden_layer_outputs = self.hidden_layer.feed_forward(inputs)
-        return self.output_layer.feed_forward(hidden_layer_outputs)
-
-    def train(self, training_inputs, training_outputs):
-        self.feed_forward(training_inputs)
-
-        # 1. 输出神经元的值
-        pd_errors_wrt_output_neuron_total_net_input = [0] * len(self.output_layer.neurons)
-        for o in range(len(self.output_layer.neurons)):
-
-            # ∂E/∂zⱼ
-            pd_errors_wrt_output_neuron_total_net_input[o] = self.output_layer.neurons[o].calculate_pd_error_wrt_total_net_input(training_outputs[o])
-
-        # 2. 隐含层神经元的值
-        pd_errors_wrt_hidden_neuron_total_net_input = [0] * len(self.hidden_layer.neurons)
-        for h in range(len(self.hidden_layer.neurons)):
-
-            # dE/dyⱼ = Σ ∂E/∂zⱼ * ∂z/∂yⱼ = Σ ∂E/∂zⱼ * wᵢⱼ
-            d_error_wrt_hidden_neuron_output = 0
-            for o in range(len(self.output_layer.neurons)):
-                d_error_wrt_hidden_neuron_output += pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].weights[h]
-
-            # ∂E/∂zⱼ = dE/dyⱼ * ∂zⱼ/∂
-            pd_errors_wrt_hidden_neuron_total_net_input[h] = d_error_wrt_hidden_neuron_output * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_input()
-
-        # 3. 更新输出层权重系数
-        for o in range(len(self.output_layer.neurons)):
-            for w_ho in range(len(self.output_layer.neurons[o].weights)):
-
-                # ∂Eⱼ/∂wᵢⱼ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢⱼ
-                pd_error_wrt_weight = pd_errors_wrt_output_neuron_total_net_input[o] * self.output_layer.neurons[o].calculate_pd_total_net_input_wrt_weight(w_ho)
-
-                # Δw = α * ∂Eⱼ/∂wᵢ
-                self.output_layer.neurons[o].weights[w_ho] -= self.LEARNING_RATE * pd_error_wrt_weight
-
-        # 4. 更新隐含层的权重系数
-        for h in range(len(self.hidden_layer.neurons)):
-            for w_ih in range(len(self.hidden_layer.neurons[h].weights)):
-
-                # ∂Eⱼ/∂wᵢ = ∂E/∂zⱼ * ∂zⱼ/∂wᵢ
-                pd_error_wrt_weight = pd_errors_wrt_hidden_neuron_total_net_input[h] * self.hidden_layer.neurons[h].calculate_pd_total_net_input_wrt_weight(w_ih)
-
-                # Δw = α * ∂Eⱼ/∂wᵢ
-                self.hidden_layer.neurons[h].weights[w_ih] -= self.LEARNING_RATE * pd_error_wrt_weight
-
-    def calculate_total_error(self, training_sets):
-        total_error = 0
-        for t in range(len(training_sets)):
-            training_inputs, training_outputs = training_sets[t]
-            self.feed_forward(training_inputs)
-            for o in range(len(training_outputs)):
-                total_error += self.output_layer.neurons[o].calculate_error(training_outputs[o])
-        return total_error
-
-class NeuronLayer:
-    def __init__(self, num_neurons, bias):
-
-        # 同一层的神经元共享一个截距项b
-        self.bias = bias if bias else random.random()
-        self.neurons = []
-        for i in range(num_neurons):
-            self.neurons.append(Neuron(self.bias))
-
-    def inspect(self):
-        print('Neurons:', len(self.neurons))
-        for n in range(len(self.neurons)):
-            print(' Neuron', n)
-            for w in range(len(self.neurons[n].weights)):
-                print('  Weight:', self.neurons[n].weights[w])
-            print('  Bias:', self.bias)
-
-    def feed_forward(self, inputs):
-        outputs = []
-        for neuron in self.neurons:
-            outputs.append(neuron.calculate_output(inputs))
-        return outputs
-
-    def get_outputs(self):
-        outputs = []
-        for neuron in self.neurons:
-            outputs.append(neuron.output)
-        return outputs
-        
-class Neuron:
-    def __init__(self, bias):
-        self.bias = bias
-        self.weights = []
-
-    def calculate_output(self, inputs):
-        self.inputs = inputs
-        self.output = self.squash(self.calculate_total_net_input())
-        return self.output
-
-    def calculate_total_net_input(self):
-        total = 0
-        for i in range(len(self.inputs)):
-            total += self.inputs[i] * self.weights[i]
-        return total + self.bias
-
-    # 激活函数sigmoid
-    def squash(self, total_net_input):
-        return 1 / (1 + math.exp(-total_net_input))
-
-    def calculate_pd_error_wrt_total_net_input(self, target_output):
-        return self.calculate_pd_error_wrt_output(target_output) * self.calculate_pd_total_net_input_wrt_input();
-
-    # 每一个神经元的误差是由平方差公式计算的
-    def calculate_error(self, target_output):
-        return 0.5 * (target_output - self.output) ** 2
-        
-    def calculate_pd_error_wrt_output(self, target_output):
-        return -(target_output - self.output)
-        
-    def calculate_pd_total_net_input_wrt_input(self):
-        return self.output * (1 - self.output)
-
-    def calculate_pd_total_net_input_wrt_weight(self, index):
-        return self.inputs[index]
-# 示例:
-
-nn = NeuralNetwork(2, 2, 2, hidden_layer_weights=[0.15, 0.2, 0.25, 0.3], hidden_layer_bias=0.35, output_layer_weights=[0.4, 0.45, 0.5, 0.55], output_layer_bias=0.6)
-for i in range(10000):
-    nn.train([0.05, 0.1], [0.01, 0.09])
-    print(i, round(nn.calculate_total_error([[[0.05, 0.1], [0.01, 0.09]]]), 9))
-
-
-#另外一个例子，可以把上面的例子注释掉再运行一下:
-
-# training_sets = [
-#     [[0, 0], [0]],
-#     [[0, 1], [1]],
-#     [[1, 0], [1]],
-#     [[1, 1], [0]]
-# ]
-
-# nn = NeuralNetwork(len(training_sets[0][0]), 5, len(training_sets[0][1]))
-# for i in range(10000):
-#     training_inputs, training_outputs = random.choice(training_sets)
-#     nn.train(training_inputs, training_outputs)
-#     print(i, nn.calculate_total_error(training_sets))
-```
+####  回归神经网络(Recurrent Neural Network)

From 241917f7ee2c8652e0f010ad10b0c1ec5591c730 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 28 Apr 2018 02:21:28 +0000
Subject: [PATCH 0879/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index e4ec1e9c..ec50156e 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
+
 反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
 反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
 

From 5dc930a8a4b175662a26f72ea5a4d6eac62d33cc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 28 Apr 2018 02:21:35 +0000
Subject: [PATCH 0880/1406] Update ANN.0.3.md


From 6202e70958f806cbf77873dcfdd399af7fce1fac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 28 Apr 2018 16:25:12 +0000
Subject: [PATCH 0881/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 9d262bd3..e9346068 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -11,4 +11,5 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
+
 ####  回归神经网络(Recurrent Neural Network)

From 75b3407d6dcca1fca84945b9b54af0894a9c7e96 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 30 Apr 2018 07:20:17 +0000
Subject: [PATCH 0882/1406] Update ANN.0.3.md

---
 assets/src/ANN/ANN.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.3.md b/assets/src/ANN/ANN.0.3.md
index ec50156e..e4ec1e9c 100644
--- a/assets/src/ANN/ANN.0.3.md
+++ b/assets/src/ANN/ANN.0.3.md
@@ -12,7 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 反向传播(Backpropagation)
-
 反向传播（Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数（Loss Function）的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。
 反向传播要求有对每个输入值想得到的已知输出，来计算损失函数梯度。因此，它通常被认为是一种监督式学习方法，虽然它也用在一些无监督网络（如自动编码器Autoencoder）中。它是多层前馈网络的Delta规则（Delta Rule）的推广，可以用链式法则对每层迭代计算梯度。反向传播要求人工神经元（Artificial Neuron）（或“节点”）的激励函数可微。
 

From ad6a50306968420c5acc1f0fe6e9b3ebfaa82321 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 1 May 2018 06:50:08 +0800
Subject: [PATCH 0883/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index e9346068..0d576892 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -13,3 +13,4 @@
 
 
 ####  回归神经网络(Recurrent Neural Network)
+循环神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视频，一个个片段组成的音频，和一个个词汇组成的句子。尽管RNN有一些传统的缺点，如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 

From 87c7e023d52b7aaa247d12430e62f5f0064a5eba Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 20:41:13 +0800
Subject: [PATCH 0884/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 0d576892..42acd2d9 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -12,5 +12,5 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 
-####  回归神经网络(Recurrent Neural Network)
-循环神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视频，一个个片段组成的音频，和一个个词汇组成的句子。尽管RNN有一些传统的缺点，如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 
+####  递归神经网络(Recurrent Neural Network)
+递归神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视频，一个个片段组成的音频，和一个个词汇组成的句子。尽管RNN有一些传统的缺点，如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 

From 81d1bacd42e4a7811d7a7b4027b402846593b69b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 20:42:25 +0800
Subject: [PATCH 0885/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d7cc59f6..2c4c61a3 100644
--- a/README.md
+++ b/README.md
@@ -123,7 +123,7 @@
  * [人工神经网络(Artificial Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.1.md)      
      * [自动编码器(Autoencoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.2.md) 
      * [反向传播(Backpropagation)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.3.md) 
-     * [回归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
+     * [递归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
      * [多层感知器(Multilayer Perceptron)]() 
      * [玻尔兹曼机(Boltzmann Machine)]() 
      * [卷积神经网络(Convolutional Neural Network)]() 

From 2e56d563d51fa4ff408bd9a11e9c7842e7736a01 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 3 May 2018 21:12:10 +0800
Subject: [PATCH 0886/1406] change page of ANN0.4

---
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diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 42acd2d9..9e260dcc 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -13,4 +13,16 @@
 
 
 ####  递归神经网络(Recurrent Neural Network)
-递归神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视频，一个个片段组成的音频，和一个个词汇组成的句子。尽管RNN有一些传统的缺点，如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 
+递归神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，
+可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，
+而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。
+RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视频，一个个片段组成的音频，和一个个词汇组成的句子。尽管RNN有一些传统的缺点，
+如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 
+
+<p align="center">
+<img width="300" align="center" src="../../images/289.jpg" />
+</p>
+
+RNN主要解决序列数据的处理，比如文本、语音、视频等等。这类数据的样本间存在顺序关系，每个样本和它之前的样本存在关联。
+比如说，在文本中，一个词和它前面的词是有关联的；在气象数据中，一天的气温和前几天的气温是有关联的。一组观察数据定义为一个序列，从分布中可以观察出多个序列。
+

From d687093cd988f412011867346528dc57132915e3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:14:01 +0800
Subject: [PATCH 0887/1406] Update ANN.0.1.md

---
 assets/src/ANN/ANN.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.1.md b/assets/src/ANN/ANN.0.1.md
index a653ef5f..063caccc 100644
--- a/assets/src/ANN/ANN.0.1.md
+++ b/assets/src/ANN/ANN.0.1.md
@@ -29,7 +29,7 @@
 人工神经网络(Artificial Neural Network)算法应用： 
  * 自动编码器(Autoencoder) 
  * 反向传播(Backpropagation)
- * 回归神经网络(Recurrent Neural Network)
+ * 递归神经网络(Recurrent Neural Network)
  * 多层感知器(Multilayer Perceptron)
  * 玻尔兹曼机(Boltzmann Machine)
  * 卷积神经网络(Convolutional Neural Network)

From 6a05faad360df0ad03652a1782302cceb5bd850c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:15:47 +0800
Subject: [PATCH 0888/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 9e260dcc..afb4aaa7 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -20,7 +20,7 @@ RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视
 如难以训练，参数较多，但近些年来关于网络结构、优化手段和并行计算的深入研究使得大规模学习算法成为可能，尤其是LSTM与BRNN算法的成熟，使得图像标注、手写识别、机器翻译等应用取得了突破性进展。 
 
 <p align="center">
-<img width="300" align="center" src="../../images/289.jpg" />
+<img width="500" align="center" src="../../images/289.jpg" />
 </p>
 
 RNN主要解决序列数据的处理，比如文本、语音、视频等等。这类数据的样本间存在顺序关系，每个样本和它之前的样本存在关联。

From 91c7fe2fd306829027d1d27e0c54cbad34504ef1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:19:14 +0800
Subject: [PATCH 0889/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index afb4aaa7..53dc5bba 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -26,3 +26,27 @@ RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视
 RNN主要解决序列数据的处理，比如文本、语音、视频等等。这类数据的样本间存在顺序关系，每个样本和它之前的样本存在关联。
 比如说，在文本中，一个词和它前面的词是有关联的；在气象数据中，一天的气温和前几天的气温是有关联的。一组观察数据定义为一个序列，从分布中可以观察出多个序列。
 
+一个序列<img width="100" align="center" src="../../images/290.jpg" />的最简单模型为
+<p align="center">
+<img width="200" align="center" src="../../images/291.jpg" />
+</p>
+也就是说，序列里的每一个元素都和排在它前面的所有元素直接相关。
+
+当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="200" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
+
+<p align="center">
+<img width="200" align="center" src="../../images/293.jpg" />
+</p>
+
+当k=1时，模型变为:
+<p align="center">
+<img width="200" align="center" src="../../images/294.jpg" />
+</p>
+
+只考虑观察值X的模型有时表现力不足，因此需要加入隐变量，将观察值建模成由隐变量所生成。隐变量的好处在于，它的数量可以比观察值多，取值范围可以比观察值更广，能够更好的表达有限的观察值背后的复杂分布。加入了隐变量hh的马尔科夫模型称为隐马尔科夫模型。
+
+<p align="center">
+<img width="200" align="center" src="../../images/295.jpg" />
+</p>
+
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为O(T)。

From 80fc9e043f218b61614b684269b9e041683b9c95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:20:03 +0800
Subject: [PATCH 0890/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 53dc5bba..50aabf67 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -32,21 +32,21 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 </p>
 也就是说，序列里的每一个元素都和排在它前面的所有元素直接相关。
 
-当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="200" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
+当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="30" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
 
 <p align="center">
-<img width="200" align="center" src="../../images/293.jpg" />
+<img width="600" align="center" src="../../images/293.jpg" />
 </p>
 
 当k=1时，模型变为:
 <p align="center">
-<img width="200" align="center" src="../../images/294.jpg" />
+<img width="600" align="center" src="../../images/294.jpg" />
 </p>
 
 只考虑观察值X的模型有时表现力不足，因此需要加入隐变量，将观察值建模成由隐变量所生成。隐变量的好处在于，它的数量可以比观察值多，取值范围可以比观察值更广，能够更好的表达有限的观察值背后的复杂分布。加入了隐变量hh的马尔科夫模型称为隐马尔科夫模型。
 
 <p align="center">
-<img width="200" align="center" src="../../images/295.jpg" />
+<img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为O(T)。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="30" align="center" src="../../images/293.jpg" />。

From 10aa0d6fc7e506a4c96fda56d83ea0c54231cc24 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:21:05 +0800
Subject: [PATCH 0891/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 50aabf67..d1b2ac5b 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -28,19 +28,19 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 
 一个序列<img width="100" align="center" src="../../images/290.jpg" />的最简单模型为
 <p align="center">
-<img width="200" align="center" src="../../images/291.jpg" />
+<img width="500" align="center" src="../../images/291.jpg" />
 </p>
 也就是说，序列里的每一个元素都和排在它前面的所有元素直接相关。
 
 当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="30" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
 
 <p align="center">
-<img width="600" align="center" src="../../images/293.jpg" />
+<img width="500" align="center" src="../../images/293.jpg" />
 </p>
 
 当k=1时，模型变为:
 <p align="center">
-<img width="600" align="center" src="../../images/294.jpg" />
+<img width="500" align="center" src="../../images/294.jpg" />
 </p>
 
 只考虑观察值X的模型有时表现力不足，因此需要加入隐变量，将观察值建模成由隐变量所生成。隐变量的好处在于，它的数量可以比观察值多，取值范围可以比观察值更广，能够更好的表达有限的观察值背后的复杂分布。加入了隐变量hh的马尔科夫模型称为隐马尔科夫模型。
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="30" align="center" src="../../images/293.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="100" align="center" src="../../images/293.jpg" />。

From eb70284ad6054380802045395bc3681e9de8927f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:21:40 +0800
Subject: [PATCH 0892/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index d1b2ac5b..3df08fb3 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -26,7 +26,7 @@ RNN广泛应用在和序列有关的场景，如如一帧帧图像组成的视
 RNN主要解决序列数据的处理，比如文本、语音、视频等等。这类数据的样本间存在顺序关系，每个样本和它之前的样本存在关联。
 比如说，在文本中，一个词和它前面的词是有关联的；在气象数据中，一天的气温和前几天的气温是有关联的。一组观察数据定义为一个序列，从分布中可以观察出多个序列。
 
-一个序列<img width="100" align="center" src="../../images/290.jpg" />的最简单模型为
+一个序列<img width="300" align="center" src="../../images/290.jpg" />的最简单模型为
 <p align="center">
 <img width="500" align="center" src="../../images/291.jpg" />
 </p>
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="100" align="center" src="../../images/293.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="300" align="center" src="../../images/293.jpg" />。

From e2ec04358ac49fee1d7c3922c1dcd83bde5f7b73 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:23:29 +0800
Subject: [PATCH 0893/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 3df08fb3..a84ea415 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -32,7 +32,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 </p>
 也就是说，序列里的每一个元素都和排在它前面的所有元素直接相关。
 
-当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="30" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
+当然，这个模型存在致命的问题：它的复杂度会爆炸性增长，<img width="50" align="center" src="../../images/292.jpg" />隐马尔科夫模型（HMM）定义每个元素只和离它最近的kk个元素相关，解决了复杂度暴增的问题，模型为:
 
 <p align="center">
 <img width="500" align="center" src="../../images/293.jpg" />
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="300" align="center" src="../../images/293.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="300" align="center" src="../../images/296.jpg" />。

From 1028321a90ea8bdaca08a65604cebb3b5111b580 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:23:49 +0800
Subject: [PATCH 0894/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index a84ea415..0d585b9e 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="300" align="center" src="../../images/296.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="100" align="center" src="../../images/296.jpg" />。

From 58bcfb769cc61c36fe2e3eb141fb44aa9dee5da3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:24:54 +0800
Subject: [PATCH 0895/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 0d585b9e..6e94613e 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="100" align="center" src="../../images/296.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="70" align="center" src="../../images/296.jpg" />。

From ef12debc91a1c81c9f463bac9678ca590abae0de Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:25:14 +0800
Subject: [PATCH 0896/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 6e94613e..1ac4d82c 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -49,4 +49,4 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="600" align="center" src="../../images/295.jpg" />
 </p>
 
-隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="70" align="center" src="../../images/296.jpg" />。
+隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="50" align="center" src="../../images/296.jpg" />。

From 2d649bd107cfa9f9f5b5c93a764be213ae08fd83 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:25:49 +0800
Subject: [PATCH 0897/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 1ac4d82c..562ec6d7 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -50,3 +50,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 </p>
 
 隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="50" align="center" src="../../images/296.jpg" />。
+
+<p align="center">
+<img width="300" align="center" src="../../images/297.jpg" />
+</p>

From 52aafbc750ff4a6c0a3944622277afa7f1113b8b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:29:36 +0800
Subject: [PATCH 0898/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 562ec6d7..1b39a8ab 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -52,5 +52,11 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 隐马尔科夫模型实际上建模的是观察值X，隐变量h和模型参数θ的联合分布,HMM的模型长度T是事先固定的，模型参数不共享，其复杂度为<img width="50" align="center" src="../../images/296.jpg" />。
 
 <p align="center">
-<img width="300" align="center" src="../../images/297.jpg" />
+<img width="380" align="center" src="../../images/297.jpg" />
+</p>
+
+把序列视作时间序列，隐含层h的自连接边实际上是和上一时刻的h相连.在每一个时刻t，<img width="30" align="center" src="../../images/299.jpg" />的取值是当前时刻的输入<img width="30" align="center" src="../../images/298.jpg" />,和上一时刻的隐含层值<img width="30" align="center" src="../../images/301.jpg" />的一个函数:
+
+<p align="center">
+<img width="380" align="center" src="../../images/300.jpg" />
 </p>

From c34971bdee8ef1fa63af838a656f8025f76f6196 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:30:15 +0800
Subject: [PATCH 0899/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 1b39a8ab..7f9472a2 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -55,7 +55,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="380" align="center" src="../../images/297.jpg" />
 </p>
 
-把序列视作时间序列，隐含层h的自连接边实际上是和上一时刻的h相连.在每一个时刻t，<img width="30" align="center" src="../../images/299.jpg" />的取值是当前时刻的输入<img width="30" align="center" src="../../images/298.jpg" />,和上一时刻的隐含层值<img width="30" align="center" src="../../images/301.jpg" />的一个函数:
+把序列视作时间序列，隐含层h的自连接边实际上是和上一时刻的h相连.在每一个时刻t，<img width="60" align="center" src="../../images/299.jpg" />的取值是当前时刻的输入<img width="50" align="center" src="../../images/298.jpg" />,和上一时刻的隐含层值<img width="30" align="center" src="../../images/301.jpg" />的一个函数:
 
 <p align="center">
 <img width="380" align="center" src="../../images/300.jpg" />

From ffb2ecb4c7512e002c64db39570486d683b7488e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:32:32 +0800
Subject: [PATCH 0900/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 7f9472a2..df8ea961 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -60,3 +60,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <p align="center">
 <img width="380" align="center" src="../../images/300.jpg" />
 </p>
+
+将h层的自连接展开，就成为了上图右边的样子，看上去和HMM很像。两者最大的区别在于，RNN的参数是跨时刻共享的。也就是说，对任意时刻t，<img width="30" align="center" src="../../images/301.jpg" />到<img width="60" align="center" src="../../images/299.jpg" />以及<img width="50" align="center" src="../../images/298.jpg" />到<img width="60" align="center" src="../../images/299.jpg" />的网络参数都是相同的。
+
+共享参数的思想和和卷积神经网络（CNN）是相通的，CNN在二维数据的空间位置之间共享卷积核参数，而RNN则是在序列数据的时刻之间共享参数。共享参数使得模型的复杂度大大减少，并使RNN可以适应任意长度的序列，带来了更好的可推广性。

From fa5c01a012b7dce982e96b1fa17f5664e01133c8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:39:22 +0800
Subject: [PATCH 0901/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 48 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index df8ea961..48e8728b 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -64,3 +64,51 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 将h层的自连接展开，就成为了上图右边的样子，看上去和HMM很像。两者最大的区别在于，RNN的参数是跨时刻共享的。也就是说，对任意时刻t，<img width="30" align="center" src="../../images/301.jpg" />到<img width="60" align="center" src="../../images/299.jpg" />以及<img width="50" align="center" src="../../images/298.jpg" />到<img width="60" align="center" src="../../images/299.jpg" />的网络参数都是相同的。
 
 共享参数的思想和和卷积神经网络（CNN）是相通的，CNN在二维数据的空间位置之间共享卷积核参数，而RNN则是在序列数据的时刻之间共享参数。共享参数使得模型的复杂度大大减少，并使RNN可以适应任意长度的序列，带来了更好的可推广性。
+
+* 双向RNN
+
+单向RNN的问题在于t时刻进行分类的时候只能利用tt时刻之前的信息， 但是在t时刻进行分类的时候可能也需要利用未来时刻的信息。双向RNN（bi-directional RNN）模型正是为了解决这个问题， 双向RNN在任意时刻tt都保持两个隐藏层，一个隐藏层用于从左往右的信息传播记作， 另一个隐藏层用于从右往左的信息传播记作。
+
+
+<p align="center">
+<img width="380" align="center" src="../../images/302.jpg" />
+</p>
+
+Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输入有多层网络。这样，该网络便有更强大的表达与学习能力，但是复杂性也提高了，同时需要更多的训练数据。
+
+<p align="center">
+<img width="380" align="center" src="../../images/303.jpg" />
+</p>
+
+* Gradient Vanishing Exploding (梯度消失和梯度爆炸)
+<p align="center">
+<img width="380" align="center" src="../../images/304.jpg" />
+</p>
+
+RNN训练困难的主要原因在于隐藏层参数w的传播：由于误差传播在展开后的RNN上，无论在前向传播过程还是在反向传播过程中w都会乘上多次，这就导致：
+
+* 梯度消失：如果梯度很小的话（<1），乘上多次指数级下降，对输出几乎就没有影响了
+* 梯度爆炸：反过来，如果梯度很大的话，乘上多次指数级增加，又导致了梯度爆炸
+
+<p align="center">
+<img width="380" align="center" src="../../images/303.jpg" />
+</p>
+
+这个问题其实存在于任何深度神经网络中，只是由于RNN的递归结构导致其尤其明显。
+
+对于梯度爆炸问题，可以通过截断的方式来有效避免：
+
+<p align="center">
+<img width="380" align="center" src="../../images/304.jpg" />
+</p>
+而对梯度消失问题，则有很多不同的方案：
+
+* 有效初始化+ReLU激活函数能够得到较好效果
+* 算法上的优化，例如截断的BPTT算法。
+* 模型上的改进，例如LSTM、GRU单元都可以有效解决长期依赖问题。
+* 在BPTT算法中加入skip connection，此时误差可以间歇的向前传播。
+* 加入一些Leaky Units，思路类似于skip connection
+
+LSTM 全称叫 Long Short-Term Memory networks，它和传统 RNN 唯一的不同就在与其中的神经元（感知机）的构造不同。传统的 RNN 每个神经元和一般神经网络的感知机没啥区别，但在 LSTM 中，每个神经元是一个“记忆细胞”（元胞状态，Cell State），将以前的信息连接到当前的任务中来。每个LSTM细胞里面都包含:
+
+* 输入门（input gate）: 一个Sigmoid层，观察<img width="60" align="center" src="../../images/299.jpg" />和<img width="50" align="center" src="../../images/298.jpg" />,对于元胞状态<img width="50" align="center" src="../../images/306.jpg" />中的每一个元素，输出一个0~1之间的数。1表示“完全保留该信息”，0表示“完全丢弃该信息”：

From 790049a451e65c88b265a9bfe6efd91c104b24e6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:42:07 +0800
Subject: [PATCH 0902/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 48e8728b..f06fa1b9 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -90,16 +90,12 @@ RNN训练困难的主要原因在于隐藏层参数w的传播：由于误差传
 * 梯度消失：如果梯度很小的话（<1），乘上多次指数级下降，对输出几乎就没有影响了
 * 梯度爆炸：反过来，如果梯度很大的话，乘上多次指数级增加，又导致了梯度爆炸
 
-<p align="center">
-<img width="380" align="center" src="../../images/303.jpg" />
-</p>
-
 这个问题其实存在于任何深度神经网络中，只是由于RNN的递归结构导致其尤其明显。
 
 对于梯度爆炸问题，可以通过截断的方式来有效避免：
 
 <p align="center">
-<img width="380" align="center" src="../../images/304.jpg" />
+<img width="380" align="center" src="../../images/305.jpg" />
 </p>
 而对梯度消失问题，则有很多不同的方案：
 

From a2e73bba222a0d4d1894d7af00ae996af8194fb9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:45:33 +0800
Subject: [PATCH 0903/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index f06fa1b9..6f0e04ba 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -108,3 +108,34 @@ RNN训练困难的主要原因在于隐藏层参数w的传播：由于误差传
 LSTM 全称叫 Long Short-Term Memory networks，它和传统 RNN 唯一的不同就在与其中的神经元（感知机）的构造不同。传统的 RNN 每个神经元和一般神经网络的感知机没啥区别，但在 LSTM 中，每个神经元是一个“记忆细胞”（元胞状态，Cell State），将以前的信息连接到当前的任务中来。每个LSTM细胞里面都包含:
 
 * 输入门（input gate）: 一个Sigmoid层，观察<img width="60" align="center" src="../../images/299.jpg" />和<img width="50" align="center" src="../../images/298.jpg" />,对于元胞状态<img width="50" align="center" src="../../images/306.jpg" />中的每一个元素，输出一个0~1之间的数。1表示“完全保留该信息”，0表示“完全丢弃该信息”：
+
+<p align="center">
+<img width="380" align="center" src="../../images/307.jpg" />
+</p>
+
+* 遗忘门（forget gate): 一个Sigmoid层决定我们要更新哪些信息，并由一个tanh层创造了一个新的候选值（结果在(-1, 1)(−1,1)范围）
+<p align="center">
+<img width="380" align="center" src="../../images/308.jpg" />
+</p>
+
+<p align="center">
+<img width="380" align="center" src="../../images/309.jpg" />
+</p>
+
+<p align="center">
+<img width="380" align="center" src="../../images/310.jpg" />
+</p>
+
+输出门（output gate）：控制哪些信息需要输出
+
+<p align="center">
+<img width="380" align="center" src="../../images/311.jpg" />
+</p>
+
+<p align="center">
+<img width="380" align="center" src="../../images/312.jpg" />
+</p>
+
+<p align="center">
+<img width="380" align="center" src="../../images/313.jpg" />
+</p>

From 1041e0c1f59131ed71691c3904c6a469e44ba7af Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:49:20 +0800
Subject: [PATCH 0904/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 36 ++++++++++++++++++++++++++++++------
 1 file changed, 30 insertions(+), 6 deletions(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 6f0e04ba..1e2b6ebe 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -115,27 +115,51 @@ LSTM 全称叫 Long Short-Term Memory networks，它和传统 RNN 唯一的不
 
 * 遗忘门（forget gate): 一个Sigmoid层决定我们要更新哪些信息，并由一个tanh层创造了一个新的候选值（结果在(-1, 1)(−1,1)范围）
 <p align="center">
-<img width="380" align="center" src="../../images/308.jpg" />
+<img width="320" align="center" src="../../images/308.jpg" />
 </p>
 
 <p align="center">
-<img width="380" align="center" src="../../images/309.jpg" />
+<img width="320" align="center" src="../../images/309.jpg" />
 </p>
 
 <p align="center">
-<img width="380" align="center" src="../../images/310.jpg" />
+<img width="320" align="center" src="../../images/310.jpg" />
 </p>
 
 输出门（output gate）：控制哪些信息需要输出
 
 <p align="center">
-<img width="380" align="center" src="../../images/311.jpg" />
+<img width="320" align="center" src="../../images/311.jpg" />
 </p>
 
 <p align="center">
-<img width="380" align="center" src="../../images/312.jpg" />
+<img width="320" align="center" src="../../images/312.jpg" />
 </p>
 
 <p align="center">
-<img width="380" align="center" src="../../images/313.jpg" />
+<img width="500" align="center" src="../../images/313.jpg" />
+</p>
+
+典型的工作流为：在“输入门”中，根据当前的数据流来控制接受细胞记忆的影响；接着，在 “遗忘门”里，更新这个细胞的记忆和数据流；然后在“输出门”里产生输出更新后的记忆和数据流。LSTM 模型的关键之一就在于这个“遗忘门”， 它能够控制训练时候梯度在这里的收敛性（从而避免了 RNN 中的梯度 vanishing/exploding 问题），同时也能够保持长期的记忆性。
+
+如果我们把LSTM的forget gate全部置0（总是忘记之前的信息），input gate全部 置1，output gate全部置1（把cell state中的信息全部输出），这样LSTM就变成一个标准的RNN。
+
+目前 LSTM 模型在实践中取得了非常好的效果， 只需要训练一个两三层的LSTM, 它就可以:
+* 模仿保罗·格雷厄姆进行写作
+* 生成维基百科的 markdown 页面
+* 手写识别
+* 写代码
+
+<p align="center">
+<img width="500" align="center" src="../../images/314.jpg" />
+</p>
+
+GRU (Gated Recurrent Unit) 是LSTM的变种，把LSTM中的遗忘门和输入门合并成为单一的“更新门(Update Gate)”，同时也将元胞状态(Cell State)和隐状态(Hidden State)合并，在计算当前时刻新信息的方法和LSTM有所不同。
+
+<p align="center">
+<img width="500" align="center" src="../../images/315.jpg" />
+</p>
+
+<p align="center">
+<img width="500" align="center" src="../../images/316.jpg" />
 </p>

From 6459a454d37ceea8824bda572d696eb40fbe6dff Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:52:02 +0800
Subject: [PATCH 0905/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 130 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 130 insertions(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 1e2b6ebe..57ddbf0a 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -160,6 +160,136 @@ GRU (Gated Recurrent Unit) 是LSTM的变种，把LSTM中的遗忘门和输入门
 <img width="500" align="center" src="../../images/315.jpg" />
 </p>
 
+GRU与RNN对比:
+
 <p align="center">
 <img width="500" align="center" src="../../images/316.jpg" />
 </p>
+
+####  应用示例
+```python
+import numpy as np
+
+def sigmoid(x):
+    x = (np.exp(x)+0.00000000001)/np.sum(np.exp(x)+0.00000000001)
+    return x
+
+class RNN:
+    def __init__(self, input_dim, hidden_nodes, output_dim):
+        self.Wxh = np.random.random([hidden_nodes, input_dim])*0.01
+        self.Bxh = np.random.random([hidden_nodes])*0.01
+        self.Whh = np.random.random([hidden_nodes, hidden_nodes])*0.01
+        self.Bhh = np.random.random([hidden_nodes])*0.01
+        self.Wyh = np.random.random([output_dim, hidden_nodes])*0.01
+        self.Byh = np.random.random([output_dim])*0.01
+        self.h = np.random.random([hidden_nodes])*0.01
+
+    def forward(self, x):
+        T = x.shape[1]
+        states = []
+        output = []
+        for i in range(T):
+            if i == 0:
+                ht = np.tanh(np.dot(self.Wxh, x[:, i]) + self.Bxh + np.dot(self.Whh, self.h))
+            else:
+                ht = np.tanh(np.dot(self.Wxh, x[:, i]) + self.Bxh + np.dot(self.Whh, states[i-1]))
+            ot = sigmoid(np.dot(self.Wyh, ht) + self.Byh)
+            states.append(ht)
+            output.append(ot)
+        return states, output
+
+    def backword(self, x, y, h, output, lr=0.002):
+        T = x.shape[1]
+        dL_T = np.dot( np.transpose(self.Wyh), output[-1]-y[:, -1])
+        loss = np.sum(-y[:, -1]*np.log(output[-1]))
+        dL_ht = dL_T
+        D_Wyh = np.zeros_like(self.Wyh)
+        D_Byh = np.zeros_like(self.Byh)
+        D_Whh = np.zeros_like(self.Whh)
+        D_Bhh = np.zeros_like(self.Bhh)
+        D_Wxh = np.zeros_like(self.Wxh)
+        D_Bxh = np.zeros_like(self.Bxh)
+        for t in range(T-2, -1, -1):
+            dQ = (output[t] - y[:, t])
+            DL_Qt = np.dot(np.transpose(self.Wyh), dQ)
+
+            dy = (1 - h[t]*h[t])
+            dL_ht += np.dot(np.transpose(self.Wyh), dQ)
+
+            D_Wyh += np.outer(dQ, h[t])
+            D_Byh += dQ
+
+            D_Wxh += np.outer(dy*dL_ht, x[:, t])
+            D_Bxh += dy*dL_ht
+
+            D_Whh += np.outer(dy*dL_ht, h[t-1])
+            D_Bhh += dy*dL_ht
+
+            loss += np.sum(-y[:, t]*np.log(output[t]))
+        for dparam in [D_Wyh, D_Byh, D_Wxh, D_Bxh, D_Whh, D_Bhh]:
+            np.clip(dparam, -5, 5, out=dparam)
+
+        self.Wyh -= lr*D_Wyh/np.sqrt(D_Wyh*D_Wyh + 0.00000001)
+        self.Wxh -= lr*D_Wxh/np.sqrt(D_Wxh*D_Wxh + 0.00000001)
+        self.Whh -= lr*D_Whh/np.sqrt(D_Whh*D_Whh + 0.00000001)
+        self.Byh -= lr*D_Byh/np.sqrt(D_Byh*D_Byh + 0.00000001)
+        self.Bhh -= lr*D_Bhh/np.sqrt(D_Bhh*D_Bhh + 0.00000001)
+        self.Bxh -= lr*D_Bxh/np.sqrt(D_Bxh*D_Bxh + 0.00000001)
+        self.h -= lr*dL_ht/np.sqrt(dL_ht*dL_ht + 0.00000001)
+        return loss, self.h
+    def sample(self, x):
+        h = self.h
+        predict = []
+        for i in range(9-1):
+            ht = np.tanh(np.dot(self.Wxh, x) + self.Bxh + np.dot(self.Whh, h))
+            ot = sigmoid(np.dot(self.Wyh, ht) + self.Byh)
+            ynext = np.argmax(ot)
+            predict.append(ynext)
+            x = np.zeros_like(x)
+            x[ynext] = 1
+        return predict
+
+#create 2000 sequences with 10 number in each sequence
+def getrandomdata(nums):
+    x = np.zeros([nums, 10, 9], dtype=float)
+    y = np.zeros([nums, 10, 9], dtype=float)
+    for i in range(nums):
+        tmpi = np.random.randint(0, 9)
+        for j in range(9):
+            if tmpi < 8:
+                x[i, tmpi, j], y[i, tmpi+1, j] = 1.0, 1.0
+                tmpi = tmpi+1
+            else:
+                x[i, tmpi, j], y[i, 0, j] = 1.0, 1.0
+                tmpi = 0
+    return x, y
+
+def test(nums):
+    testx = np.zeros([nums, 10], dtype=float)
+    for i in range(nums):
+        tmpi = np.random.randint(0, 9)
+        testx[i, tmpi] = 1
+    for i in range(nums):
+        print('the given start number:', np.argmax(testx[i]))
+        print('the created numbers:   ', model.sample(testx[i]) )
+
+if __name__ == '__main__':
+    #x0 = [0, 1, 2, 3, 4, 5, 6, 7, 8]--> y0 = [1, 2, 3, 4, 5, 6, 7, 8, 0],            x1 = [5, 6, 7, 8, 0, 1, 2, 3, 4]--> y1 = [6, 7, 8, 0, 1, 2, 3, 4, 5]
+    model = RNN(10, 200, 10)
+    state = np.random.random(100)
+    epoches = 5;
+    smooth_loss = 0
+    for ll in range(epoches):
+        print('epoch i:', ll)
+        x, y = getrandomdata(2000)
+        for i in range(x.shape[0]):
+            h, output = model.forward(x[i])
+            loss, state = model.backword(x[i], y[i], h, output, lr=0.001)
+            if i == 1:
+                smooth_loss = loss
+            else:
+                smooth_loss = smooth_loss * 0.999 + loss * 0.001
+            #print('loss ----  ', smooth_loss)             
+            #if you want to see the cost, you can uncomment this line to observe the cost
+        test(7)
+```

From 8fccaea3168612dd41072cf04ee0ee2de199b4ed Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 3 May 2018 21:53:16 +0800
Subject: [PATCH 0906/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 57ddbf0a..064d96aa 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -274,7 +274,8 @@ def test(nums):
         print('the created numbers:   ', model.sample(testx[i]) )
 
 if __name__ == '__main__':
-    #x0 = [0, 1, 2, 3, 4, 5, 6, 7, 8]--> y0 = [1, 2, 3, 4, 5, 6, 7, 8, 0],            x1 = [5, 6, 7, 8, 0, 1, 2, 3, 4]--> y1 = [6, 7, 8, 0, 1, 2, 3, 4, 5]
+    #x0 = [0, 1, 2, 3, 4, 5, 6, 7, 8]--> y0 = [1, 2, 3, 4, 5, 6, 7, 8, 0],            
+    #x1 = [5, 6, 7, 8, 0, 1, 2, 3, 4]--> y1 = [6, 7, 8, 0, 1, 2, 3, 4, 5]
     model = RNN(10, 200, 10)
     state = np.random.random(100)
     epoches = 5;

From 80d97d5d3d6a0c22fac31cc05a12dd28549c4684 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 3 May 2018 21:55:07 +0800
Subject: [PATCH 0907/1406] change page of ANN0.5

---
 README.md                 |  2 +-
 assets/src/ANN/ANN.0.5.md | 14 ++++++++++++++
 2 files changed, 15 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/ANN/ANN.0.5.md

diff --git a/README.md b/README.md
index 2c4c61a3..38ce2969 100644
--- a/README.md
+++ b/README.md
@@ -124,7 +124,7 @@
      * [自动编码器(Autoencoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.2.md) 
      * [反向传播(Backpropagation)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.3.md) 
      * [递归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
-     * [多层感知器(Multilayer Perceptron)]() 
+     * [多层感知器(Multilayer Perceptron)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.5.md) 
      * [玻尔兹曼机(Boltzmann Machine)]() 
      * [卷积神经网络(Convolutional Neural Network)]() 
      * [Hopfield网络(Hopfield Network)]() 
diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
new file mode 100644
index 00000000..cd499df4
--- /dev/null
+++ b/assets/src/ANN/ANN.0.5.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 多层感知器(Multilayer Perceptron)

From fe6d8565a1725b76c87c4293310b1022f3aac1ce Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 4 May 2018 17:21:32 +0800
Subject: [PATCH 0908/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 064d96aa..a62b663b 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -13,6 +13,7 @@
 
 
 ####  递归神经网络(Recurrent Neural Network)
+
 递归神经网络（Recurrent neural networks，简称RNN）是一种通过隐藏层节点周期性的连接，来捕捉序列化数据中动态信息的神经网络，
 可以对序列化的数据进行分类。和其他前向神经网络不同，RNN可以保存一种上下文的状态，甚至能够在任意长的上下文窗口中存储、学习、表达相关信息，
 而且不再局限于传统神经网络在空间上的边界，可以在时间序列上有延拓，直观上讲，就是本时间的隐藏层和下一时刻的隐藏层之间的节点间有边。

From 1596dec3a66f6bc1f5f9d2c1dfbcdfa02689d7c0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 16:46:36 +0800
Subject: [PATCH 0909/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index cd499df4..67495940 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -12,3 +12,4 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 多层感知器(Multilayer Perceptron)
+多层感知器（Multilayer Perceptron,缩写MLP）是一种前向结构的人工神经网络，映射一组输入向量到一组输出向量。MLP可以被看作是一个有向图，由多个的节点层所组成，每一层都全连接到下一层。除了输入节点，每个节点都是一个带有非线性激活函数的神经元（或称处理单元）。一种被称为反向传播算法的监督学习方法常被用来训练MLP。MLP是感知器的推广，克服了感知器不能对线性不可分数据进行识别的弱点

From 7bb003cd3527844f5fdc881a6aef138ab40e97aa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 16:47:23 +0800
Subject: [PATCH 0910/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 67495940..be7fac4d 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -13,3 +13,7 @@
 
 #### 多层感知器(Multilayer Perceptron)
 多层感知器（Multilayer Perceptron,缩写MLP）是一种前向结构的人工神经网络，映射一组输入向量到一组输出向量。MLP可以被看作是一个有向图，由多个的节点层所组成，每一层都全连接到下一层。除了输入节点，每个节点都是一个带有非线性激活函数的神经元（或称处理单元）。一种被称为反向传播算法的监督学习方法常被用来训练MLP。MLP是感知器的推广，克服了感知器不能对线性不可分数据进行识别的弱点
+
+若每个神经元的激活函数都是线性函数，那么，任意层数的MLP都可被约简成一个等价的单层感知器。
+
+实际上，MLP本身可以使用任何形式的激活函数，譬如阶梯函数或逻辑乙形函数（logistic sigmoid function），但为了使用反向传播算法进行有效学习，激活函数必须限制为可微函数。由于具有良好可微性，很多S函数，尤其是双曲正切函数（Hyperbolic tangent）及逻辑函数，被采用为激活函数。

From 22d9be7e879c76f7d6dd2bd10bdda4c4e40ef1b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 16:47:41 +0800
Subject: [PATCH 0911/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index be7fac4d..538aa1ae 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -17,3 +17,7 @@
 若每个神经元的激活函数都是线性函数，那么，任意层数的MLP都可被约简成一个等价的单层感知器。
 
 实际上，MLP本身可以使用任何形式的激活函数，譬如阶梯函数或逻辑乙形函数（logistic sigmoid function），但为了使用反向传播算法进行有效学习，激活函数必须限制为可微函数。由于具有良好可微性，很多S函数，尤其是双曲正切函数（Hyperbolic tangent）及逻辑函数，被采用为激活函数。
+
+通常MLP用来进行学习的反向传播算法，在模式识别的领域中算是标准监督学习算法，并在计算神经学及并行分布式处理领域中，持续成为被研究的课题。MLP已被证明是一种通用的函数近似方法，可以被用来拟合复杂的函数，或解决分类问题。
+
+MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的应用场景，譬如语音识别、图像识别、机器翻译等等，但自90年代以来，MLP遇到来自更为简单的支持向量机的强劲竞争。近来，由于深度学习的成功，MLP又重新得到了关注。

From 23b25d8b49075c73180751e45be5570d76ccf12d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 9 May 2018 23:34:01 +0800
Subject: [PATCH 0912/1406] change page of ANN

---
 assets/images/317.jpg     | Bin 0 -> 23828 bytes
 assets/src/ANN/ANN.0.5.md |   7 +++++++
 2 files changed, 7 insertions(+)
 create mode 100644 assets/images/317.jpg

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diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 538aa1ae..586f65c9 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -21,3 +21,10 @@
 通常MLP用来进行学习的反向传播算法，在模式识别的领域中算是标准监督学习算法，并在计算神经学及并行分布式处理领域中，持续成为被研究的课题。MLP已被证明是一种通用的函数近似方法，可以被用来拟合复杂的函数，或解决分类问题。
 
 MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的应用场景，譬如语音识别、图像识别、机器翻译等等，但自90年代以来，MLP遇到来自更为简单的支持向量机的强劲竞争。近来，由于深度学习的成功，MLP又重新得到了关注。
+
+通常一个单一隐藏层的多层感知机（或人工神经网络—ANN）可以用图表现为：
+
+<p align="center">
+<img width="100" align="center" src="../../images/317.jpg" />
+</p>
+

From d02b7efb7b0e76ccbadf0120983cd4d4a1adec08 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 9 May 2018 23:37:18 +0800
Subject: [PATCH 0913/1406] change page

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From da2e6bdf7d6a8e9d11b18050a6cd7dee2b37a049 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:40:32 +0800
Subject: [PATCH 0914/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 586f65c9..60dc7b3f 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -25,6 +25,13 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 通常一个单一隐藏层的多层感知机（或人工神经网络—ANN）可以用图表现为：
 
 <p align="center">
-<img width="100" align="center" src="../../images/317.jpg" />
+<img width="300" align="center" src="../../images/317.jpg" />
 </p>
 
+
+正式的单一隐藏层的MLP可以表现为：<img width="70" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="70" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
+
+向量<img width="70" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="70" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="70" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="70" align="center" src="../../images/323.jpg" />。
+
+这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
+

From 80dd1b8b3bc1b89b0723c78ba470e80afab3d732 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:42:46 +0800
Subject: [PATCH 0915/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 60dc7b3f..24649980 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -29,9 +29,18 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 </p>
 
 
-正式的单一隐藏层的MLP可以表现为：<img width="70" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="70" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
+正式的单一隐藏层的MLP可以表现为：<img width="130" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="130" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
 
-向量<img width="70" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="70" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="70" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="70" align="center" src="../../images/323.jpg" />。
+向量<img width="130" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="130" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="130" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="130" align="center" src="../../images/323.jpg" />。
 
 这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
 
+输出向量通过以下公式得到<img width="130" align="center" src="../../images/324.jpg" />。
+
+我们此前在使用逻辑回归区分MNIST数字时提到过这一公式。如前，在多类区分中，通过使用softmax作为G的函数，可以获得类成员的概率。
+
+训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="130" align="center" src="../../images/325.jpg" />。
+
+梯度<img width="130" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
+
+从逻辑回归到多层感知机我们将聚焦单隐藏层的多层感知机。 我们从构建一个单隐藏层的类开始。之后只要在此基础之上加一个逻辑回归层就构建了MLP。

From 5b25667d29e0d39525ca079df57e19a6c9cdc24e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:43:41 +0800
Subject: [PATCH 0916/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 24649980..63f99ecb 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -29,7 +29,7 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 </p>
 
 
-正式的单一隐藏层的MLP可以表现为：<img width="130" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="130" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
+正式的单一隐藏层的MLP可以表现为：<img width="200" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="200" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
 
 向量<img width="130" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="130" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="130" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="130" align="center" src="../../images/323.jpg" />。
 
@@ -41,6 +41,6 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 
 训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="130" align="center" src="../../images/325.jpg" />。
 
-梯度<img width="130" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
+梯度<img width="70" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
 
 从逻辑回归到多层感知机我们将聚焦单隐藏层的多层感知机。 我们从构建一个单隐藏层的类开始。之后只要在此基础之上加一个逻辑回归层就构建了MLP。

From 68d58959a19f919d96beabf14e01591b57005e9e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:45:52 +0800
Subject: [PATCH 0917/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 63f99ecb..389c4c70 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -29,17 +29,17 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 </p>
 
 
-正式的单一隐藏层的MLP可以表现为：<img width="200" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="200" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
+正式的单一隐藏层的MLP可以表现为：<img width="100" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="300" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
 
-向量<img width="130" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="130" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="130" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="130" align="center" src="../../images/323.jpg" />。
+向量<img width="300" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="300" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="300" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
 
 这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
 
-输出向量通过以下公式得到<img width="130" align="center" src="../../images/324.jpg" />。
+输出向量通过以下公式得到<img width="300" align="center" src="../../images/324.jpg" />。
 
 我们此前在使用逻辑回归区分MNIST数字时提到过这一公式。如前，在多类区分中，通过使用softmax作为G的函数，可以获得类成员的概率。
 
-训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="130" align="center" src="../../images/325.jpg" />。
+训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="200" align="center" src="../../images/325.jpg" />。
 
 梯度<img width="70" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
 

From 0bd9cbb981a06e11d71ec2cb0d87c2e54890d60a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:46:29 +0800
Subject: [PATCH 0918/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 389c4c70..16e9bbd8 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -31,7 +31,7 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 
 正式的单一隐藏层的MLP可以表现为：<img width="100" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="300" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
 
-向量<img width="300" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="300" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="300" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
+向量<img width="260" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="200" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="260" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
 
 这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
 

From f4de0b67789b935f95b8128259086d1f03b91f66 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:47:30 +0800
Subject: [PATCH 0919/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 16e9bbd8..1630ac19 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -31,11 +31,11 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 
 正式的单一隐藏层的MLP可以表现为：<img width="100" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="300" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
 
-向量<img width="260" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="200" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="260" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
+向量<img width="260" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="160" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="260" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
 
 这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
 
-输出向量通过以下公式得到<img width="300" align="center" src="../../images/324.jpg" />。
+输出向量通过以下公式得到<img width="200" align="center" src="../../images/324.jpg" />。
 
 我们此前在使用逻辑回归区分MNIST数字时提到过这一公式。如前，在多类区分中，通过使用softmax作为G的函数，可以获得类成员的概率。
 

From f7663db62c0f46cfae6dd345fdf4a7fff859cb0b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:49:36 +0800
Subject: [PATCH 0920/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 1630ac19..6ccbbf76 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -44,3 +44,36 @@ MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的
 梯度<img width="70" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
 
 从逻辑回归到多层感知机我们将聚焦单隐藏层的多层感知机。 我们从构建一个单隐藏层的类开始。之后只要在此基础之上加一个逻辑回归层就构建了MLP。
+
+```python
+class HiddenLayer(object):  
+    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
+                 activation=T.tanh):  
+        """ 
+        Typical hidden layer of a MLP: units are fully-connected and have 
+        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
+        and the bias vector b is of shape (n_out,). 
+ 
+        NOTE : The nonlinearity used here is tanh 
+ 
+        Hidden unit activation is given by: tanh(dot(input,W) + b) 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.dmatrix 
+        :param input: a symbolic tensor of shape (n_examples, n_in) 
+ 
+        :type n_in: int 
+        :param n_in: dimensionality of input 
+ 
+        :type n_out: int 
+        :param n_out: number of hidden units 
+ 
+        :type activation: theano.Op or function 
+        :param activation: Non linearity to be applied in the hidden 
+                           layer 
+        """  
+        self.input = input  
+```
+隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。

From c159f0c51e4a5298d10fb38f02d3b20a2c31f451 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 9 May 2018 23:49:59 +0800
Subject: [PATCH 0921/1406] change page of ANN

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From 0b116e41367c01683c7f3d10d4b597bbdc6ccdf7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:50:47 +0800
Subject: [PATCH 0922/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 6ccbbf76..8c4cff41 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -77,3 +77,10 @@ class HiddenLayer(object):
         self.input = input  
 ```
 隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。
+
+
+对于tanh函数，区间在<img width="70" align="center" src="../../images/327.jpg" />
+
+对于sigmoid函数，区间在<img width="70" align="center" src="../../images/328.jpg" />
+
+这种初始化方式保证了在训练早期，每一个神经元在它的激活函数内操作，信息可以便利的向上（输入到输出）或反向（输出到输入）传播。

From 2ded18314d8b1d98856416149d733963ae4cc033 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:51:07 +0800
Subject: [PATCH 0923/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 8c4cff41..71afd97d 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -79,8 +79,8 @@ class HiddenLayer(object):
 隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。
 
 
-对于tanh函数，区间在<img width="70" align="center" src="../../images/327.jpg" />
+对于tanh函数，区间在<img width="270" align="center" src="../../images/327.jpg" />
 
-对于sigmoid函数，区间在<img width="70" align="center" src="../../images/328.jpg" />
+对于sigmoid函数，区间在<img width="270" align="center" src="../../images/328.jpg" />
 
 这种初始化方式保证了在训练早期，每一个神经元在它的激活函数内操作，信息可以便利的向上（输入到输出）或反向（输出到输入）传播。

From 20afe147434789ce07eda3511a72a1c36602688a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:51:25 +0800
Subject: [PATCH 0924/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 71afd97d..e81dc6c8 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -78,7 +78,6 @@ class HiddenLayer(object):
 ```
 隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。
 
-
 对于tanh函数，区间在<img width="270" align="center" src="../../images/327.jpg" />
 
 对于sigmoid函数，区间在<img width="270" align="center" src="../../images/328.jpg" />

From 3ad7114a0f66ad3b0d513e71114a159871277caf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 9 May 2018 23:52:41 +0800
Subject: [PATCH 0925/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 416 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 416 insertions(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index e81dc6c8..5d0bc2c4 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -83,3 +83,419 @@ class HiddenLayer(object):
 对于sigmoid函数，区间在<img width="270" align="center" src="../../images/328.jpg" />
 
 这种初始化方式保证了在训练早期，每一个神经元在它的激活函数内操作，信息可以便利的向上（输入到输出）或反向（输出到输入）传播。
+
+#### 应用示例
+
+```python
+""" 
+This tutorial introduces the multilayer perceptron using Theano. 
+ 
+ A multilayer perceptron is a logistic regressor where 
+instead of feeding the input to the logistic regression you insert a 
+intermediate layer, called the hidden layer, that has a nonlinear 
+activation function (usually tanh or sigmoid) . One can use many such 
+hidden layers making the architecture deep. The tutorial will also tackle 
+the problem of MNIST digit classification. 
+ 
+.. math:: 
+ 
+    f(x) = G( b^{(2)} + W^{(2)}( s( b^{(1)} + W^{(1)} x))), 
+ 
+References: 
+ 
+    - textbooks: "Pattern Recognition and Machine Learning" - 
+                 Christopher M. Bishop, section 5 
+ 
+"""  
+  
+from __future__ import print_function  
+  
+__docformat__ = 'restructedtext en'  
+  
+  
+import os  
+import sys  
+import timeit  
+  
+import numpy  
+  
+import theano  
+import theano.tensor as T  
+  
+  
+from logistic_sgd import LogisticRegression, load_data  
+  
+  
+# start-snippet-1  
+class HiddenLayer(object):  
+    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
+                 activation=T.tanh):  
+        """ 
+        Typical hidden layer of a MLP: units are fully-connected and have 
+        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
+        and the bias vector b is of shape (n_out,). 
+ 
+        NOTE : The nonlinearity used here is tanh 
+ 
+        Hidden unit activation is given by: tanh(dot(input,W) + b) 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.dmatrix 
+        :param input: a symbolic tensor of shape (n_examples, n_in) 
+ 
+        :type n_in: int 
+        :param n_in: dimensionality of input 
+ 
+        :type n_out: int 
+        :param n_out: number of hidden units 
+ 
+        :type activation: theano.Op or function 
+        :param activation: Non linearity to be applied in the hidden 
+                           layer 
+        """  
+        self.input = input  
+        # end-snippet-1  
+  
+        # `W` is initialized with `W_values` which is uniformely sampled  
+        # from sqrt(-6./(n_in+n_hidden)) and sqrt(6./(n_in+n_hidden))  
+        # for tanh activation function  
+        # the output of uniform if converted using asarray to dtype  
+        # theano.config.floatX so that the code is runable on GPU  
+        # Note : optimal initialization of weights is dependent on the  
+        #        activation function used (among other things).  
+        #        For example, results presented in [Xavier10] suggest that you  
+        #        should use 4 times larger initial weights for sigmoid  
+        #        compared to tanh  
+        #        We have no info for other function, so we use the same as  
+        #        tanh.  
+        if W is None:  
+            W_values = numpy.asarray(  
+                rng.uniform(  
+                    low=-numpy.sqrt(6. / (n_in + n_out)),  
+                    high=numpy.sqrt(6. / (n_in + n_out)),  
+                    size=(n_in, n_out)  
+                ),  
+                dtype=theano.config.floatX  
+            )  
+            if activation == theano.tensor.nnet.sigmoid:  
+                W_values *= 4  
+  
+            W = theano.shared(value=W_values, name='W', borrow=True)  
+  
+        if b is None:  
+            b_values = numpy.zeros((n_out,), dtype=theano.config.floatX)  
+            b = theano.shared(value=b_values, name='b', borrow=True)  
+  
+        self.W = W  
+        self.b = b  
+  
+        lin_output = T.dot(input, self.W) + self.b  
+        self.output = (  
+            lin_output if activation is None  
+            else activation(lin_output)  
+        )  
+        # parameters of the model  
+        self.params = [self.W, self.b]  
+  
+  
+# start-snippet-2  
+class MLP(object):  
+    """Multi-Layer Perceptron Class 
+ 
+    A multilayer perceptron is a feedforward artificial neural network model 
+    that has one layer or more of hidden units and nonlinear activations. 
+    Intermediate layers usually have as activation function tanh or the 
+    sigmoid function (defined here by a ``HiddenLayer`` class)  while the 
+    top layer is a softmax layer (defined here by a ``LogisticRegression`` 
+    class). 
+    """  
+  
+    def __init__(self, rng, input, n_in, n_hidden, n_out):  
+        """Initialize the parameters for the multilayer perceptron 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.TensorType 
+        :param input: symbolic variable that describes the input of the 
+        architecture (one minibatch) 
+ 
+        :type n_in: int 
+        :param n_in: number of input units, the dimension of the space in 
+        which the datapoints lie 
+ 
+        :type n_hidden: int 
+        :param n_hidden: number of hidden units 
+ 
+        :type n_out: int 
+        :param n_out: number of output units, the dimension of the space in 
+        which the labels lie 
+ 
+        """  
+  
+        # Since we are dealing with a one hidden layer MLP, this will translate  
+        # into a HiddenLayer with a tanh activation function connected to the  
+        # LogisticRegression layer; the activation function can be replaced by  
+        # sigmoid or any other nonlinear function  
+        self.hiddenLayer = HiddenLayer(  
+            rng=rng,  
+            input=input,  
+            n_in=n_in,  
+            n_out=n_hidden,  
+            activation=T.tanh  
+        )  
+  
+        # The logistic regression layer gets as input the hidden units  
+        # of the hidden layer  
+        self.logRegressionLayer = LogisticRegression(  
+            input=self.hiddenLayer.output,  
+            n_in=n_hidden,  
+            n_out=n_out  
+        )  
+        # end-snippet-2 start-snippet-3  
+        # L1 norm ; one regularization option is to enforce L1 norm to  
+        # be small  
+        self.L1 = (  
+            abs(self.hiddenLayer.W).sum()  
+            + abs(self.logRegressionLayer.W).sum()  
+        )  
+  
+        # square of L2 norm ; one regularization option is to enforce  
+        # square of L2 norm to be small  
+        self.L2_sqr = (  
+            (self.hiddenLayer.W ** 2).sum()  
+            + (self.logRegressionLayer.W ** 2).sum()  
+        )  
+  
+        # negative log likelihood of the MLP is given by the negative  
+        # log likelihood of the output of the model, computed in the  
+        # logistic regression layer  
+        self.negative_log_likelihood = (  
+            self.logRegressionLayer.negative_log_likelihood  
+        )  
+        # same holds for the function computing the number of errors  
+        self.errors = self.logRegressionLayer.errors  
+  
+        # the parameters of the model are the parameters of the two layer it is  
+        # made out of  
+        self.params = self.hiddenLayer.params + self.logRegressionLayer.params  
+        # end-snippet-3  
+  
+        # keep track of model input  
+        self.input = input  
+  
+  
+def test_mlp(learning_rate=0.01, L1_reg=0.00, L2_reg=0.0001, n_epochs=1000,  
+             dataset='mnist.pkl.gz', batch_size=20, n_hidden=500):  
+    """ 
+    Demonstrate stochastic gradient descent optimization for a multilayer 
+    perceptron 
+ 
+    This is demonstrated on MNIST. 
+ 
+    :type learning_rate: float 
+    :param learning_rate: learning rate used (factor for the stochastic 
+    gradient 
+ 
+    :type L1_reg: float 
+    :param L1_reg: L1-norm's weight when added to the cost (see 
+    regularization) 
+ 
+    :type L2_reg: float 
+    :param L2_reg: L2-norm's weight when added to the cost (see 
+    regularization) 
+ 
+    :type n_epochs: int 
+    :param n_epochs: maximal number of epochs to run the optimizer 
+ 
+    :type dataset: string 
+    :param dataset: the path of the MNIST dataset file from 
+                 http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz 
+ 
+ 
+   """  
+    datasets = load_data(dataset)  
+  
+    train_set_x, train_set_y = datasets[0]  
+    valid_set_x, valid_set_y = datasets[1]  
+    test_set_x, test_set_y = datasets[2]  
+  
+    # compute number of minibatches for training, validation and testing  
+    n_train_batches = train_set_x.get_value(borrow=True).shape[0] // batch_size  
+    n_valid_batches = valid_set_x.get_value(borrow=True).shape[0] // batch_size  
+    n_test_batches = test_set_x.get_value(borrow=True).shape[0] // batch_size  
+  
+    ######################  
+    # BUILD ACTUAL MODEL #  
+    ######################  
+    print('... building the model')  
+  
+    # allocate symbolic variables for the data  
+    index = T.lscalar()  # index to a [mini]batch  
+    x = T.matrix('x')  # the data is presented as rasterized images  
+    y = T.ivector('y')  # the labels are presented as 1D vector of  
+                        # [int] labels  
+  
+    rng = numpy.random.RandomState(1234)  
+  
+    # construct the MLP class  
+    classifier = MLP(  
+        rng=rng,  
+        input=x,  
+        n_in=28 * 28,  
+        n_hidden=n_hidden,  
+        n_out=10  
+    )  
+  
+    # start-snippet-4  
+    # the cost we minimize during training is the negative log likelihood of  
+    # the model plus the regularization terms (L1 and L2); cost is expressed  
+    # here symbolically  
+    cost = (  
+        classifier.negative_log_likelihood(y)  
+        + L1_reg * classifier.L1  
+        + L2_reg * classifier.L2_sqr  
+    )  
+    # end-snippet-4  
+  
+    # compiling a Theano function that computes the mistakes that are made  
+    # by the model on a minibatch  
+    test_model = theano.function(  
+        inputs=[index],  
+        outputs=classifier.errors(y),  
+        givens={  
+            x: test_set_x[index * batch_size:(index + 1) * batch_size],  
+            y: test_set_y[index * batch_size:(index + 1) * batch_size]  
+        }  
+    )  
+  
+    validate_model = theano.function(  
+        inputs=[index],  
+        outputs=classifier.errors(y),  
+        givens={  
+            x: valid_set_x[index * batch_size:(index + 1) * batch_size],  
+            y: valid_set_y[index * batch_size:(index + 1) * batch_size]  
+        }  
+    )  
+  
+    # start-snippet-5  
+    # compute the gradient of cost with respect to theta (sorted in params)  
+    # the resulting gradients will be stored in a list gparams  
+    gparams = [T.grad(cost, param) for param in classifier.params]  
+  
+    # specify how to update the parameters of the model as a list of  
+    # (variable, update expression) pairs  
+  
+    # given two lists of the same length, A = [a1, a2, a3, a4] and  
+    # B = [b1, b2, b3, b4], zip generates a list C of same size, where each  
+    # element is a pair formed from the two lists :  
+    #    C = [(a1, b1), (a2, b2), (a3, b3), (a4, b4)]  
+    updates = [  
+        (param, param - learning_rate * gparam)  
+        for param, gparam in zip(classifier.params, gparams)  
+    ]  
+  
+    # compiling a Theano function `train_model` that returns the cost, but  
+    # in the same time updates the parameter of the model based on the rules  
+    # defined in `updates`  
+    train_model = theano.function(  
+        inputs=[index],  
+        outputs=cost,  
+        updates=updates,  
+        givens={  
+            x: train_set_x[index * batch_size: (index + 1) * batch_size],  
+            y: train_set_y[index * batch_size: (index + 1) * batch_size]  
+        }  
+    )  
+    # end-snippet-5  
+  
+    ###############  
+    # TRAIN MODEL #  
+    ###############  
+    print('... training')  
+  
+    # early-stopping parameters  
+    patience = 10000  # look as this many examples regardless  
+    patience_increase = 2  # wait this much longer when a new best is  
+                           # found  
+    improvement_threshold = 0.995  # a relative improvement of this much is  
+                                   # considered significant  
+    validation_frequency = min(n_train_batches, patience // 2)  
+                                  # go through this many  
+                                  # minibatche before checking the network  
+                                  # on the validation set; in this case we  
+                                  # check every epoch  
+  
+    best_validation_loss = numpy.inf  
+    best_iter = 0  
+    test_score = 0.  
+    start_time = timeit.default_timer()  
+  
+    epoch = 0  
+    done_looping = False  
+  
+    while (epoch < n_epochs) and (not done_looping):  
+        epoch = epoch + 1  
+        for minibatch_index in range(n_train_batches):  
+  
+            minibatch_avg_cost = train_model(minibatch_index)  
+            # iteration number  
+            iter = (epoch - 1) * n_train_batches + minibatch_index  
+  
+            if (iter + 1) % validation_frequency == 0:  
+                # compute zero-one loss on validation set  
+                validation_losses = [validate_model(i) for i  
+                                     in range(n_valid_batches)]  
+                this_validation_loss = numpy.mean(validation_losses)  
+  
+                print(  
+                    'epoch %i, minibatch %i/%i, validation error %f %%' %  
+                    (  
+                        epoch,  
+                        minibatch_index + 1,  
+                        n_train_batches,  
+                        this_validation_loss * 100.  
+                    )  
+                )  
+  
+                # if we got the best validation score until now  
+                if this_validation_loss < best_validation_loss:  
+                    #improve patience if loss improvement is good enough  
+                    if (  
+                        this_validation_loss < best_validation_loss *  
+                        improvement_threshold  
+                    ):  
+                        patience = max(patience, iter * patience_increase)  
+  
+                    best_validation_loss = this_validation_loss  
+                    best_iter = iter  
+  
+                    # test it on the test set  
+                    test_losses = [test_model(i) for i  
+                                   in range(n_test_batches)]  
+                    test_score = numpy.mean(test_losses)  
+  
+                    print(('     epoch %i, minibatch %i/%i, test error of '  
+                           'best model %f %%') %  
+                          (epoch, minibatch_index + 1, n_train_batches,  
+                           test_score * 100.))  
+  
+            if patience <= iter:  
+                done_looping = True  
+                break  
+  
+    end_time = timeit.default_timer()  
+    print(('Optimization complete. Best validation score of %f %% '  
+           'obtained at iteration %i, with test performance %f %%') %  
+          (best_validation_loss * 100., best_iter + 1, test_score * 100.))  
+    print(('The code for file ' +  
+           os.path.split(__file__)[1] +  
+           ' ran for %.2fm' % ((end_time - start_time) / 60.)), file=sys.stderr)  
+  
+  
+if __name__ == '__main__':  
+    test_mlp()  
+
+```

From 84a9c94dcc61a53056d3fd1114f78355f34df5a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 10 May 2018 08:55:30 +0800
Subject: [PATCH 0926/1406] Update ANN.0.5.md

---
 assets/src/ANN/ANN.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.5.md b/assets/src/ANN/ANN.0.5.md
index 5d0bc2c4..af25f655 100644
--- a/assets/src/ANN/ANN.0.5.md
+++ b/assets/src/ANN/ANN.0.5.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 多层感知器(Multilayer Perceptron)
+
 多层感知器（Multilayer Perceptron,缩写MLP）是一种前向结构的人工神经网络，映射一组输入向量到一组输出向量。MLP可以被看作是一个有向图，由多个的节点层所组成，每一层都全连接到下一层。除了输入节点，每个节点都是一个带有非线性激活函数的神经元（或称处理单元）。一种被称为反向传播算法的监督学习方法常被用来训练MLP。MLP是感知器的推广，克服了感知器不能对线性不可分数据进行识别的弱点
 
 若每个神经元的激活函数都是线性函数，那么，任意层数的MLP都可被约简成一个等价的单层感知器。

From 5ece91bfb44a677e3292a0608808e095bf1c37b8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 10 May 2018 10:55:38 +0800
Subject: [PATCH 0927/1406] Update BP.md

---
 assets/src/BP/BP.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BP/BP.md b/assets/src/BP/BP.md
index 54e22b2b..9134f049 100644
--- a/assets/src/BP/BP.md
+++ b/assets/src/BP/BP.md
@@ -12,7 +12,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/1.jpg" />
 </p>
 
-
 人工神经网络中，神经元处理单元可表示不同的对象，例如特征、字母、概念，或者一些有意义的抽象模式。网络中处理单元的类型分为三类：输入单元、输出单元和隐单元。输入单元接受外部世界的信号与数据；输出单元实现系统处理结果的输出；隐单元是处在输入和输出单元之间，不能由系统外部观察的单元。神经元间的连接权值反映了单元间的连接强度，信息的表示和处理体现在网络处理单元的连接关系中。
 
 #### 算法描述

From 34d0ec77adcb850d0406cc4aaa2613128f5af42c Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 10 May 2018 11:03:39 +0800
Subject: [PATCH 0928/1406] change page of ANN

---
 assets/src/ANN/ANN.0.6.md | 502 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 502 insertions(+)
 create mode 100644 assets/src/ANN/ANN.0.6.md

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
new file mode 100644
index 00000000..af25f655
--- /dev/null
+++ b/assets/src/ANN/ANN.0.6.md
@@ -0,0 +1,502 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 多层感知器(Multilayer Perceptron)
+
+多层感知器（Multilayer Perceptron,缩写MLP）是一种前向结构的人工神经网络，映射一组输入向量到一组输出向量。MLP可以被看作是一个有向图，由多个的节点层所组成，每一层都全连接到下一层。除了输入节点，每个节点都是一个带有非线性激活函数的神经元（或称处理单元）。一种被称为反向传播算法的监督学习方法常被用来训练MLP。MLP是感知器的推广，克服了感知器不能对线性不可分数据进行识别的弱点
+
+若每个神经元的激活函数都是线性函数，那么，任意层数的MLP都可被约简成一个等价的单层感知器。
+
+实际上，MLP本身可以使用任何形式的激活函数，譬如阶梯函数或逻辑乙形函数（logistic sigmoid function），但为了使用反向传播算法进行有效学习，激活函数必须限制为可微函数。由于具有良好可微性，很多S函数，尤其是双曲正切函数（Hyperbolic tangent）及逻辑函数，被采用为激活函数。
+
+通常MLP用来进行学习的反向传播算法，在模式识别的领域中算是标准监督学习算法，并在计算神经学及并行分布式处理领域中，持续成为被研究的课题。MLP已被证明是一种通用的函数近似方法，可以被用来拟合复杂的函数，或解决分类问题。
+
+MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的应用场景，譬如语音识别、图像识别、机器翻译等等，但自90年代以来，MLP遇到来自更为简单的支持向量机的强劲竞争。近来，由于深度学习的成功，MLP又重新得到了关注。
+
+通常一个单一隐藏层的多层感知机（或人工神经网络—ANN）可以用图表现为：
+
+<p align="center">
+<img width="300" align="center" src="../../images/317.jpg" />
+</p>
+
+
+正式的单一隐藏层的MLP可以表现为：<img width="100" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="300" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
+
+向量<img width="260" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="160" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="260" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
+
+这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
+
+输出向量通过以下公式得到<img width="200" align="center" src="../../images/324.jpg" />。
+
+我们此前在使用逻辑回归区分MNIST数字时提到过这一公式。如前，在多类区分中，通过使用softmax作为G的函数，可以获得类成员的概率。
+
+训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="200" align="center" src="../../images/325.jpg" />。
+
+梯度<img width="70" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
+
+从逻辑回归到多层感知机我们将聚焦单隐藏层的多层感知机。 我们从构建一个单隐藏层的类开始。之后只要在此基础之上加一个逻辑回归层就构建了MLP。
+
+```python
+class HiddenLayer(object):  
+    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
+                 activation=T.tanh):  
+        """ 
+        Typical hidden layer of a MLP: units are fully-connected and have 
+        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
+        and the bias vector b is of shape (n_out,). 
+ 
+        NOTE : The nonlinearity used here is tanh 
+ 
+        Hidden unit activation is given by: tanh(dot(input,W) + b) 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.dmatrix 
+        :param input: a symbolic tensor of shape (n_examples, n_in) 
+ 
+        :type n_in: int 
+        :param n_in: dimensionality of input 
+ 
+        :type n_out: int 
+        :param n_out: number of hidden units 
+ 
+        :type activation: theano.Op or function 
+        :param activation: Non linearity to be applied in the hidden 
+                           layer 
+        """  
+        self.input = input  
+```
+隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。
+
+对于tanh函数，区间在<img width="270" align="center" src="../../images/327.jpg" />
+
+对于sigmoid函数，区间在<img width="270" align="center" src="../../images/328.jpg" />
+
+这种初始化方式保证了在训练早期，每一个神经元在它的激活函数内操作，信息可以便利的向上（输入到输出）或反向（输出到输入）传播。
+
+#### 应用示例
+
+```python
+""" 
+This tutorial introduces the multilayer perceptron using Theano. 
+ 
+ A multilayer perceptron is a logistic regressor where 
+instead of feeding the input to the logistic regression you insert a 
+intermediate layer, called the hidden layer, that has a nonlinear 
+activation function (usually tanh or sigmoid) . One can use many such 
+hidden layers making the architecture deep. The tutorial will also tackle 
+the problem of MNIST digit classification. 
+ 
+.. math:: 
+ 
+    f(x) = G( b^{(2)} + W^{(2)}( s( b^{(1)} + W^{(1)} x))), 
+ 
+References: 
+ 
+    - textbooks: "Pattern Recognition and Machine Learning" - 
+                 Christopher M. Bishop, section 5 
+ 
+"""  
+  
+from __future__ import print_function  
+  
+__docformat__ = 'restructedtext en'  
+  
+  
+import os  
+import sys  
+import timeit  
+  
+import numpy  
+  
+import theano  
+import theano.tensor as T  
+  
+  
+from logistic_sgd import LogisticRegression, load_data  
+  
+  
+# start-snippet-1  
+class HiddenLayer(object):  
+    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
+                 activation=T.tanh):  
+        """ 
+        Typical hidden layer of a MLP: units are fully-connected and have 
+        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
+        and the bias vector b is of shape (n_out,). 
+ 
+        NOTE : The nonlinearity used here is tanh 
+ 
+        Hidden unit activation is given by: tanh(dot(input,W) + b) 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.dmatrix 
+        :param input: a symbolic tensor of shape (n_examples, n_in) 
+ 
+        :type n_in: int 
+        :param n_in: dimensionality of input 
+ 
+        :type n_out: int 
+        :param n_out: number of hidden units 
+ 
+        :type activation: theano.Op or function 
+        :param activation: Non linearity to be applied in the hidden 
+                           layer 
+        """  
+        self.input = input  
+        # end-snippet-1  
+  
+        # `W` is initialized with `W_values` which is uniformely sampled  
+        # from sqrt(-6./(n_in+n_hidden)) and sqrt(6./(n_in+n_hidden))  
+        # for tanh activation function  
+        # the output of uniform if converted using asarray to dtype  
+        # theano.config.floatX so that the code is runable on GPU  
+        # Note : optimal initialization of weights is dependent on the  
+        #        activation function used (among other things).  
+        #        For example, results presented in [Xavier10] suggest that you  
+        #        should use 4 times larger initial weights for sigmoid  
+        #        compared to tanh  
+        #        We have no info for other function, so we use the same as  
+        #        tanh.  
+        if W is None:  
+            W_values = numpy.asarray(  
+                rng.uniform(  
+                    low=-numpy.sqrt(6. / (n_in + n_out)),  
+                    high=numpy.sqrt(6. / (n_in + n_out)),  
+                    size=(n_in, n_out)  
+                ),  
+                dtype=theano.config.floatX  
+            )  
+            if activation == theano.tensor.nnet.sigmoid:  
+                W_values *= 4  
+  
+            W = theano.shared(value=W_values, name='W', borrow=True)  
+  
+        if b is None:  
+            b_values = numpy.zeros((n_out,), dtype=theano.config.floatX)  
+            b = theano.shared(value=b_values, name='b', borrow=True)  
+  
+        self.W = W  
+        self.b = b  
+  
+        lin_output = T.dot(input, self.W) + self.b  
+        self.output = (  
+            lin_output if activation is None  
+            else activation(lin_output)  
+        )  
+        # parameters of the model  
+        self.params = [self.W, self.b]  
+  
+  
+# start-snippet-2  
+class MLP(object):  
+    """Multi-Layer Perceptron Class 
+ 
+    A multilayer perceptron is a feedforward artificial neural network model 
+    that has one layer or more of hidden units and nonlinear activations. 
+    Intermediate layers usually have as activation function tanh or the 
+    sigmoid function (defined here by a ``HiddenLayer`` class)  while the 
+    top layer is a softmax layer (defined here by a ``LogisticRegression`` 
+    class). 
+    """  
+  
+    def __init__(self, rng, input, n_in, n_hidden, n_out):  
+        """Initialize the parameters for the multilayer perceptron 
+ 
+        :type rng: numpy.random.RandomState 
+        :param rng: a random number generator used to initialize weights 
+ 
+        :type input: theano.tensor.TensorType 
+        :param input: symbolic variable that describes the input of the 
+        architecture (one minibatch) 
+ 
+        :type n_in: int 
+        :param n_in: number of input units, the dimension of the space in 
+        which the datapoints lie 
+ 
+        :type n_hidden: int 
+        :param n_hidden: number of hidden units 
+ 
+        :type n_out: int 
+        :param n_out: number of output units, the dimension of the space in 
+        which the labels lie 
+ 
+        """  
+  
+        # Since we are dealing with a one hidden layer MLP, this will translate  
+        # into a HiddenLayer with a tanh activation function connected to the  
+        # LogisticRegression layer; the activation function can be replaced by  
+        # sigmoid or any other nonlinear function  
+        self.hiddenLayer = HiddenLayer(  
+            rng=rng,  
+            input=input,  
+            n_in=n_in,  
+            n_out=n_hidden,  
+            activation=T.tanh  
+        )  
+  
+        # The logistic regression layer gets as input the hidden units  
+        # of the hidden layer  
+        self.logRegressionLayer = LogisticRegression(  
+            input=self.hiddenLayer.output,  
+            n_in=n_hidden,  
+            n_out=n_out  
+        )  
+        # end-snippet-2 start-snippet-3  
+        # L1 norm ; one regularization option is to enforce L1 norm to  
+        # be small  
+        self.L1 = (  
+            abs(self.hiddenLayer.W).sum()  
+            + abs(self.logRegressionLayer.W).sum()  
+        )  
+  
+        # square of L2 norm ; one regularization option is to enforce  
+        # square of L2 norm to be small  
+        self.L2_sqr = (  
+            (self.hiddenLayer.W ** 2).sum()  
+            + (self.logRegressionLayer.W ** 2).sum()  
+        )  
+  
+        # negative log likelihood of the MLP is given by the negative  
+        # log likelihood of the output of the model, computed in the  
+        # logistic regression layer  
+        self.negative_log_likelihood = (  
+            self.logRegressionLayer.negative_log_likelihood  
+        )  
+        # same holds for the function computing the number of errors  
+        self.errors = self.logRegressionLayer.errors  
+  
+        # the parameters of the model are the parameters of the two layer it is  
+        # made out of  
+        self.params = self.hiddenLayer.params + self.logRegressionLayer.params  
+        # end-snippet-3  
+  
+        # keep track of model input  
+        self.input = input  
+  
+  
+def test_mlp(learning_rate=0.01, L1_reg=0.00, L2_reg=0.0001, n_epochs=1000,  
+             dataset='mnist.pkl.gz', batch_size=20, n_hidden=500):  
+    """ 
+    Demonstrate stochastic gradient descent optimization for a multilayer 
+    perceptron 
+ 
+    This is demonstrated on MNIST. 
+ 
+    :type learning_rate: float 
+    :param learning_rate: learning rate used (factor for the stochastic 
+    gradient 
+ 
+    :type L1_reg: float 
+    :param L1_reg: L1-norm's weight when added to the cost (see 
+    regularization) 
+ 
+    :type L2_reg: float 
+    :param L2_reg: L2-norm's weight when added to the cost (see 
+    regularization) 
+ 
+    :type n_epochs: int 
+    :param n_epochs: maximal number of epochs to run the optimizer 
+ 
+    :type dataset: string 
+    :param dataset: the path of the MNIST dataset file from 
+                 http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz 
+ 
+ 
+   """  
+    datasets = load_data(dataset)  
+  
+    train_set_x, train_set_y = datasets[0]  
+    valid_set_x, valid_set_y = datasets[1]  
+    test_set_x, test_set_y = datasets[2]  
+  
+    # compute number of minibatches for training, validation and testing  
+    n_train_batches = train_set_x.get_value(borrow=True).shape[0] // batch_size  
+    n_valid_batches = valid_set_x.get_value(borrow=True).shape[0] // batch_size  
+    n_test_batches = test_set_x.get_value(borrow=True).shape[0] // batch_size  
+  
+    ######################  
+    # BUILD ACTUAL MODEL #  
+    ######################  
+    print('... building the model')  
+  
+    # allocate symbolic variables for the data  
+    index = T.lscalar()  # index to a [mini]batch  
+    x = T.matrix('x')  # the data is presented as rasterized images  
+    y = T.ivector('y')  # the labels are presented as 1D vector of  
+                        # [int] labels  
+  
+    rng = numpy.random.RandomState(1234)  
+  
+    # construct the MLP class  
+    classifier = MLP(  
+        rng=rng,  
+        input=x,  
+        n_in=28 * 28,  
+        n_hidden=n_hidden,  
+        n_out=10  
+    )  
+  
+    # start-snippet-4  
+    # the cost we minimize during training is the negative log likelihood of  
+    # the model plus the regularization terms (L1 and L2); cost is expressed  
+    # here symbolically  
+    cost = (  
+        classifier.negative_log_likelihood(y)  
+        + L1_reg * classifier.L1  
+        + L2_reg * classifier.L2_sqr  
+    )  
+    # end-snippet-4  
+  
+    # compiling a Theano function that computes the mistakes that are made  
+    # by the model on a minibatch  
+    test_model = theano.function(  
+        inputs=[index],  
+        outputs=classifier.errors(y),  
+        givens={  
+            x: test_set_x[index * batch_size:(index + 1) * batch_size],  
+            y: test_set_y[index * batch_size:(index + 1) * batch_size]  
+        }  
+    )  
+  
+    validate_model = theano.function(  
+        inputs=[index],  
+        outputs=classifier.errors(y),  
+        givens={  
+            x: valid_set_x[index * batch_size:(index + 1) * batch_size],  
+            y: valid_set_y[index * batch_size:(index + 1) * batch_size]  
+        }  
+    )  
+  
+    # start-snippet-5  
+    # compute the gradient of cost with respect to theta (sorted in params)  
+    # the resulting gradients will be stored in a list gparams  
+    gparams = [T.grad(cost, param) for param in classifier.params]  
+  
+    # specify how to update the parameters of the model as a list of  
+    # (variable, update expression) pairs  
+  
+    # given two lists of the same length, A = [a1, a2, a3, a4] and  
+    # B = [b1, b2, b3, b4], zip generates a list C of same size, where each  
+    # element is a pair formed from the two lists :  
+    #    C = [(a1, b1), (a2, b2), (a3, b3), (a4, b4)]  
+    updates = [  
+        (param, param - learning_rate * gparam)  
+        for param, gparam in zip(classifier.params, gparams)  
+    ]  
+  
+    # compiling a Theano function `train_model` that returns the cost, but  
+    # in the same time updates the parameter of the model based on the rules  
+    # defined in `updates`  
+    train_model = theano.function(  
+        inputs=[index],  
+        outputs=cost,  
+        updates=updates,  
+        givens={  
+            x: train_set_x[index * batch_size: (index + 1) * batch_size],  
+            y: train_set_y[index * batch_size: (index + 1) * batch_size]  
+        }  
+    )  
+    # end-snippet-5  
+  
+    ###############  
+    # TRAIN MODEL #  
+    ###############  
+    print('... training')  
+  
+    # early-stopping parameters  
+    patience = 10000  # look as this many examples regardless  
+    patience_increase = 2  # wait this much longer when a new best is  
+                           # found  
+    improvement_threshold = 0.995  # a relative improvement of this much is  
+                                   # considered significant  
+    validation_frequency = min(n_train_batches, patience // 2)  
+                                  # go through this many  
+                                  # minibatche before checking the network  
+                                  # on the validation set; in this case we  
+                                  # check every epoch  
+  
+    best_validation_loss = numpy.inf  
+    best_iter = 0  
+    test_score = 0.  
+    start_time = timeit.default_timer()  
+  
+    epoch = 0  
+    done_looping = False  
+  
+    while (epoch < n_epochs) and (not done_looping):  
+        epoch = epoch + 1  
+        for minibatch_index in range(n_train_batches):  
+  
+            minibatch_avg_cost = train_model(minibatch_index)  
+            # iteration number  
+            iter = (epoch - 1) * n_train_batches + minibatch_index  
+  
+            if (iter + 1) % validation_frequency == 0:  
+                # compute zero-one loss on validation set  
+                validation_losses = [validate_model(i) for i  
+                                     in range(n_valid_batches)]  
+                this_validation_loss = numpy.mean(validation_losses)  
+  
+                print(  
+                    'epoch %i, minibatch %i/%i, validation error %f %%' %  
+                    (  
+                        epoch,  
+                        minibatch_index + 1,  
+                        n_train_batches,  
+                        this_validation_loss * 100.  
+                    )  
+                )  
+  
+                # if we got the best validation score until now  
+                if this_validation_loss < best_validation_loss:  
+                    #improve patience if loss improvement is good enough  
+                    if (  
+                        this_validation_loss < best_validation_loss *  
+                        improvement_threshold  
+                    ):  
+                        patience = max(patience, iter * patience_increase)  
+  
+                    best_validation_loss = this_validation_loss  
+                    best_iter = iter  
+  
+                    # test it on the test set  
+                    test_losses = [test_model(i) for i  
+                                   in range(n_test_batches)]  
+                    test_score = numpy.mean(test_losses)  
+  
+                    print(('     epoch %i, minibatch %i/%i, test error of '  
+                           'best model %f %%') %  
+                          (epoch, minibatch_index + 1, n_train_batches,  
+                           test_score * 100.))  
+  
+            if patience <= iter:  
+                done_looping = True  
+                break  
+  
+    end_time = timeit.default_timer()  
+    print(('Optimization complete. Best validation score of %f %% '  
+           'obtained at iteration %i, with test performance %f %%') %  
+          (best_validation_loss * 100., best_iter + 1, test_score * 100.))  
+    print(('The code for file ' +  
+           os.path.split(__file__)[1] +  
+           ' ran for %.2fm' % ((end_time - start_time) / 60.)), file=sys.stderr)  
+  
+  
+if __name__ == '__main__':  
+    test_mlp()  
+
+```

From 6f781b15b0770a00571747a4409fda19fcae1373 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 10 May 2018 11:04:58 +0800
Subject: [PATCH 0929/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 38ce2969..2c6845e3 100644
--- a/README.md
+++ b/README.md
@@ -125,7 +125,7 @@
      * [反向传播(Backpropagation)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.3.md) 
      * [递归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
      * [多层感知器(Multilayer Perceptron)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.5.md) 
-     * [玻尔兹曼机(Boltzmann Machine)]() 
+     * [玻尔兹曼机(Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.6.md) 
      * [卷积神经网络(Convolutional Neural Network)]() 
      * [Hopfield网络(Hopfield Network)]() 
      * [径向基函数网络(Radial Basis Function Network)]() 

From 945bb2b9d9b2d25a658b6784791188ddbd2a51ed Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 10 May 2018 11:05:38 +0800
Subject: [PATCH 0930/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 490 +-------------------------------------
 1 file changed, 1 insertion(+), 489 deletions(-)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index af25f655..2c9cff35 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -11,492 +11,4 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
-#### 多层感知器(Multilayer Perceptron)
-
-多层感知器（Multilayer Perceptron,缩写MLP）是一种前向结构的人工神经网络，映射一组输入向量到一组输出向量。MLP可以被看作是一个有向图，由多个的节点层所组成，每一层都全连接到下一层。除了输入节点，每个节点都是一个带有非线性激活函数的神经元（或称处理单元）。一种被称为反向传播算法的监督学习方法常被用来训练MLP。MLP是感知器的推广，克服了感知器不能对线性不可分数据进行识别的弱点
-
-若每个神经元的激活函数都是线性函数，那么，任意层数的MLP都可被约简成一个等价的单层感知器。
-
-实际上，MLP本身可以使用任何形式的激活函数，譬如阶梯函数或逻辑乙形函数（logistic sigmoid function），但为了使用反向传播算法进行有效学习，激活函数必须限制为可微函数。由于具有良好可微性，很多S函数，尤其是双曲正切函数（Hyperbolic tangent）及逻辑函数，被采用为激活函数。
-
-通常MLP用来进行学习的反向传播算法，在模式识别的领域中算是标准监督学习算法，并在计算神经学及并行分布式处理领域中，持续成为被研究的课题。MLP已被证明是一种通用的函数近似方法，可以被用来拟合复杂的函数，或解决分类问题。
-
-MLP在80年代的时候曾是相当流行的机器学习方法，拥有广泛的应用场景，譬如语音识别、图像识别、机器翻译等等，但自90年代以来，MLP遇到来自更为简单的支持向量机的强劲竞争。近来，由于深度学习的成功，MLP又重新得到了关注。
-
-通常一个单一隐藏层的多层感知机（或人工神经网络—ANN）可以用图表现为：
-
-<p align="center">
-<img width="300" align="center" src="../../images/317.jpg" />
-</p>
-
-
-正式的单一隐藏层的MLP可以表现为：<img width="100" align="center" src="../../images/318.jpg" />，其中D是输入向量x的大小，L是输出向量f(x)的大小，矩阵表现为：<img width="300" align="center" src="../../images/319.jpg" />, b是偏差向量，W是权重矩阵，G和s是激活函数。
-
-向量<img width="260" align="center" src="../../images/320.jpg" />构成隐藏层。<img width="160" align="center" src="../../images/321.jpg" />是连接输入向量和隐藏层的权重矩阵。Wi代表输入单元到第i个隐藏单元的权重。一般选择tanh作为s的激活函数，使用<img width="260" align="center" src="../../images/322.jpg" />或者使用逻辑sigmoid函数，<img width="300" align="center" src="../../images/323.jpg" />。
-
-这里我们使用Tanh因为一般它训练速度更快（有时也有利于解决局部最优）。tanh和sigmoid都是标量到标量函数，但通过点积运算向量和张量自然延伸（将向量分解成元素，生成同样大小的向量）。
-
-输出向量通过以下公式得到<img width="200" align="center" src="../../images/324.jpg" />。
-
-我们此前在使用逻辑回归区分MNIST数字时提到过这一公式。如前，在多类区分中，通过使用softmax作为G的函数，可以获得类成员的概率。
-
-训练一个MLP，我们学习模型所有的参数，这里我们使用随机梯度下降和批处理。要学习的参数为：<img width="200" align="center" src="../../images/325.jpg" />。
-
-梯度<img width="70" align="center" src="../../images/326.jpg" />可以使用反向传播算法获得（连续微分的特殊形式），Theano可以自动计算这一微分过程。
-
-从逻辑回归到多层感知机我们将聚焦单隐藏层的多层感知机。 我们从构建一个单隐藏层的类开始。之后只要在此基础之上加一个逻辑回归层就构建了MLP。
-
-```python
-class HiddenLayer(object):  
-    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
-                 activation=T.tanh):  
-        """ 
-        Typical hidden layer of a MLP: units are fully-connected and have 
-        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
-        and the bias vector b is of shape (n_out,). 
- 
-        NOTE : The nonlinearity used here is tanh 
- 
-        Hidden unit activation is given by: tanh(dot(input,W) + b) 
- 
-        :type rng: numpy.random.RandomState 
-        :param rng: a random number generator used to initialize weights 
- 
-        :type input: theano.tensor.dmatrix 
-        :param input: a symbolic tensor of shape (n_examples, n_in) 
- 
-        :type n_in: int 
-        :param n_in: dimensionality of input 
- 
-        :type n_out: int 
-        :param n_out: number of hidden units 
- 
-        :type activation: theano.Op or function 
-        :param activation: Non linearity to be applied in the hidden 
-                           layer 
-        """  
-        self.input = input  
-```
-隐藏层i权重的初始值应当根据激活函数以对称间断的方式取得样本。
-
-对于tanh函数，区间在<img width="270" align="center" src="../../images/327.jpg" />
-
-对于sigmoid函数，区间在<img width="270" align="center" src="../../images/328.jpg" />
-
-这种初始化方式保证了在训练早期，每一个神经元在它的激活函数内操作，信息可以便利的向上（输入到输出）或反向（输出到输入）传播。
-
-#### 应用示例
-
-```python
-""" 
-This tutorial introduces the multilayer perceptron using Theano. 
- 
- A multilayer perceptron is a logistic regressor where 
-instead of feeding the input to the logistic regression you insert a 
-intermediate layer, called the hidden layer, that has a nonlinear 
-activation function (usually tanh or sigmoid) . One can use many such 
-hidden layers making the architecture deep. The tutorial will also tackle 
-the problem of MNIST digit classification. 
- 
-.. math:: 
- 
-    f(x) = G( b^{(2)} + W^{(2)}( s( b^{(1)} + W^{(1)} x))), 
- 
-References: 
- 
-    - textbooks: "Pattern Recognition and Machine Learning" - 
-                 Christopher M. Bishop, section 5 
- 
-"""  
-  
-from __future__ import print_function  
-  
-__docformat__ = 'restructedtext en'  
-  
-  
-import os  
-import sys  
-import timeit  
-  
-import numpy  
-  
-import theano  
-import theano.tensor as T  
-  
-  
-from logistic_sgd import LogisticRegression, load_data  
-  
-  
-# start-snippet-1  
-class HiddenLayer(object):  
-    def __init__(self, rng, input, n_in, n_out, W=None, b=None,  
-                 activation=T.tanh):  
-        """ 
-        Typical hidden layer of a MLP: units are fully-connected and have 
-        sigmoidal activation function. Weight matrix W is of shape (n_in,n_out) 
-        and the bias vector b is of shape (n_out,). 
- 
-        NOTE : The nonlinearity used here is tanh 
- 
-        Hidden unit activation is given by: tanh(dot(input,W) + b) 
- 
-        :type rng: numpy.random.RandomState 
-        :param rng: a random number generator used to initialize weights 
- 
-        :type input: theano.tensor.dmatrix 
-        :param input: a symbolic tensor of shape (n_examples, n_in) 
- 
-        :type n_in: int 
-        :param n_in: dimensionality of input 
- 
-        :type n_out: int 
-        :param n_out: number of hidden units 
- 
-        :type activation: theano.Op or function 
-        :param activation: Non linearity to be applied in the hidden 
-                           layer 
-        """  
-        self.input = input  
-        # end-snippet-1  
-  
-        # `W` is initialized with `W_values` which is uniformely sampled  
-        # from sqrt(-6./(n_in+n_hidden)) and sqrt(6./(n_in+n_hidden))  
-        # for tanh activation function  
-        # the output of uniform if converted using asarray to dtype  
-        # theano.config.floatX so that the code is runable on GPU  
-        # Note : optimal initialization of weights is dependent on the  
-        #        activation function used (among other things).  
-        #        For example, results presented in [Xavier10] suggest that you  
-        #        should use 4 times larger initial weights for sigmoid  
-        #        compared to tanh  
-        #        We have no info for other function, so we use the same as  
-        #        tanh.  
-        if W is None:  
-            W_values = numpy.asarray(  
-                rng.uniform(  
-                    low=-numpy.sqrt(6. / (n_in + n_out)),  
-                    high=numpy.sqrt(6. / (n_in + n_out)),  
-                    size=(n_in, n_out)  
-                ),  
-                dtype=theano.config.floatX  
-            )  
-            if activation == theano.tensor.nnet.sigmoid:  
-                W_values *= 4  
-  
-            W = theano.shared(value=W_values, name='W', borrow=True)  
-  
-        if b is None:  
-            b_values = numpy.zeros((n_out,), dtype=theano.config.floatX)  
-            b = theano.shared(value=b_values, name='b', borrow=True)  
-  
-        self.W = W  
-        self.b = b  
-  
-        lin_output = T.dot(input, self.W) + self.b  
-        self.output = (  
-            lin_output if activation is None  
-            else activation(lin_output)  
-        )  
-        # parameters of the model  
-        self.params = [self.W, self.b]  
-  
-  
-# start-snippet-2  
-class MLP(object):  
-    """Multi-Layer Perceptron Class 
- 
-    A multilayer perceptron is a feedforward artificial neural network model 
-    that has one layer or more of hidden units and nonlinear activations. 
-    Intermediate layers usually have as activation function tanh or the 
-    sigmoid function (defined here by a ``HiddenLayer`` class)  while the 
-    top layer is a softmax layer (defined here by a ``LogisticRegression`` 
-    class). 
-    """  
-  
-    def __init__(self, rng, input, n_in, n_hidden, n_out):  
-        """Initialize the parameters for the multilayer perceptron 
- 
-        :type rng: numpy.random.RandomState 
-        :param rng: a random number generator used to initialize weights 
- 
-        :type input: theano.tensor.TensorType 
-        :param input: symbolic variable that describes the input of the 
-        architecture (one minibatch) 
- 
-        :type n_in: int 
-        :param n_in: number of input units, the dimension of the space in 
-        which the datapoints lie 
- 
-        :type n_hidden: int 
-        :param n_hidden: number of hidden units 
- 
-        :type n_out: int 
-        :param n_out: number of output units, the dimension of the space in 
-        which the labels lie 
- 
-        """  
-  
-        # Since we are dealing with a one hidden layer MLP, this will translate  
-        # into a HiddenLayer with a tanh activation function connected to the  
-        # LogisticRegression layer; the activation function can be replaced by  
-        # sigmoid or any other nonlinear function  
-        self.hiddenLayer = HiddenLayer(  
-            rng=rng,  
-            input=input,  
-            n_in=n_in,  
-            n_out=n_hidden,  
-            activation=T.tanh  
-        )  
-  
-        # The logistic regression layer gets as input the hidden units  
-        # of the hidden layer  
-        self.logRegressionLayer = LogisticRegression(  
-            input=self.hiddenLayer.output,  
-            n_in=n_hidden,  
-            n_out=n_out  
-        )  
-        # end-snippet-2 start-snippet-3  
-        # L1 norm ; one regularization option is to enforce L1 norm to  
-        # be small  
-        self.L1 = (  
-            abs(self.hiddenLayer.W).sum()  
-            + abs(self.logRegressionLayer.W).sum()  
-        )  
-  
-        # square of L2 norm ; one regularization option is to enforce  
-        # square of L2 norm to be small  
-        self.L2_sqr = (  
-            (self.hiddenLayer.W ** 2).sum()  
-            + (self.logRegressionLayer.W ** 2).sum()  
-        )  
-  
-        # negative log likelihood of the MLP is given by the negative  
-        # log likelihood of the output of the model, computed in the  
-        # logistic regression layer  
-        self.negative_log_likelihood = (  
-            self.logRegressionLayer.negative_log_likelihood  
-        )  
-        # same holds for the function computing the number of errors  
-        self.errors = self.logRegressionLayer.errors  
-  
-        # the parameters of the model are the parameters of the two layer it is  
-        # made out of  
-        self.params = self.hiddenLayer.params + self.logRegressionLayer.params  
-        # end-snippet-3  
-  
-        # keep track of model input  
-        self.input = input  
-  
-  
-def test_mlp(learning_rate=0.01, L1_reg=0.00, L2_reg=0.0001, n_epochs=1000,  
-             dataset='mnist.pkl.gz', batch_size=20, n_hidden=500):  
-    """ 
-    Demonstrate stochastic gradient descent optimization for a multilayer 
-    perceptron 
- 
-    This is demonstrated on MNIST. 
- 
-    :type learning_rate: float 
-    :param learning_rate: learning rate used (factor for the stochastic 
-    gradient 
- 
-    :type L1_reg: float 
-    :param L1_reg: L1-norm's weight when added to the cost (see 
-    regularization) 
- 
-    :type L2_reg: float 
-    :param L2_reg: L2-norm's weight when added to the cost (see 
-    regularization) 
- 
-    :type n_epochs: int 
-    :param n_epochs: maximal number of epochs to run the optimizer 
- 
-    :type dataset: string 
-    :param dataset: the path of the MNIST dataset file from 
-                 http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz 
- 
- 
-   """  
-    datasets = load_data(dataset)  
-  
-    train_set_x, train_set_y = datasets[0]  
-    valid_set_x, valid_set_y = datasets[1]  
-    test_set_x, test_set_y = datasets[2]  
-  
-    # compute number of minibatches for training, validation and testing  
-    n_train_batches = train_set_x.get_value(borrow=True).shape[0] // batch_size  
-    n_valid_batches = valid_set_x.get_value(borrow=True).shape[0] // batch_size  
-    n_test_batches = test_set_x.get_value(borrow=True).shape[0] // batch_size  
-  
-    ######################  
-    # BUILD ACTUAL MODEL #  
-    ######################  
-    print('... building the model')  
-  
-    # allocate symbolic variables for the data  
-    index = T.lscalar()  # index to a [mini]batch  
-    x = T.matrix('x')  # the data is presented as rasterized images  
-    y = T.ivector('y')  # the labels are presented as 1D vector of  
-                        # [int] labels  
-  
-    rng = numpy.random.RandomState(1234)  
-  
-    # construct the MLP class  
-    classifier = MLP(  
-        rng=rng,  
-        input=x,  
-        n_in=28 * 28,  
-        n_hidden=n_hidden,  
-        n_out=10  
-    )  
-  
-    # start-snippet-4  
-    # the cost we minimize during training is the negative log likelihood of  
-    # the model plus the regularization terms (L1 and L2); cost is expressed  
-    # here symbolically  
-    cost = (  
-        classifier.negative_log_likelihood(y)  
-        + L1_reg * classifier.L1  
-        + L2_reg * classifier.L2_sqr  
-    )  
-    # end-snippet-4  
-  
-    # compiling a Theano function that computes the mistakes that are made  
-    # by the model on a minibatch  
-    test_model = theano.function(  
-        inputs=[index],  
-        outputs=classifier.errors(y),  
-        givens={  
-            x: test_set_x[index * batch_size:(index + 1) * batch_size],  
-            y: test_set_y[index * batch_size:(index + 1) * batch_size]  
-        }  
-    )  
-  
-    validate_model = theano.function(  
-        inputs=[index],  
-        outputs=classifier.errors(y),  
-        givens={  
-            x: valid_set_x[index * batch_size:(index + 1) * batch_size],  
-            y: valid_set_y[index * batch_size:(index + 1) * batch_size]  
-        }  
-    )  
-  
-    # start-snippet-5  
-    # compute the gradient of cost with respect to theta (sorted in params)  
-    # the resulting gradients will be stored in a list gparams  
-    gparams = [T.grad(cost, param) for param in classifier.params]  
-  
-    # specify how to update the parameters of the model as a list of  
-    # (variable, update expression) pairs  
-  
-    # given two lists of the same length, A = [a1, a2, a3, a4] and  
-    # B = [b1, b2, b3, b4], zip generates a list C of same size, where each  
-    # element is a pair formed from the two lists :  
-    #    C = [(a1, b1), (a2, b2), (a3, b3), (a4, b4)]  
-    updates = [  
-        (param, param - learning_rate * gparam)  
-        for param, gparam in zip(classifier.params, gparams)  
-    ]  
-  
-    # compiling a Theano function `train_model` that returns the cost, but  
-    # in the same time updates the parameter of the model based on the rules  
-    # defined in `updates`  
-    train_model = theano.function(  
-        inputs=[index],  
-        outputs=cost,  
-        updates=updates,  
-        givens={  
-            x: train_set_x[index * batch_size: (index + 1) * batch_size],  
-            y: train_set_y[index * batch_size: (index + 1) * batch_size]  
-        }  
-    )  
-    # end-snippet-5  
-  
-    ###############  
-    # TRAIN MODEL #  
-    ###############  
-    print('... training')  
-  
-    # early-stopping parameters  
-    patience = 10000  # look as this many examples regardless  
-    patience_increase = 2  # wait this much longer when a new best is  
-                           # found  
-    improvement_threshold = 0.995  # a relative improvement of this much is  
-                                   # considered significant  
-    validation_frequency = min(n_train_batches, patience // 2)  
-                                  # go through this many  
-                                  # minibatche before checking the network  
-                                  # on the validation set; in this case we  
-                                  # check every epoch  
-  
-    best_validation_loss = numpy.inf  
-    best_iter = 0  
-    test_score = 0.  
-    start_time = timeit.default_timer()  
-  
-    epoch = 0  
-    done_looping = False  
-  
-    while (epoch < n_epochs) and (not done_looping):  
-        epoch = epoch + 1  
-        for minibatch_index in range(n_train_batches):  
-  
-            minibatch_avg_cost = train_model(minibatch_index)  
-            # iteration number  
-            iter = (epoch - 1) * n_train_batches + minibatch_index  
-  
-            if (iter + 1) % validation_frequency == 0:  
-                # compute zero-one loss on validation set  
-                validation_losses = [validate_model(i) for i  
-                                     in range(n_valid_batches)]  
-                this_validation_loss = numpy.mean(validation_losses)  
-  
-                print(  
-                    'epoch %i, minibatch %i/%i, validation error %f %%' %  
-                    (  
-                        epoch,  
-                        minibatch_index + 1,  
-                        n_train_batches,  
-                        this_validation_loss * 100.  
-                    )  
-                )  
-  
-                # if we got the best validation score until now  
-                if this_validation_loss < best_validation_loss:  
-                    #improve patience if loss improvement is good enough  
-                    if (  
-                        this_validation_loss < best_validation_loss *  
-                        improvement_threshold  
-                    ):  
-                        patience = max(patience, iter * patience_increase)  
-  
-                    best_validation_loss = this_validation_loss  
-                    best_iter = iter  
-  
-                    # test it on the test set  
-                    test_losses = [test_model(i) for i  
-                                   in range(n_test_batches)]  
-                    test_score = numpy.mean(test_losses)  
-  
-                    print(('     epoch %i, minibatch %i/%i, test error of '  
-                           'best model %f %%') %  
-                          (epoch, minibatch_index + 1, n_train_batches,  
-                           test_score * 100.))  
-  
-            if patience <= iter:  
-                done_looping = True  
-                break  
-  
-    end_time = timeit.default_timer()  
-    print(('Optimization complete. Best validation score of %f %% '  
-           'obtained at iteration %i, with test performance %f %%') %  
-          (best_validation_loss * 100., best_iter + 1, test_score * 100.))  
-    print(('The code for file ' +  
-           os.path.split(__file__)[1] +  
-           ' ran for %.2fm' % ((end_time - start_time) / 60.)), file=sys.stderr)  
-  
-  
-if __name__ == '__main__':  
-    test_mlp()  
-
-```
+#### 玻尔兹曼机(Boltzmann Machine)

From fdef6faf1e88001f5dd2d646199f493ec5171af0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 May 2018 09:08:45 +0800
Subject: [PATCH 0931/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 2c9cff35..fd553195 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -12,3 +12,5 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 玻尔兹曼机(Boltzmann Machine)
+
+受限玻尔兹曼机是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。

From a457ded1267708217b70b5281d78f784785830ce Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Fri, 11 May 2018 09:12:53 +0800
Subject: [PATCH 0932/1406] change ANNN

---
 assets/images/329.jpg     | Bin 0 -> 105838 bytes
 assets/src/ANN/ANN.0.6.md |   7 ++++++-
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/329.jpg

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diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index fd553195..2515ac80 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -13,4 +13,9 @@
 
 #### 玻尔兹曼机(Boltzmann Machine)
 
-受限玻尔兹曼机是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
+受限玻尔兹曼机是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。
+BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
+
+<p align="center">
+<img width="300" align="center" src="../../images/329.jpg" />
+</p>
\ No newline at end of file

From 0bc82170e096262b0467badd951328b1e5461f81 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 May 2018 09:15:13 +0800
Subject: [PATCH 0933/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 2515ac80..05557a96 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -17,5 +17,7 @@
 BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
 
 <p align="center">
-<img width="300" align="center" src="../../images/329.jpg" />
-</p>
\ No newline at end of file
+<img width="500" align="center" src="../../images/329.jpg" />
+</p>
+
+Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。

From f8c88f0eff07cdc8628375e8d5fb3c7fc50314f3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 May 2018 16:57:09 +0800
Subject: [PATCH 0934/1406] Update README.md

---
 README.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/README.md b/README.md
index 2c6845e3..69fddecf 100644
--- a/README.md
+++ b/README.md
@@ -194,6 +194,9 @@
 
 觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,加入我们的交流群一起交流学习！
 
+<p style="left">
+  <img src="https://github.com/KeKe-Li/book/blob/master/images/1.jpg" width="260">
+</p>
 
 ### License
 This is free software distributed under the terms of the MIT license

From 7d7c32e37127e474ac0fcb9cbab07b92264db552 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 May 2018 16:59:42 +0800
Subject: [PATCH 0935/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 69fddecf..0a57ef21 100644
--- a/README.md
+++ b/README.md
@@ -192,7 +192,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信Sen0676,加入我们的交流群一起交流学习！
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信,加入我们的交流群一起交流学习！
 
 <p style="left">
   <img src="https://github.com/KeKe-Li/book/blob/master/images/1.jpg" width="260">

From e49d56b1a7c7fb60bb6c1155395c44e1ab27450f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 May 2018 17:14:51 +0800
Subject: [PATCH 0936/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0a57ef21..2ee5f255 100644
--- a/README.md
+++ b/README.md
@@ -192,7 +192,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信,加入我们的交流群一起交流学习！
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信,加入我们的交流群一起交流机器学习！
 
 <p style="left">
   <img src="https://github.com/KeKe-Li/book/blob/master/images/1.jpg" width="260">

From da071dae7364093195de646ed9613fbee193b166 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Sat, 12 May 2018 09:03:16 +0800
Subject: [PATCH 0937/1406] change page of ANN

---
 README.md                  | 12 ++++++------
 assets/src/ANN/ANN.0.10.md | 23 +++++++++++++++++++++++
 assets/src/ANN/ANN.0.11.md | 15 +++++++++++++++
 assets/src/ANN/ANN.0.12.md | 15 +++++++++++++++
 assets/src/ANN/ANN.0.7.md  | 15 +++++++++++++++
 assets/src/ANN/ANN.0.8.md  | 15 +++++++++++++++
 assets/src/ANN/ANN.0.9.md  | 14 ++++++++++++++
 7 files changed, 103 insertions(+), 6 deletions(-)
 create mode 100644 assets/src/ANN/ANN.0.10.md
 create mode 100644 assets/src/ANN/ANN.0.11.md
 create mode 100644 assets/src/ANN/ANN.0.12.md
 create mode 100644 assets/src/ANN/ANN.0.7.md
 create mode 100644 assets/src/ANN/ANN.0.8.md
 create mode 100644 assets/src/ANN/ANN.0.9.md

diff --git a/README.md b/README.md
index 2ee5f255..06f26a30 100644
--- a/README.md
+++ b/README.md
@@ -126,12 +126,12 @@
      * [递归神经网络(Recurrent Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.4.md)) 
      * [多层感知器(Multilayer Perceptron)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.5.md) 
      * [玻尔兹曼机(Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.6.md) 
-     * [卷积神经网络(Convolutional Neural Network)]() 
-     * [Hopfield网络(Hopfield Network)]() 
-     * [径向基函数网络(Radial Basis Function Network)]() 
-     * [受限玻尔兹曼机(Restricted Boltzmann Machine)]() 
-     * [自组织映射(Self-Organizing Map)]() 
-     * [尖峰神经网络(Spiking Neural Network)]() 
+     * [卷积神经网络(Convolutional Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.7.md) 
+     * [Hopfield网络(Hopfield Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.8.md) 
+     * [径向基函数网络(Radial Basis Function Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.9.md) 
+     * [受限玻尔兹曼机(Restricted Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.10.md) 
+     * [自组织映射(Self-Organizing Map)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.11.md) 
+     * [尖峰神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
  * [深度学习(Deep Learning)]() 
      * [深度信念网络(Deep Belief Machines)]() 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
new file mode 100644
index 00000000..f233881e
--- /dev/null
+++ b/assets/src/ANN/ANN.0.10.md
@@ -0,0 +1,23 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 受限玻尔兹曼机(Restricted Boltzmann Machine)
+
+受限玻尔兹曼机(Restricted Boltzmann Machine)是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。
+BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
+
+<p align="center">
+<img width="500" align="center" src="../../images/329.jpg" />
+</p>
+
+Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。
diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
new file mode 100644
index 00000000..1a8d4a49
--- /dev/null
+++ b/assets/src/ANN/ANN.0.11.md
@@ -0,0 +1,15 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 自组织映射(Self-Organizing Map)
+
diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
new file mode 100644
index 00000000..cc04305f
--- /dev/null
+++ b/assets/src/ANN/ANN.0.12.md
@@ -0,0 +1,15 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 尖峰神经网络(Spiking Neural Network)
+
diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
new file mode 100644
index 00000000..89f1365a
--- /dev/null
+++ b/assets/src/ANN/ANN.0.7.md
@@ -0,0 +1,15 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 卷积神经网络(Convolutional Neural Network)
+
diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
new file mode 100644
index 00000000..1f1ffe5e
--- /dev/null
+++ b/assets/src/ANN/ANN.0.8.md
@@ -0,0 +1,15 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### Hopfield网络(Hopfield Network)
+
diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
new file mode 100644
index 00000000..136abfc6
--- /dev/null
+++ b/assets/src/ANN/ANN.0.9.md
@@ -0,0 +1,14 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
+机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
+
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+
+（2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
+
+（3）半监督学习：介于监督学习和无监督学习之间,例如EM算法。
+
+如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
+
+#### 径向基函数网络(Radial Basis Function Network)

From 78d1206dffe57e1c84552b53f44c200d75892377 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:06:21 +0800
Subject: [PATCH 0938/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 05557a96..bb19dc3d 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -13,6 +13,7 @@
 
 #### 玻尔兹曼机(Boltzmann Machine)
 
+
 受限玻尔兹曼机是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。
 BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
 

From 0295c13d5adfa03b8ae48875b51701747c3f0cab Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:06:34 +0800
Subject: [PATCH 0939/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index bb19dc3d..41e728a3 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -13,12 +13,3 @@
 
 #### 玻尔兹曼机(Boltzmann Machine)
 
-
-受限玻尔兹曼机是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。
-BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
-
-<p align="center">
-<img width="500" align="center" src="../../images/329.jpg" />
-</p>
-
-Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。

From 1db76a6643722654cd6fddfe0843cbb879f823b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:08:45 +0800
Subject: [PATCH 0940/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 41e728a3..53bd04ed 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -12,4 +12,8 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 玻尔兹曼机(Boltzmann Machine)
+玻尔兹曼机（Boltzmann machine）是随机神经网络和递归神经网络的一种，由杰弗里·辛顿(Geoffrey Hinton)和特里·谢泽诺斯基(Terry Sejnowski)在1985年发明。
 
+玻尔兹曼机可被视作随机过程的，可生成的相应的Hopfield神经网络。它是最早能够学习内部表达，并能表达和（给定充足的时间）解决复杂的组合优化问题的神经网络。但是，没有特定限制连接方式的玻尔兹曼机目前为止并未被证明对机器学习的实际问题有什么用。所以它目前只在理论上显得有趣。然而，由于局部性和训练算法的赫布性质(Hebbian nature)，以及它们和简单物理过程相似的并行性，如果连接方式是受约束的（即受限玻尔兹曼机），学习方式在解决实际问题上将会足够高效。
+
+它由玻尔兹曼分布得名。该分布用于玻尔兹曼机的抽样函数。

From aa912cda6769d4e8674f45879afcfdd6beb5d6b6 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Sat, 12 May 2018 09:10:58 +0800
Subject: [PATCH 0941/1406] change page of ANN.0.6

---
 assets/images/330.jpg     | Bin 0 -> 31034 bytes
 assets/src/ANN/ANN.0.6.md |   5 +++++
 2 files changed, 5 insertions(+)
 create mode 100644 assets/images/330.jpg

diff --git a/assets/images/330.jpg b/assets/images/330.jpg
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HcmV?d00001

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 53bd04ed..64460d99 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -17,3 +17,8 @@
 玻尔兹曼机可被视作随机过程的，可生成的相应的Hopfield神经网络。它是最早能够学习内部表达，并能表达和（给定充足的时间）解决复杂的组合优化问题的神经网络。但是，没有特定限制连接方式的玻尔兹曼机目前为止并未被证明对机器学习的实际问题有什么用。所以它目前只在理论上显得有趣。然而，由于局部性和训练算法的赫布性质(Hebbian nature)，以及它们和简单物理过程相似的并行性，如果连接方式是受约束的（即受限玻尔兹曼机），学习方式在解决实际问题上将会足够高效。
 
 它由玻尔兹曼分布得名。该分布用于玻尔兹曼机的抽样函数。
+
+<p align="center">
+<img width="300" align="center" src="../../images/330.jpg" />
+</p>
+

From dbb793d884da53267120de2d3e6847c967c0f94b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:11:53 +0800
Subject: [PATCH 0942/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 64460d99..ba29a0b7 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -22,3 +22,4 @@
 <img width="300" align="center" src="../../images/330.jpg" />
 </p>
 
+玻尔兹曼机的图像表示. 每条无向边都表示一对依赖关系. 在这个例子中有三个隐藏节点和四个可见节点，它并不是一个约束玻尔兹曼机（restricted Boltzmann machine）

From 62ce7736a2d2edef8e4aaaadde8e07e8b3e5097c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:15:51 +0800
Subject: [PATCH 0943/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index ba29a0b7..6a3fdd15 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -14,6 +14,8 @@
 #### 玻尔兹曼机(Boltzmann Machine)
 玻尔兹曼机（Boltzmann machine）是随机神经网络和递归神经网络的一种，由杰弗里·辛顿(Geoffrey Hinton)和特里·谢泽诺斯基(Terry Sejnowski)在1985年发明。
 
+玻尔兹曼机是一种特殊形式的对数线性的马尔科夫随机场（Markov Random Field，MRF），即能量函数是自由变量的线性函数。 通过引入隐含单元，我们可以提升模型的表达能力，表示非常复杂的概率分布。
+
 玻尔兹曼机可被视作随机过程的，可生成的相应的Hopfield神经网络。它是最早能够学习内部表达，并能表达和（给定充足的时间）解决复杂的组合优化问题的神经网络。但是，没有特定限制连接方式的玻尔兹曼机目前为止并未被证明对机器学习的实际问题有什么用。所以它目前只在理论上显得有趣。然而，由于局部性和训练算法的赫布性质(Hebbian nature)，以及它们和简单物理过程相似的并行性，如果连接方式是受约束的（即受限玻尔兹曼机），学习方式在解决实际问题上将会足够高效。
 
 它由玻尔兹曼分布得名。该分布用于玻尔兹曼机的抽样函数。

From 056262c3cf197458a8973c0e670e5f126944a18e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 12 May 2018 09:42:14 +0800
Subject: [PATCH 0944/1406] Update ANN.0.6.md

---
 assets/src/ANN/ANN.0.6.md | 210 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 210 insertions(+)

diff --git a/assets/src/ANN/ANN.0.6.md b/assets/src/ANN/ANN.0.6.md
index 6a3fdd15..eb3ad5f5 100644
--- a/assets/src/ANN/ANN.0.6.md
+++ b/assets/src/ANN/ANN.0.6.md
@@ -25,3 +25,213 @@
 </p>
 
 玻尔兹曼机的图像表示. 每条无向边都表示一对依赖关系. 在这个例子中有三个隐藏节点和四个可见节点，它并不是一个约束玻尔兹曼机（restricted Boltzmann machine）
+
+
+#### 应用示例
+```python
+from unittest import TestCase
+from matplotlib import pyplot
+
+__author__ = 'riri'
+import numpy as np
+epsilon = 0.000001
+def sigmoid(v):
+    return 1/(1+np.exp(-v))
+
+def hidden_activation_probability(v,W,c):
+    # x is size k*v
+    # W is size h*v
+    #  W.T is size v*h
+    # c is length h
+    # result is size k*h
+    return sigmoid(c + np.dot(v, W.T))
+
+def hidden_activation_probability_naive(v,W,c):
+    activations = np.zeros(W.shape[0])
+    if v.size != W.shape[1]:
+        #print v.size
+        #print v.shape
+        #print W.shape
+        pass
+    assert(v.size == W.shape[1])
+    for i in range(W.shape[0]):
+        activations[i] = sigmoid(c[i] + sum([W[i,j]*v[j] for j in range(W.shape[1])]))
+    return activations
+
+def visible_activation_probability(h,W,b):
+    # h is length k*h
+    # W is size h*v
+    # b is length v
+    # result is size k*v
+    return sigmoid(b + np.dot(h,W))
+
+def visible_activation_probability_naive(h,W,b):
+    activations = np.zeros(W.shape[1])
+    assert(h.size == W.shape[0])
+    for j in range(W.shape[1]):
+        activations[j] = sigmoid(b[j] + sum([W[i,j]*h[i] for i in range(W.shape[0])]))
+    return activations
+
+def sample_hidden_units(v,W,c):
+    hidden_probabilities = hidden_activation_probability(v,W,c)
+    return np.random.uniform(size=hidden_probabilities.shape) < hidden_probabilities
+
+def sample_hidden_units_naive(v,W,c):
+    hidden_probabilities = hidden_activation_probability_naive(v,W,c)
+    return np.random.uniform(size=hidden_probabilities.shape) < hidden_probabilities
+
+def sample_visible_units(h,W,b):
+    visible_probabilities = visible_activation_probability(h,W,b)
+    return np.random.uniform(size=visible_probabilities.shape) < visible_activation_probability(h,W,b)
+
+def sample_visible_units_naive(h,W,b):
+    visible_probabilities = visible_activation_probability_naive(h,W,b)
+    return np.random.uniform(size=visible_probabilities.shape) < visible_activation_probability(h,W,b)
+
+def rbmUpdate_naive(x, W, b, c, lr=0.1):
+    h1 = sample_hidden_units_naive(x,W,c)
+    v2 = sample_visible_units_naive(h1,W,b)
+    q_v2 = visible_activation_probability_naive(h1,W,b)
+    q_h2 = hidden_activation_probability_naive(v2,W,c)
+    new_b = b + lr*(x-v2)
+    new_c = c + lr*(h1-q_h2)
+    a = np.outer(h1,x)
+    b = np.outer(q_h2,v2.T)
+    new_W = W + lr*(a-b)
+    error = np.sum((x-q_v2)**2)
+    return new_W,new_b,new_c,error
+
+def rbmUpdate(x,W,b,c,lr=0.1):
+    h1 = sample_hidden_units(x,W,c)
+    v2 = sample_visible_units(h1,W,b)
+    q_v2 = visible_activation_probability(h1,W,b)
+    q_h2 = hidden_activation_probability(v2,W,c)
+    new_b = b + lr*(x-v2)
+    new_c = c + lr*(h1-q_h2)
+    a = np.outer(h1,x)
+    b = np.outer(q_h2,v2.T)
+    new_W = W + lr*(a-b)
+    error = np.sum(np.sum((x-q_v2)**2))
+    return new_W,new_b,new_c,error
+
+class RBM(object):
+    def __init__(self, visible_units, hidden_units):
+        self.v = visible_units
+        self.h = hidden_units
+        self.W = np.random.random(size=(hidden_units, visible_units))
+        self.b = np.random.random(visible_units)
+        self.c = np.random.random(hidden_units)
+
+    def train(self, data, lr=0.05, max_iterations=1000, eps=0.1):
+        iteration = 0
+        last_error = eps+1
+        while iteration < max_iterations and last_error > eps:
+            for item in data:
+                self.W,self.b,self.c,last_error = rbmUpdate(item, self.W,self.b,self.c,lr)
+            iteration += 1
+            if iteration % 10 == 0:
+                print last_error
+
+    def train_naive(self,data,lr=0.05,max_iterations=1000,eps=0.1):
+        iteration = 0
+        last_error = eps+1
+        while iteration < max_iterations and last_error > eps:
+            for item in data:
+                self.W,self.b,self.c,last_error = rbmUpdate_naive(item, self.W,self.b,self.c,lr)
+            iteration += 1
+            if iteration % 10 == 0:
+                print last_error
+class TestAgainstNaive(object):
+    def __init__(self, h_size, v_size):
+        self.h_size = h_size
+        self.v_size = v_size
+    def test_hidden(self):
+        h_size = self.h_size
+        v_size = self.v_size
+        ww = np.random.uniform(size=(h_size,v_size))
+        bb = np.random.uniform(size=v_size)
+        cc = np.random.uniform(size=h_size)
+        vv = np.random.uniform(size=v_size)
+        h1 = hidden_activation_probability_naive(vv,ww,cc)
+        h2 = hidden_activation_probability(vv,ww,cc)
+        assert(h1.shape == h2.shape)
+        assert(h1.size == h_size)
+        assert(all(np.abs(h1 - h2) < epsilon))
+    def test_visible(self):
+        h_size = self.h_size
+        v_size = self.v_size
+        ww = np.random.uniform(size=(h_size,v_size))
+        bb = np.random.uniform(size=v_size)
+        hh = np.random.uniform(size=h_size)
+        v1 = visible_activation_probability_naive(hh,ww,bb)
+        v2 = visible_activation_probability(hh,ww,bb)
+        assert(v1.shape == v2.shape)
+        assert(v1.size == v_size)
+        assert(all(np.abs(v1 - v2) < epsilon))
+    def test_update(self):
+        h_size = self.h_size
+        v_size = self.v_size
+        ww = np.random.uniform(size=(h_size,v_size))
+        bb = np.random.uniform(size=v_size)
+        cc = np.random.uniform(size=h_size)
+        vv = np.random.uniform(size=v_size)
+        (nw1,nb1,nc1,e1) = rbmUpdate(vv,ww,bb,cc)
+        (nw2,nb2,nc2,e2) = rbmUpdate_naive(vv,ww,bb,cc)
+
+        # The bounds for this are a bit larger, because
+        # more goes one, so there are more chances for
+        # divergence.
+        assert(np.all(np.abs(nw1-nw2) < epsilon*5))
+        assert(np.all(np.abs(nb1-nb2) < epsilon*5))
+        assert(np.all(np.abs(nc1-nc2) < epsilon*5))
+        assert(np.all(np.abs(e1-e2) < epsilon*5))
+
+def chunkfiles(files):
+    splitwords = []
+    vocab = set()
+    for f in files:
+        for line in f.readlines():
+            splitwords.append(set(line.split()))
+            vocab = vocab.union(line.split())
+    entries = []
+    vocablist = list(vocab)
+    for entry in splitwords:
+        entries.append([1 if word in entry else 0 for word in vocablist])
+    return entries
+
+def splitfiles(files):
+    splitwords = []
+    vocab = set()
+    for f in files:
+        for line in f.readlines():
+            splitwords.append(set(line.split()))
+            vocab = vocab.union(line.split())
+    return splitwords
+
+
+def go():
+    tests = 1
+    magnitude_mat = np.zeros((7,4*tests))
+    with open('./movies.txt') as movies:
+        with open('./matrices.txt') as matrices:
+            terms = chunkfiles([movies, matrices])
+    for i in range(tests):
+        training_data = np.array(terms[1:-1])
+        print training_data.shape
+        r = RBM(399, 2)
+        r.train(training_data ,max_iterations=500,lr=0.1)
+        movterm = np.array([terms[1]])
+        matterm = np.array([terms[-1]])
+        print hidden_activation_probability(movterm,r.W,r.c)
+        print hidden_activation_probability(matterm,r.W,r.c)
+    pyplot.imshow(magnitude_mat, interpolation='nearest')
+
+if __name__=='__main__':
+    h_size = np.floor(np.random.rand()*100)
+    v_size = np.floor(np.random.rand()*100)
+    test = TestAgainstNaive(h_size,v_size)
+    test.test_visible()
+    test.test_hidden()
+    test.test_update()
+    go()
+```

From f175bf44418cfb7af99cd4b36ff674ccc006e39b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 May 2018 20:51:46 +0800
Subject: [PATCH 0945/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 89f1365a..f6fef02d 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -12,4 +12,11 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 卷积神经网络(Convolutional Neural Network)
+卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
+
+卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。
+
+CNN的基本结构包括两层，其一为特征提取层，每个神经元的输入与前一层的局部接受域相连，并提取该局部的特征。一旦该局部特征被提取后，它与其它特征间的位置关系也随之确定下来；其二是特征映射层，网络的每个计算层由多个特征映射组成，每个特征映射是一个平面，平面上所有神经元的权值相等。特征映射结构采用影响函数核小的sigmoid函数作为卷积网络的激活函数，使得特征映射具有位移不变性。此外，由于一个映射面上的神经元共享权值，因而减少了网络自由参数的个数。卷积神经网络中的每一个卷积层都紧跟着一个用来求局部平均与二次提取的计算层，这种特有的两次特征提取结构减小了特征分辨率。
+
+CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 

From 58a9be8f081ec5de0d034a527a6e12625534c21a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 May 2018 20:53:04 +0800
Subject: [PATCH 0946/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index f6fef02d..2fd7db4a 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -20,3 +20,7 @@ CNN的基本结构包括两层，其一为特征提取层，每个神经元的
 
 CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 
+<p align="center">
+<img width="300" align="center" src="../images/2.jpg" />
+</p>
+

From ed11be645e4a624aa6ff98113e585ef94c52560a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 May 2018 20:54:28 +0800
Subject: [PATCH 0947/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 2fd7db4a..bd96319a 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -21,6 +21,6 @@ CNN的基本结构包括两层，其一为特征提取层，每个神经元的
 CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 
 <p align="center">
-<img width="300" align="center" src="../images/2.jpg" />
+<img width="300" align="center" src="../../images/1.jpg" />
 </p>
 

From 74317767790bc9dfcf049b906b98891172ce2d98 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 May 2018 20:58:53 +0800
Subject: [PATCH 0948/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index bd96319a..5e7d2894 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 卷积神经网络(Convolutional Neural Network)
+
 卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。

From ca9f99cc21186e1bf5d8d6d1a9ba1aaf2e541741 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 May 2018 21:01:37 +0800
Subject: [PATCH 0949/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 365 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 365 insertions(+)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 5e7d2894..8418b6b2 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -25,3 +25,368 @@ CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图
 <img width="300" align="center" src="../../images/1.jpg" />
 </p>
 
+
+#### 应用示例
+```python
+import numpy as np
+import scipy.signal as signal
+import cPickle
+import gzip
+import gc
+import scipy
+#import objgraph  
+def sigmoid(input):
+    '激励函数'
+    out=1.7159*scipy.tanh(2.0/3.0*input)
+    return out
+def dsigmoid(input):
+    'sigmoid的导函数已知input=sigmod(out)'
+    out=2.0/3.0/1.7159*(1.7159+input)*(1.7159-input)
+    return out
+def convolutional(fm,ct,kernel,bias):
+    '卷积函数'
+    "fm 特征图 三维"
+    "ct 连接权矩阵"
+    "kernel 卷积核 三维"
+    "bias 偏置 向量"
+    map_width=fm.shape[2]
+    map_height=fm.shape[1]
+    kernel_width=kernel.shape[2]
+    kernel_height=kernel.shape[1]
+    '计算特征图的尺寸'
+    dst_height=map_height-kernel_height+1
+    dst_width=map_width-kernel_width+1
+    '计算输出特征图的数量'
+    cfmDims=np.max(ct[1])+1
+    n_kernels=kernel.shape[0]
+    #print("ct's shape%d:%d"%(ct.shape[0],ct.shape[1]))
+    ' 初始化结果特征图' 
+    cfm=np.zeros((cfmDims,dst_height,dst_width))
+    for index in xrange(0,cfmDims):
+        "首先加上偏置值"
+        cfm[index]+=bias[index]
+    for index in xrange(0,n_kernels):
+        #print(index)
+        this_fm=fm[ct[0,index]]
+        this_kernel=kernel[index]
+        "计算卷积"
+        this_conv=signal.convolve2d(this_fm, this_kernel, mode='valid')
+        cfm_index=ct[1,index]
+        cfm[cfm_index]+=this_conv
+    "使用sigmoid压制"
+    return sigmoid(cfm)
+def subsampling(fm,sW,sb,pool_size,pool_stride):
+    "重采样函数"
+    "fm 特征图"
+    "sW 重采样权值 向量"
+    "sb 重采样偏置 向量"
+    "pool_size 重采样窗口大小 二维矩阵"
+    "pool_stride 步长 int"
+    sfm_width=int((fm.shape[2]-pool_size[1])/pool_stride)+1
+    sfm_height=int((fm.shape[1]-pool_size[0])/pool_stride)+1
+    sfmDims=fm.shape[0]
+    sfm=np.zeros((sfmDims,sfm_width,sfm_height))
+    #sfm=[]
+    "使用权值为1的核进行采样"
+    kernel=np.ones(pool_size)
+    for index in xrange(0,sfmDims):
+        this_fm=fm[index]
+        this_kernel=kernel*sW[index]
+        "采样实际就是一次卷积过程"
+        this_sfm=signal.convolve2d(this_fm, this_kernel, mode='valid')
+        sfm[index]=copy_fm(this_sfm,pool_stride)
+        sfm[index]=sfm[index]+sb[index]
+    sfm=sigmoid(sfm)
+    return sfm
+def copy_fm(fm,stride):
+    height=fm.shape[0]
+    width=fm.shape[1]
+    result=[]
+    for y in xrange(0,height,stride):
+        y_result=[]
+        y_data=fm[y]
+        for x in xrange(0,width,stride):
+            y_result.append(y_data[x])
+        result.append(y_result)
+    return np.array(result)
+def max_with_index(value):
+    "返回最大值，及最大值的下标"
+    "结果 [下标,最大值]"
+    d=np.max(value)
+    i=np.argmax(value)
+    return [i,d]
+def grade(dout,out,input,w):
+    dout=dout*dsigmoid(out)
+    db=dout
+    dw=np.zeros(w.shape)
+    out=out*dsigmoid(out)
+    for i in xrange(w.shape[1]):
+        dw[:,i]=dout[i]*input
+    din=np.zeros(input.shape)
+    for i in xrange(db.shape[0]):
+        this_kernel=w[:,i]
+        #print("this kernrl:%s\n"%(this_kernel))
+        this_dout=dout[i]*this_kernel
+        #print("this dout: %s"%(this_dout))
+        din+=this_dout
+    return [din,dw,db]
+def dconv2_in(dout,input,kernel):
+    return signal.convolve2d(dout,kernel,mode='full')
+def dconv2_kernel(dout,input,kernel):
+    return signal.convolve2d(input,dout,mode='valid')
+def initWeight(ct,kernel_shape):
+    kernel_num=ct[0].shape[0]
+    kernel_height=kernel_shape[0]
+    kernel_width=kernel_shape[1]
+    weights=np.zeros((kernel_num,kernel_height,kernel_width))
+    for i in xrange(kernel_num):
+        connected=np.array((ct[1]==ct[0,i]),dtype='int')
+        connected=np.array(np.nonzero(connected))
+        connected=connected.shape[0]
+        fanin=connected*kernel_height*kernel_width
+        sd=1.0/np.sqrt(fanin)
+        weights[i]=-1.0*sd+2*sd*np.random.random_sample((kernel_height,kernel_width))
+    return weights    
+class convlayer:
+    def __init__(self,cw,cb,sw,sb,ct,stride):
+        self.sw=sw
+        self.sb=sb
+        self.cw=cw
+        self.cb=cb
+        self.ct=ct
+        self.stride=stride
+class bplayer:
+    def __init__(self,n_in,n_out):
+        sd=1.0/np.sqrt(n_in)
+        self.w=-sd+2*sd*np.random.random_sample((n_in,n_out))
+        self.b=np.zeros(n_out)
+        self.n_in=n_in
+        self.n_out=n_out
+class convnet:
+    def __init__(self,image_shape):
+        self.eta=0.01
+        self.decay=0.8
+        self.step=2
+        ct1=np.array([[1,1,1,1]])
+        ct2=np.array([[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0],
+                      [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1],
+                      [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1],
+                      [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]])
+        ct1=np.transpose(ct1)
+        ct2=np.transpose(ct2)
+        conv_ct1=np.nonzero(ct1)
+        conv_ct1=np.array((conv_ct1[1],conv_ct1[0]))
+        conv_ct2=np.nonzero(ct2)
+        conv_ct2=np.array((conv_ct2[1],conv_ct2[0]))
+        image_height=image_shape[0]
+        image_width=image_shape[1]
+        self.image_shape=image_shape
+        self.kernel_shape=[5,5]
+        self.pool_shape=[2,2]
+        self.stride=2
+        stride=self.stride
+        kernel_height=self.kernel_shape[0]
+        kernel_width=self.kernel_shape[1]
+        pool_height=self.pool_shape[0]
+        pool_width=self.pool_shape[1]
+        nofms1=ct1.shape[0]
+        "初始化卷积层1"
+        cmfHeight1=image_height-kernel_height+1
+        cfmWidth1=image_width-kernel_width+1
+        conv_layer1_cw=initWeight(conv_ct1, self.kernel_shape)
+        conv_layer2_cb=np.zeros(nofms1)
+        sfmHeight1=((cmfHeight1-pool_height)/stride)+1
+        sfmWidth1=((cfmWidth1-pool_width)/stride)+1
+        fanin=pool_height*pool_width
+        sd=1.0/np.sqrt(fanin)
+        conv_layer1_sw=-sd+2*sd*np.random.random_sample(nofms1)
+        conv_layer1_sb=np.zeros(nofms1)
+        self.conv1=convlayer(conv_layer1_cw,conv_layer2_cb,conv_layer1_sw,conv_layer1_sb,conv_ct1,stride)
+        "初始化卷基层2"
+        nofms2=ct2.shape[0]
+        conv_layer2_cw=initWeight(conv_ct2, self.kernel_shape)
+        conv_layer2_cb=np.zeros(nofms2)
+        cfmHeight2=sfmHeight1-kernel_height+1
+        cfmWidth2=sfmWidth1-kernel_width+1
+        sfmHeight2=((cfmHeight2-pool_height)/stride)+1
+        sfmWidth2=((cfmWidth2-pool_width)/stride)+1
+        fanin=pool_width*pool_height
+        sd=1.0/np.sqrt(fanin)
+        conv_layer2_sw=-sd+2*sd*np.random.random_sample(nofms2)
+        conv_layer2_sb=np.zeros(nofms2)
+        self.conv2=convlayer(conv_layer2_cw,conv_layer2_cb,conv_layer2_sw,conv_layer2_sb,conv_ct2,stride)
+        "BP分类器第一层"
+        self.bp1=bplayer(nofms2*sfmHeight2*sfmWidth2,20)
+        self.bp2=bplayer(20,10)
+        self.noErrors=0
+    def forwardPropConv(self,input):
+        "开始第一层的卷积操作"
+        ct=self.conv1.ct
+        cw=self.conv1.cw
+        cb=self.conv1.cb
+        cfm1=convolutional(input, ct, cw, cb)
+        sw=self.conv1.sw
+        sb=self.conv1.sb
+        sfm1=subsampling(cfm1, sw, sb, self.pool_shape, self.stride)
+        "开始第二层的卷积操作"
+        ct=self.conv2.ct
+        cw=self.conv2.cw
+        cb=self.conv2.cb
+        cfm2=convolutional(sfm1, ct, cw, cb)
+        sw=self.conv2.sw
+        sb=self.conv2.sb
+        sfm2=subsampling(cfm2, sw, sb, self.pool_shape, self.stride)
+        return [cfm1,sfm1,cfm2,sfm2]
+    def forwradPropBp(self,input):
+        "开始第一层分类器的操作"
+        w=self.bp1.w
+        b=self.bp1.b
+        out1=np.dot(input,w)
+        for i in xrange(b.shape[0]):
+            out1[i]+=b[i]
+        out1=sigmoid(out1)
+        "开始第二层的操作"
+        w=self.bp2.w
+        b=self.bp2.b
+        out2=np.dot(out1,w)
+        for i in xrange(b.shape[0]):
+            out2[i]+=b[i]
+        out2=sigmoid(out2)
+        return [out1,out2]
+    def backPropBp(self,sfm,tartget,fm1,fm2,w1,w2,b1,b2):
+        "对BP层进行反向传播"
+        "sfm 卷积层的S神经元的输出"
+        "target 目标值"
+        "fm1 BP层第一层输出"
+        "fm2 BP层第二层输出"
+        "w1 b1 第一层参数"
+        "w2 b2 第二层参数"
+        dtarget=-np.ones(self.bp2.n_out)*0.8
+        dtarget[target]=0.8
+        dfm2=np.zeros(self.bp2.n_out)
+        dfm2=dfm2-dtarget
+        dmf2=dfm2*dsigmoid(dfm2)
+        dfm1,dw2,db2=grade(dfm2,fm2,fm1,w2)
+        dsfm,dw1,db1=grade(dfm1,fm1,sfm,w1)
+        return [dsfm,dw1,db1,dw2,db2]
+    def backPropSubsampling(self,dsfm,sfm,cfm,sw,sb,pool_shape,stride):
+        "对S神经元进行反向传播"
+        "dsfm s神经元的输出的偏导数"
+        "sfm s神经元的输出"
+        "cfm 上层c神经元的输出"
+        "sw sb 神经元参数"
+        "pool_shape 采样窗口"
+        "stride 采样步长"
+        dims,height,width=cfm.shape
+        dfm=np.zeros(cfm.shape)
+        dsw=np.zeros(sw.shape)
+        dsb=np.zeros(sb.shape)
+        dsfm=dsfm*dsigmoid(sfm)
+        kernel=np.ones(pool_shape)
+        for i in xrange(dims):
+            this_dsfm=dsfm[i]
+            dthis_kernel=kernel*sw[i]
+            dsb[i]=np.sum(this_dsfm)
+            cfm_height=height-pool_shape[0]+1
+            cfm_width=width-pool_shape[1]+1
+            #print("height:%d,width:%d\n"%(cfm_height,cfm_width))
+            dsfm_beforeSubsampling=np.zeros((cfm_height, cfm_width))
+            y=0
+            x=0
+            for dy in xrange(0,dsfm_beforeSubsampling.shape[0],stride):
+                x=0
+                for dx in xrange(0,dsfm_beforeSubsampling.shape[1],stride):
+                    dsfm_beforeSubsampling[dy,dx]=this_dsfm[y,x]
+                    x+=1
+                y+=1
+            dfm[i]=dconv2_in(dsfm_beforeSubsampling,cfm[i],dthis_kernel)
+            dsw[i]=np.sum(dthis_kernel)
+        return [dfm,dsw,dsb]
+    def backPropConvulution(self,dcfm,cfm,fm,ct,w,b):
+        dfm=np.zeros(fm.shape)
+        dw=np.zeros(w.shape)
+        db=np.zeros(b.shape)
+        dcfm=dcfm*dsigmoid(cfm)
+        for i in xrange(b.shape[0]):
+            this_dcfm=dcfm[i]
+            db[i]=np.sum(this_dcfm)
+        for i in xrange(w.shape[0]):
+            this_fm=fm[ct[0,i]]
+            this_w=w[i]
+            this_dcfm=dcfm[ct[1,i]]
+            this_dfm=dconv2_in(this_dcfm,this_fm,this_w)
+            dfm[ct[0,i]]=dfm[ct[0,i]]+this_dfm
+            dw[i]=dconv2_kernel(this_dcfm,this_fm,this_w)
+        return [dfm,dw,db]
+    def trian(self,input,target): 
+        cfm1,sfm1,cfm2,sfm2=self.forwardPropConv(input)
+        bp_input=sfm2.reshape(self.bp1.n_in)
+        bp1_out,bp2_out=self.forwradPropBp(bp_input)
+        out=max_with_index(bp2_out)
+        if out[0]==target:
+            self.noErrors+=1
+        eta=self.eta
+        w1=self.bp1.w
+        b1=self.bp1.b
+        w2=self.bp2.w
+        b2=self.bp2.b
+        dsfm,dw1,db1,dw2,db2=self.backPropBp(bp_input, target, bp1_out, bp2_out, w1, w2, b1, b2)
+        self.bp1.w=self.bp1.w-dw1*eta
+        self.bp1.b=self.bp1.b-db1*eta
+        self.bp2.w=self.bp2.w-dw2*eta
+        self.bp2.b=self.bp2.b-db2*eta
+        dsfm=dsfm.reshape(sfm2.shape)
+        sw2=self.conv2.sw
+        sb2=self.conv2.sb
+        ct2=self.conv2.ct
+        cw2=self.conv2.cw
+        cb2=self.conv2.cb
+        pool_shape=self.pool_shape
+        stride=self.stride
+        dcfm2,dsw2,dsb2=self.backPropSubsampling(dsfm, sfm2,cfm2, sw2, sb2, pool_shape, stride)
+        dsfm1,dcw2,dcb2=self.backPropConvulution(dcfm2, cfm2, sfm1, ct2, cw2, cb2)
+        self.conv2.sw=self.conv2.sw-dsw2*eta
+        self.conv2.sb=self.conv2.sb-dsb2*eta
+        self.conv2.cw=self.conv2.cw-dcw2*eta
+        self.conv2.cb=self.conv2.cb-dcb2*eta
+        sw1=self.conv1.sw
+        sb1=self.conv1.sb
+        ct1=self.conv1.ct
+        cw1=self.conv1.cw
+        cb1=self.conv1.cb
+        dcfm1,dsw1,dsb1=self.backPropSubsampling(dsfm1, sfm1,cfm1, sw1, sb1, pool_shape, stride)
+        dfm,dcw1,dcb1=self.backPropConvulution(dcfm1, cfm1, input, ct1, cw1, cb1)
+        self.conv1.sw=sw1-dsw1*eta
+        self.conv1.sb=sb1-dsb1*eta
+        self.conv1.cw=cw1-dcw1*eta
+        self.conv1.cb=cb1-dcb1*eta
+        #print(out)
+def load_data(path):
+    f=gzip.open(path,'rb')
+    train_set,valid_set,test_set=cPickle.load(f)
+    del f.f
+    return [train_set,valid_set,test_set]
+if __name__=='__main__':
+    gc.enable()
+    gc.set_debug(gc.DEBUG_COLLECTABLE | gc.DEBUG_UNCOLLECTABLE | gc.DEBUG_INSTANCES | gc.DEBUG_OBJECTS)
+    train_set,valid_set,test_set=load_data('d:/data/mnist.pkl.gz')
+    num=train_set[0].shape[0]
+    cnn=convnet([28,28])
+    for train in xrange(1,21):
+        cnn.noErrors=0
+        print("第%d次训练"%(train))
+        for i in xrange(1,num+1):
+            image=train_set[0][i-1]
+            data=image.reshape([1,28,28])
+            target=train_set[1][i-1]
+            cnn.trian(data, target)
+            if i%1000==0:
+                print("train %d,noErrors %d\n"%(i,cnn.noErrors)) 
+                _unreachable = gc.collect()
+                print("unreachable %d\n"%(_unreachable))
+        if train%cnn.step==0:
+            cnn.eta=cnn.eta*cnn.decay
+            del data
+            del image
+```
+

From b996445b9c12f3599839e71b1cc52c6bbbdb22a3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 17 May 2018 08:32:19 +0800
Subject: [PATCH 0950/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index 06f26a30..5b598022 100644
--- a/README.md
+++ b/README.md
@@ -16,7 +16,6 @@
 * 2016.10.Hybrid computing using a neural network with dynamic external memory
 * 2017.10.Mastering the game of Go without human knowledge
 
-
 #### 机器学习步骤框架
 * 把数据拆分为训练集合测试集
 * 用训练集合训练集的特征向量来训练算法

From c51291a25490a47bc0ab14a7e016f6f765704a41 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 May 2018 08:22:32 +0800
Subject: [PATCH 0951/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index ed0b9df2..7952183e 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -41,7 +41,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Hopfield神经网络
 
-Hopfield提出了连续和离散的Hopfield神经网络模型，并采用全互联型神经网络尝试对非多项式复杂度的旅行商问题（Travelling Salesman Problem，TSP）进行了求解，促进神经网络的研究再次进入了蓬勃发展的时期
+Hopfield提出了连续和离散的Hopfield神经网络模型，并采用全互联型神经网络尝试对非多项式复杂度的旅行商问题（Travelling Salesman Problem，TSP）进行了求解，促进神经网络的研究再次进入了蓬勃发展的时期。
 
 Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大器等元件组成的模拟电路实现了对网络神经元的描述，把最优化问题的目标函数转换成Hopfield神经网络的能量函数，通过网络能量函数最小化来寻找对应问题的最优解．Hopfield网络是一种循环神经网络，从输出到输入有反馈连接，典型的Hopfield神经网络模型如图所示．
 <p align="center">

From b5988698eb12e9e2ea4e8b23905800f20925a9f7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 May 2018 08:23:31 +0800
Subject: [PATCH 0952/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index 1f1ffe5e..8fe3e918 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -13,3 +13,4 @@
 
 #### Hopfield网络(Hopfield Network)
 
+Hopfield神经网络是一种递归神经网络，由约翰·霍普菲尔德在1982年发明。Hopfield网络是一种结合存储系统和二元系统的神经网络。它保证了向局部极小的收敛，但收敛到错误的局部极小值（local minimum），而非全局极小（global minimum）的情况也可能发生。Hopfield网络也提供了模拟人类记忆的模型。

From 8b8b66e5ed98be8c6cd4a8ac1a65a8f263771918 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 May 2018 13:34:01 +0000
Subject: [PATCH 0953/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index 5b598022..11bdcf53 100644
--- a/README.md
+++ b/README.md
@@ -21,7 +21,6 @@
 * 用训练集合训练集的特征向量来训练算法
 * 用学习来的算法运用在测试集上累评估算法(可能要设计到调整参数(parameter tuning) 用来验证集(validation set))
 
-
 #### 机器学习
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！

From 505936760edfc22cec9a0187217f2576fc8ca8bc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:27:14 +0800
Subject: [PATCH 0954/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index 8fe3e918..91304f0f 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -14,3 +14,18 @@
 #### Hopfield网络(Hopfield Network)
 
 Hopfield神经网络是一种递归神经网络，由约翰·霍普菲尔德在1982年发明。Hopfield网络是一种结合存储系统和二元系统的神经网络。它保证了向局部极小的收敛，但收敛到错误的局部极小值（local minimum），而非全局极小（global minimum）的情况也可能发生。Hopfield网络也提供了模拟人类记忆的模型。
+
+Hopfield提出了连续和离散的Hopfield神经网络模型，并采用全互联型神经网络尝试对非多项式复杂度的旅行商问题（Travelling Salesman Problem，TSP）进行了求解，促进神经网络的研究再次进入了蓬勃发展的时期。
+
+Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大器等元件组成的模拟电路实现了对网络神经元的描述，把最优化问题的目标函数转换成Hopfield神经网络的能量函数，通过网络能量函数最小化来寻找对应问题的最优解．Hopfield网络是一种循环神经网络，从输出到输入有反馈连接，典型的Hopfield神经网络模型如图所示．
+<p align="center">
+<img width="300" align="center" src="../../images/92.jpg" />
+</p>
+在图中每组运算放大器及其相关的电阻、电容组成的网络代表一个神经元。每个神经元有两组输入，一组是恒定的外部电流，另一组是来自其他运算放大器输出的正向或反向的反馈连接。假设第i个神经元的内部膜电位为Ui(i=1,2,…,n)，细胞膜的输入电容和传递电阻分别为Ci和Ri，神经元的输出电位为Vi，外部输入电流为Ii，并用电阻Rij(i，j=1,2,…,n)来模拟第i个和第j个神经元之间的突触特性。由基尔霍夫电流定律(Kirchhoff’s Cureent Law ,KCL)可知，放大器输入节点处的流入电流和流出电流保持平衡，亦即有下式成立：
+<p align="center">
+<img width="300" align="center" src="../../images/93.jpg" />
+</p>
+同时，每一个运算放大器模拟了神经元输入和输出之间的非线性特性，即有
+<p align="center">
+<img width="300" align="center" src="../../images/94.jpg" />
+</p>

From 96ec7c03737b050b3ecd2cce44f916daf03a7e1e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:30:27 +0800
Subject: [PATCH 0955/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index 91304f0f..dfd530b3 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -29,3 +29,12 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 <p align="center">
 <img width="300" align="center" src="../../images/94.jpg" />
 </p>
+
+其中，fi代表了第i个神经元的传递函数，并定义W=Rij-1 （i,j＝1,2,…,n）为网络的权系数矩阵．为证明连续型网络的稳定性，Hopfield定义了如下的能量函数：
+<p align="center">
+<img width="300" align="center" src="../../images/95.jpg" />
+</p>
+
+其中，f-1为神经元传递函数的反函数．经过推导后得出以下两点结论：一是对于具有单调递增传递函数且对称权系数矩阵的网络来说，其能量会随着时间的变化而趋于稳定；二是当且仅当网络中所有神经元的输出不再随时间变化时，则可以认为网络的能量保持不变。在将网络用于求解诸如旅行商的组合优化问题时，Hopfield将优化的目标函数转化为网络的能量函数，对应地将待求解问题的变量用网络中神经元的状态来表示。由这样的表示方式可知当网络的能量衰减到稳定值时，问题的最优解也随之求出。
+
+Hopfield网络按网络输入和输出的数字形式不同可分为离散型和连续型两种网络,即：离散型Hopfield神经网络----DHNN(Discrete Hopfield Neural Network)；连续型Hopfield神经网络----CHNN(ContinuesHopfield Neural Network)。

From ecd520314c2baeb44f1c218079d4308edf7a79c9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:31:33 +0800
Subject: [PATCH 0956/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index dfd530b3..3da7e963 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -38,3 +38,11 @@ Hopfield强调工程实践的重要性，他利用电阻、电容和运算放大
 其中，f-1为神经元传递函数的反函数．经过推导后得出以下两点结论：一是对于具有单调递增传递函数且对称权系数矩阵的网络来说，其能量会随着时间的变化而趋于稳定；二是当且仅当网络中所有神经元的输出不再随时间变化时，则可以认为网络的能量保持不变。在将网络用于求解诸如旅行商的组合优化问题时，Hopfield将优化的目标函数转化为网络的能量函数，对应地将待求解问题的变量用网络中神经元的状态来表示。由这样的表示方式可知当网络的能量衰减到稳定值时，问题的最优解也随之求出。
 
 Hopfield网络按网络输入和输出的数字形式不同可分为离散型和连续型两种网络,即：离散型Hopfield神经网络----DHNN(Discrete Hopfield Neural Network)；连续型Hopfield神经网络----CHNN(ContinuesHopfield Neural Network)。
+
+DHNN结构：它是一种单层全反馈网络,共有n个神经元。每个神经元都通过连接权接收所有其它神经元输出反馈来的信息，其目的是为了让任一神经元的输出能接受所有神经元输出的控制,从而使各神经元能相互制约。
+
+DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）决定的，设计吸引子的核心就是如何设计一组合适的权值。为了使所设计的权值满足要求，权值矩阵应符合以下要求：(1)为保证异步方式工作时网络收敛，W应为对称阵；(2)为保证同步方式工作时网络收敛，W应为非负定对称阵；(3)保证给定的样本是网络的吸引子，并且要有一定的吸引域。
+
+具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
+
+CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。

From 201520ca3164749644e852f25527e730a7de44a0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:33:29 +0800
Subject: [PATCH 0957/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index 3da7e963..f8f51961 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -46,3 +46,11 @@ DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）
 具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
 
 CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
+
+#### 优缺点
+
+Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。
+
+Hopfield神经网络的提出就是与其实际应用密切相关。具有联系记忆的功能，具体为：
+
+联想记忆：输入--输出模式的各元素之间，并不存在一对一的映射关系，输入--输出模式的维数也不要求相同；联想记忆时，只给出输入模式部分信息，就能联想出完整的输出模式。即具有容错性。

From 73aea696fed79b6023878eb36fdd63a86bda5aef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:37:48 +0800
Subject: [PATCH 0958/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 74 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index f8f51961..7e6e6bc4 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -47,6 +47,80 @@ DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）
 
 CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
 
+
+#### 应用领域
+```python
+import numpy as np
+from random import randint, shuffle
+
+class InvalidWeightsException(Exception):
+    pass
+
+
+class InvalidNetworkInputException(Exception):
+    pass
+
+class HopfieldNetwork(object):
+    def __init__(self, num_inputs):
+        self._num_inputs = num_inputs
+        self._weights = np.random.uniform(-1.0, 1.0, (num_inputs, num_inputs))
+
+    def set_weights(self, weights):
+        """Update the weights array"""
+        if weights.shape != (self._num_inputs, self._num_inputs):
+            raise InvalidWeightsException()
+
+        self._weights = weights
+
+    def get_weights(self):
+        """Return the weights array"""
+        return self._weights
+    
+    def calculate_neuron_output(self, neuron, input_pattern):
+        """Calculate the output of the given neuron"""
+        num_neurons = len(input_pattern)
+
+        s = 0.0
+
+        for j in range(num_neurons):
+            s += self._weights[neuron][j] * input_pattern[j]
+
+        return 1.0 if s > 0.0 else -1.0
+
+    def run_once(self, update_list, input_pattern):
+        """Iterate over every neuron and update it's output"""
+        result = input_pattern.copy()
+
+        changed = False
+        for neuron in update_list:
+            neuron_output = self.calculate_neuron_output(neuron, result)
+
+            if neuron_output != result[neuron]:
+                result[neuron] = neuron_output
+                changed = True
+
+        return changed, result
+
+    def run(self, input_pattern, max_iterations=10):
+        """Run the network using the input data until the output state doesn't change
+        or a maximum number of iteration has been reached."""
+        iteration_count = 0
+
+        result = input_pattern.copy()
+
+        while True:
+            update_list = range(self._num_inputs)
+            shuffle(update_list)
+
+            changed, result = self.run_once(update_list, result)
+
+            iteration_count += 1
+
+            if not changed or iteration_count == max_iterations:
+                return result
+```
+
+
 #### 优缺点
 
 Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。

From e73c25b0b56d0b5df9aaec762aa636522b957075 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:38:20 +0800
Subject: [PATCH 0959/1406] Update ANN.0.8.md

---
 assets/src/ANN/ANN.0.8.md | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/assets/src/ANN/ANN.0.8.md b/assets/src/ANN/ANN.0.8.md
index 7e6e6bc4..dd265ac0 100644
--- a/assets/src/ANN/ANN.0.8.md
+++ b/assets/src/ANN/ANN.0.8.md
@@ -47,6 +47,13 @@ DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）
 
 CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
 
+#### 优缺点
+
+Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。
+
+Hopfield神经网络的提出就是与其实际应用密切相关。具有联系记忆的功能，具体为：
+
+联想记忆：输入--输出模式的各元素之间，并不存在一对一的映射关系，输入--输出模式的维数也不要求相同；联想记忆时，只给出输入模式部分信息，就能联想出完整的输出模式。即具有容错性。
 
 #### 应用领域
 ```python
@@ -121,10 +128,4 @@ class HopfieldNetwork(object):
 ```
 
 
-#### 优缺点
-
-Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。
 
-Hopfield神经网络的提出就是与其实际应用密切相关。具有联系记忆的功能，具体为：
-
-联想记忆：输入--输出模式的各元素之间，并不存在一对一的映射关系，输入--输出模式的维数也不要求相同；联想记忆时，只给出输入模式部分信息，就能联想出完整的输出模式。即具有容错性。

From a587fa96435b4cabf02503a08ac1fcee384bfd29 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 23 May 2018 21:44:51 +0800
Subject: [PATCH 0960/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 136abfc6..bc04ca7a 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -12,3 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 径向基函数网络(Radial Basis Function Network)
+
+在数学建模领域，径向基函数网络（Radial basis function network，缩写 RBF network）是一种使用径向基函数作为激活函数的人工神经网络。径向基函数网络的输出是输入的径向基函数和神经元参数的线性组合。径向基函数网络具有多种用途，包括包括函数近似法、时间序列预测、分类和系统控制。他们最早由布鲁姆赫德（Broomhead）和洛维（Lowe）在1988年建立。
+径向基函数网络通常有三层：输入层、隐藏层和一个非线性激活函数和线性径向基神经网络输出层。输入可以被建模为实数向量。输出是输入向量的一个标量函数。

From 3d3c9bda3a1f8799d62e3953a6b8a3de6c032b51 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 08:48:39 +0800
Subject: [PATCH 0961/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index bc04ca7a..3d0051b3 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -13,5 +13,7 @@
 
 #### 径向基函数网络(Radial Basis Function Network)
 
-在数学建模领域，径向基函数网络（Radial basis function network，缩写 RBF network）是一种使用径向基函数作为激活函数的人工神经网络。径向基函数网络的输出是输入的径向基函数和神经元参数的线性组合。径向基函数网络具有多种用途，包括包括函数近似法、时间序列预测、分类和系统控制。他们最早由布鲁姆赫德（Broomhead）和洛维（Lowe）在1988年建立。
+在数学建模领域，径向基函数网络（Radial basis function network，缩写 RBF network）是一种使用径向基函数作为激活函数的人工神经网络。
+RBF神经网络是基于人脑的神经元细胞对外界反应的局部性而提出的新颖的、有效的前馈式神经网络，具有良好的局部逼近特性。它的数学理论基础成形于1985年由Powell首先提出的多变量插值的径向基函数，1988年被Broomhead和Lowe应用到神经网络设计领域，最终形成了RBF神经网络。
+径向基函数网络的输出是输入的径向基函数和神经元参数的线性组合。径向基函数网络具有多种用途，包括包括函数近似法、时间序列预测、分类和系统控制。他们最早由布鲁姆赫德（Broomhead）和洛维（Lowe）在1988年建立。
 径向基函数网络通常有三层：输入层、隐藏层和一个非线性激活函数和线性径向基神经网络输出层。输入可以被建模为实数向量。输出是输入向量的一个标量函数。

From c7c915cf2de663e73d48b4bef7e5d903c38b951b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 08:50:27 +0800
Subject: [PATCH 0962/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 3d0051b3..e73a7590 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -16,4 +16,5 @@
 在数学建模领域，径向基函数网络（Radial basis function network，缩写 RBF network）是一种使用径向基函数作为激活函数的人工神经网络。
 RBF神经网络是基于人脑的神经元细胞对外界反应的局部性而提出的新颖的、有效的前馈式神经网络，具有良好的局部逼近特性。它的数学理论基础成形于1985年由Powell首先提出的多变量插值的径向基函数，1988年被Broomhead和Lowe应用到神经网络设计领域，最终形成了RBF神经网络。
 径向基函数网络的输出是输入的径向基函数和神经元参数的线性组合。径向基函数网络具有多种用途，包括包括函数近似法、时间序列预测、分类和系统控制。他们最早由布鲁姆赫德（Broomhead）和洛维（Lowe）在1988年建立。
-径向基函数网络通常有三层：输入层、隐藏层和一个非线性激活函数和线性径向基神经网络输出层。输入可以被建模为实数向量。输出是输入向量的一个标量函数。
+
+RBF神经网络是一种三层前馈神经网络。第一层为输入层，由信号源节点构成，将网络与外界环境连结起来，节点数由输入信号的维数确定；第二层为隐含层（径向基层），其节点由径向基函数构成，实现输入空间到隐层空间的非线性变换；第三层为输出层（线性层），对输入模式做出响应，其节点由隐含层节点给出的基函数的线性组合来计算。

From e67813131c54bf8fbc843907c7ddd74b1339aaa8 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 24 May 2018 08:53:46 +0800
Subject: [PATCH 0963/1406] change page of ANN

---
 assets/images/331.jpg     | Bin 0 -> 43376 bytes
 assets/src/ANN/ANN.0.9.md |   4 ++++
 2 files changed, 4 insertions(+)
 create mode 100644 assets/images/331.jpg

diff --git a/assets/images/331.jpg b/assets/images/331.jpg
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diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index e73a7590..6307f7c7 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -18,3 +18,7 @@ RBF神经网络是基于人脑的神经元细胞对外界反应的局部性而
 径向基函数网络的输出是输入的径向基函数和神经元参数的线性组合。径向基函数网络具有多种用途，包括包括函数近似法、时间序列预测、分类和系统控制。他们最早由布鲁姆赫德（Broomhead）和洛维（Lowe）在1988年建立。
 
 RBF神经网络是一种三层前馈神经网络。第一层为输入层，由信号源节点构成，将网络与外界环境连结起来，节点数由输入信号的维数确定；第二层为隐含层（径向基层），其节点由径向基函数构成，实现输入空间到隐层空间的非线性变换；第三层为输出层（线性层），对输入模式做出响应，其节点由隐含层节点给出的基函数的线性组合来计算。
+
+<p align="center">
+<img width="300" align="center" src="../../images/331.jpg" />
+</p>
\ No newline at end of file

From acb2124a996adefaddfd49726f77050b87a381a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Thu, 24 May 2018 23:20:31 +0800
Subject: [PATCH 0964/1406] change page of ann

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HcmV?d00001


From edc29f540d68c9694a2c5a1a13d80cd92f49251f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:21:23 +0800
Subject: [PATCH 0965/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 6307f7c7..a3e19cdd 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -20,5 +20,5 @@ RBF神经网络是基于人脑的神经元细胞对外界反应的局部性而
 RBF神经网络是一种三层前馈神经网络。第一层为输入层，由信号源节点构成，将网络与外界环境连结起来，节点数由输入信号的维数确定；第二层为隐含层（径向基层），其节点由径向基函数构成，实现输入空间到隐层空间的非线性变换；第三层为输出层（线性层），对输入模式做出响应，其节点由隐含层节点给出的基函数的线性组合来计算。
 
 <p align="center">
-<img width="300" align="center" src="../../images/331.jpg" />
-</p>
\ No newline at end of file
+<img width="500" align="center" src="../../images/331.jpg" />
+</p>

From b512967caf5bdb0051f315df69677b15e44479ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:22:52 +0800
Subject: [PATCH 0966/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index a3e19cdd..2541c81c 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -22,3 +22,8 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <p align="center">
 <img width="500" align="center" src="../../images/331.jpg" />
 </p>
+
+径向基神经网络的激活函数采用径向基函数，通常定义为空间任一点到某一中心之间欧氏距离的单调函数。径向基神经网络的激活函数是以输入向量和权值向量之间的距离<img width="70" align="center" src="../../images/332.jpg" /> 为自变量的。径向神经网络的激活函数一般表达式为
+<p align="center">
+<img width="300" align="center" src="../../images/333.jpg" />
+</p>

From aeeb888d725ab83ddc673125b53cf1595f0bdeb7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:25:24 +0800
Subject: [PATCH 0967/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 2541c81c..1c9a7d45 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -27,3 +27,15 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <p align="center">
 <img width="300" align="center" src="../../images/333.jpg" />
 </p>
+
+随着权值和输入向量之间距离的减少，网络输出是递增的，当输入向量和权值向量一致时，神经元输出1。b为阈值，用于调整神经元的灵敏度。利用径向基神经元和线性神经元可以建立广义回归神经网络，该种神经网络适用于函数逼近方面的应用；径向基神经元和竞争神经元可以组件概率神经网络，此种神经网络适用于解决分类问题。输出层和隐含层所完成的任务是不同的，因而它们的学习策略也不相同。输出层是对线性权进行调整，采用的是线性优化策略，因而学习速度较快。而隐函数是对激活函数（格林函数或高斯函数，一般为高斯函数）的参数进行调整，采用的是非线性优化策略，因而学习速度较慢。
+
+尽管RBF网络的输出是隐单元输出的线性加权和，学习速度加快，但并不等于径向基神经网络就可以取代其他前馈网络。这是因为径向神经网络很可能需要比BP网络多得多的隐含层神经元来完成工作。
+
+径向基神经网络中需要求解的参数有三个基函数的中心、方差以及隐含层到输出层的权值。根据径向基函数中心选取方法的不同，RBF网络有多种学习方法。下面介绍自组织选取中心的RBF神经网络学习法。此方法由两个阶段组成：
+
+* 自组织学习阶段，此阶段为无监督学习过程，求解隐含层基函数的中心与方差。
+
+* 监督学习阶段，此阶段求解隐含层到输出层之间的权值。
+
+监督学习阶段，此阶段求解隐含层到输出层之间的权值。

From ae65dab0b358d9ae8491ecdf72e3011fe3ec63d2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:25:59 +0800
Subject: [PATCH 0968/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 1c9a7d45..8f246ba9 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -38,4 +38,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 
 * 监督学习阶段，此阶段求解隐含层到输出层之间的权值。
 
-监督学习阶段，此阶段求解隐含层到输出层之间的权值。
+径向基神经网络中常用的径向基函数是高斯函数，因此径向基神经网络的激活函数可表示为：
+<p align="center">
+<img width="300" align="center" src="../../images/334.jpg" />
+</p>

From ad2d2854915e07a961cf23cec9721729776cf9bc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:27:19 +0800
Subject: [PATCH 0969/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 8f246ba9..bc3f73c5 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -42,3 +42,18 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <p align="center">
 <img width="300" align="center" src="../../images/334.jpg" />
 </p>
+
+由此可得，径向基神经网络的结构可得到网络的输出为：
+
+<p align="center">
+<img width="300" align="center" src="../../images/335.jpg" />
+</p>
+
+其中<img width="60" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
+
+如果d是样本的期望输出值，那么基函数的方差可表示为：
+<p align="center">
+<img width="300" align="center" src="../../images/337.jpg" />
+</p>
+
+

From f4542181ed8d6f384efafca4b13c8abdc911b9e9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:29:30 +0800
Subject: [PATCH 0970/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index bc3f73c5..9056f972 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -46,7 +46,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 由此可得，径向基神经网络的结构可得到网络的输出为：
 
 <p align="center">
-<img width="300" align="center" src="../../images/335.jpg" />
+<img width="360" align="center" src="../../images/335.jpg" />
 </p>
 
 其中<img width="60" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
@@ -56,4 +56,8 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="300" align="center" src="../../images/337.jpg" />
 </p>
 
+基于K-均值聚类方法求取基函数中心c:
+* 网络初始化 随机选取h个训练样本作为聚类中心<img width="60" align="center" src="../../images/338.jpg" />
+* 将输入的训练样本集合按最近邻规则分组，按照<img width="60" align="center" src="../../images/336.jpg" /> 与中心为<img width="60" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="60" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="600" align="center" src="../../images/339.jpg" />之中。
+
 

From 8185a86eae925c4cb6c61c608714612d00b6acc4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:30:28 +0800
Subject: [PATCH 0971/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 9056f972..324683de 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -58,6 +58,6 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 
 基于K-均值聚类方法求取基函数中心c:
 * 网络初始化 随机选取h个训练样本作为聚类中心<img width="60" align="center" src="../../images/338.jpg" />
-* 将输入的训练样本集合按最近邻规则分组，按照<img width="60" align="center" src="../../images/336.jpg" /> 与中心为<img width="60" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="60" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="600" align="center" src="../../images/339.jpg" />之中。
+* 将输入的训练样本集合按最近邻规则分组，按照<img width="60" align="center" src="../../images/336.jpg" /> 与中心为<img width="60" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="60" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="60" align="center" src="../../images/339.jpg" />之中。
 
 

From 793cca5968ded39cb0a9504bbc8a3b718fb0615f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:34:32 +0800
Subject: [PATCH 0972/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 22 +++++++++++++++++++---
 1 file changed, 19 insertions(+), 3 deletions(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 324683de..17356430 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -49,7 +49,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="360" align="center" src="../../images/335.jpg" />
 </p>
 
-其中<img width="60" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
+其中<img width="50" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
 
 如果d是样本的期望输出值，那么基函数的方差可表示为：
 <p align="center">
@@ -57,7 +57,23 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 </p>
 
 基于K-均值聚类方法求取基函数中心c:
-* 网络初始化 随机选取h个训练样本作为聚类中心<img width="60" align="center" src="../../images/338.jpg" />
-* 将输入的训练样本集合按最近邻规则分组，按照<img width="60" align="center" src="../../images/336.jpg" /> 与中心为<img width="60" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="60" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="60" align="center" src="../../images/339.jpg" />之中。
 
+* 网络初始化 随机选取h个训练样本作为聚类中心<img width="50" align="center" src="../../images/338.jpg" />
+* 将输入的训练样本集合按最近邻规则分组，按照<img width="50" align="center" src="../../images/336.jpg" /> 与中心为<img width="50" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="50" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="50" align="center" src="../../images/339.jpg" />之中。
+* 重新调整聚类中心 计算各个聚类集合<img width="50" align="center" src="../../images/339.jpg" /> 中训练样本的平均值，即新的聚类中心<img width="50" align="center" src="../../images/338.jpg" />， 如果新的聚类中心不再发生变化，所得到的<img width="50" align="center" src="../../images/338.jpg" />就是RBF神经网络最终的基函数中心，否则返回上一步进行下一轮求解.
 
+求解方差<img width="50" align="center" src="../../images/339.jpg" />:
+
+* 该RBF神经网络的基函数为高斯函数，因此方差<img width="50" align="center" src="../../images/339.jpg" />可由下式求解得出:
+<p align="center">
+<img width="300" align="center" src="../../images/340.jpg" />
+</p>
+
+其中<img width="50" align="center" src="../../images/343.jpg" />是所选取中心之间的最大距离.
+
+计算隐含层和输出层之间的权值：
+
+* 用最小二乘法直接计算得到：
+<p align="center">
+<img width="300" align="center" src="../../images/342.jpg" />
+</p>

From 186f24b7d89189a0980cb5c71ce8f78d1d24c80a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:37:35 +0800
Subject: [PATCH 0973/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 17356430..d04be112 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -58,18 +58,18 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 
 基于K-均值聚类方法求取基函数中心c:
 
-* 网络初始化 随机选取h个训练样本作为聚类中心<img width="50" align="center" src="../../images/338.jpg" />
-* 将输入的训练样本集合按最近邻规则分组，按照<img width="50" align="center" src="../../images/336.jpg" /> 与中心为<img width="50" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="50" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="50" align="center" src="../../images/339.jpg" />之中。
-* 重新调整聚类中心 计算各个聚类集合<img width="50" align="center" src="../../images/339.jpg" /> 中训练样本的平均值，即新的聚类中心<img width="50" align="center" src="../../images/338.jpg" />， 如果新的聚类中心不再发生变化，所得到的<img width="50" align="center" src="../../images/338.jpg" />就是RBF神经网络最终的基函数中心，否则返回上一步进行下一轮求解.
+* 网络初始化 随机选取h个训练样本作为聚类中心<img width="30" align="center" src="../../images/338.jpg" />
+* 将输入的训练样本集合按最近邻规则分组，按照<img width="30" align="center" src="../../images/336.jpg" /> 与中心为<img width="30" align="center" src="../../images/338.jpg" />之间的欧式距离将<img width="30" align="center" src="../../images/336.jpg" />分配到输入样本的各个聚类集合<img width="30" align="center" src="../../images/339.jpg" />之中。
+* 重新调整聚类中心 计算各个聚类集合<img width="30" align="center" src="../../images/339.jpg" /> 中训练样本的平均值，即新的聚类中心<img width="30" align="center" src="../../images/338.jpg" />， 如果新的聚类中心不再发生变化，所得到的<img width="30" align="center" src="../../images/338.jpg" />就是RBF神经网络最终的基函数中心，否则返回上一步进行下一轮求解.
 
-求解方差<img width="50" align="center" src="../../images/339.jpg" />:
+求解方差<img width="30" align="center" src="../../images/340.jpg" />:
 
-* 该RBF神经网络的基函数为高斯函数，因此方差<img width="50" align="center" src="../../images/339.jpg" />可由下式求解得出:
+* 该RBF神经网络的基函数为高斯函数，因此方差<img width="30" align="center" src="../../images/340.jpg" />可由下式求解得出:
 <p align="center">
-<img width="300" align="center" src="../../images/340.jpg" />
+<img width="300" align="center" src="../../images/341.jpg" />
 </p>
 
-其中<img width="50" align="center" src="../../images/343.jpg" />是所选取中心之间的最大距离.
+其中<img width="30" align="center" src="../../images/342.jpg" />是所选取中心之间的最大距离.
 
 计算隐含层和输出层之间的权值：
 

From 98ed0a449ddb947e46ae5e2af893102f4d3bd0f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:39:39 +0800
Subject: [PATCH 0974/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index d04be112..c6fcb54a 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -23,7 +23,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="500" align="center" src="../../images/331.jpg" />
 </p>
 
-径向基神经网络的激活函数采用径向基函数，通常定义为空间任一点到某一中心之间欧氏距离的单调函数。径向基神经网络的激活函数是以输入向量和权值向量之间的距离<img width="70" align="center" src="../../images/332.jpg" /> 为自变量的。径向神经网络的激活函数一般表达式为
+径向基神经网络的激活函数采用径向基函数，通常定义为空间任一点到某一中心之间欧氏距离的单调函数。径向基神经网络的激活函数是以输入向量和权值向量之间的距离<img width="30" align="center" src="../../images/332.jpg" /> 为自变量的。径向神经网络的激活函数一般表达式为
 <p align="center">
 <img width="300" align="center" src="../../images/333.jpg" />
 </p>
@@ -69,11 +69,11 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="300" align="center" src="../../images/341.jpg" />
 </p>
 
-其中<img width="30" align="center" src="../../images/342.jpg" />是所选取中心之间的最大距离.
+其中<img width="60" align="center" src="../../images/342.jpg" />是所选取中心之间的最大距离.
 
 计算隐含层和输出层之间的权值：
 
 * 用最小二乘法直接计算得到：
 <p align="center">
-<img width="300" align="center" src="../../images/342.jpg" />
+<img width="300" align="center" src="../../images/343.jpg" />
 </p>

From ae552d57bacd75ef61f80d0c9e767ad2843136fc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:40:15 +0800
Subject: [PATCH 0975/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index c6fcb54a..1122c416 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -23,7 +23,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="500" align="center" src="../../images/331.jpg" />
 </p>
 
-径向基神经网络的激活函数采用径向基函数，通常定义为空间任一点到某一中心之间欧氏距离的单调函数。径向基神经网络的激活函数是以输入向量和权值向量之间的距离<img width="30" align="center" src="../../images/332.jpg" /> 为自变量的。径向神经网络的激活函数一般表达式为
+径向基神经网络的激活函数采用径向基函数，通常定义为空间任一点到某一中心之间欧氏距离的单调函数。径向基神经网络的激活函数是以输入向量和权值向量之间的距离<img width="60" align="center" src="../../images/332.jpg" /> 为自变量的。径向神经网络的激活函数一般表达式为
 <p align="center">
 <img width="300" align="center" src="../../images/333.jpg" />
 </p>
@@ -49,7 +49,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 <img width="360" align="center" src="../../images/335.jpg" />
 </p>
 
-其中<img width="50" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
+其中<img width="30" align="center" src="../../images/336.jpg" />为第p个输入样本。h为隐含层的结点数。
 
 如果d是样本的期望输出值，那么基函数的方差可表示为：
 <p align="center">

From d8583067ba7b47f2eb48b29a6fbb00908cbc6f7c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 May 2018 23:41:50 +0800
Subject: [PATCH 0976/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 356 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 355 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index 1122c416..bc3e482a 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -75,5 +75,359 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 
 * 用最小二乘法直接计算得到：
 <p align="center">
-<img width="300" align="center" src="../../images/343.jpg" />
+<img width="500" align="center" src="../../images/343.jpg" />
 </p>
+
+
+#### 应用示例
+```python
+from __future__ import division
+
+import random
+import pylab
+import math
+
+
+SAMPLES = 75
+EPOCHS = 100
+
+TESTS = 12
+RUNS = 3
+MOD = 12
+
+
+def h(x):
+  """Function to approximate: y = 0.5 + 0.4sin(2πx)."""
+  # note: pylab.sin can accept a numpy.ndarray, but math.sin cannot
+  return 0.5 + 0.4*pylab.sin(pylab.pi*2*x)
+
+def noise(x):
+  """Add uniform noise in intervale [-0.1, 0.1]."""
+  return x + random.uniform(-0.1, 0.1)
+
+def sample(n):
+  """Return sample of n random points uniformly distributed in [0, 1]."""
+  a = [random.random() for x in range(n)]
+  a.sort()
+  return a
+
+def gaussian(radial, x):
+  """Return gaussian radial function.
+  Args:
+    radial: (num, num) of gaussian (base, width^2) pair
+    x: num of input
+  Returns:
+    num of gaussian output
+  """
+  base, width2 = radial
+  power = -1 / width2 / 2 * (x-base)**2
+  y = pylab.exp(power)
+  return y
+
+
+def output(radials, weights, x):
+  """Return set of linearly combined gaussian functions.
+  Args:
+    radials: [(num, num) of (base, width^2) pairs
+    weights: [num] of radial weights, |weights| -1 = |radials|
+    x: num of input
+  Returns:
+    num of linear combination of radial functions.
+  """
+  y = 0
+  for radial, weight in zip(radials, weights[:-1]):
+    y += gaussian(radial, x) * weight
+  # add bias
+  y += weights[-1]
+  return y
+
+
+def update_weights(eta, weights, radials, x, y, d):
+  """Update weight vector.
+  Returns:
+    [num] of updated weight vector, len = |weights|
+  """
+  new_weights = []
+  err = d-y
+  for radial, weight in zip(radials, weights[:-1]):
+    w = weight + (eta * err * gaussian(radial, x))
+    new_weights.append(w)
+  # update bias
+  w = weights[-1] + (eta * err)
+  new_weights.append(w)
+  return new_weights
+
+
+def k_means(input, k):
+  """Return n Gaussian centers computed by K-means algorithm from sample x.
+  Args:
+    input: [num] of input vector
+    k: int number of bases, <= |set(input)|
+  Returns:
+    [(num, [num])] k-size list of (center, input cluster) pairs.
+  """
+  # initialize k bases as randomly selected unique elements from input
+  bases = random.sample(set(input), k)
+
+  # place all inputs in the first cluster to initialize
+  clusters = [ (x, 0) for x in input ]
+  updated = True
+
+  while(updated):
+    updated=False
+    for i in range(0, len(clusters)):
+      x, m = clusters[i]
+      distances = [(abs(b-x), j) for j, b in enumerate(bases)]
+      d, j = min(distances)
+      # update to move x to a new base cluster
+      if m != j:
+        updated = True
+        clusters[i] = (x, j)
+
+    # update bases
+    if updated:
+      base_sums = [ [0,0] for s in range(k)]
+      for x, m in clusters:
+        base_sums[m][0] += x
+        base_sums[m][1] += 1
+      # check for divide by zero errors
+      new_bases = []
+      for s, n in base_sums:
+        # avoid rare edge case, <1% @ n=25
+        # division by zero: select a new base from input
+        if n == 0:
+          base = random.sample(set(input), 1)[0]
+        else:
+          base = s / n
+        new_bases.append(base)
+      bases = new_bases
+
+  # generate returned value
+  response = [ (b, []) for b in bases ]
+  for x, m in clusters:
+    response[m][1].append(x)
+    
+  return response
+      
+
+def variance_width(k_meaned_x):
+  """Return mean, variance pairs computed from k_means(x, k).
+  Args:
+    k_meaned_x: [(num, [num])] of (base, input cluster) pairs
+  Returns:
+    [(num, num)] of (center, width^2) pairs.
+  """
+  response = []
+  for base, cluster in k_meaned_x:
+    if len(cluster) > 1:
+      var = sum([(base-x)**2 for x in cluster]) / len(cluster)
+      # this actually produces excellent approximations
+      # var = sum([(base-x)**2 for x in cluster])
+    else:
+      var = None
+    response.append((base, var))
+
+  # set |cluster| widths to mean variance of other clusters
+  vars = [v for b, v in response if v]
+  if len(vars) == 0:
+    raise Exception("No variance: cannot compute mean variance")
+  else:
+    var_mean = sum(vars) / len(vars)
+
+  for i in range(len(response)):
+    base, var = response[i]
+    if not var:
+      response[i] = (base, var_mean)
+
+  return response
+
+
+def shared_width(k_meaned_x):
+  """Return shared gaussian widths computed from k_means(x, k).
+  Args:
+    k_meaned_x: [(num, [num])] of (base, input cluster) pairs
+  Returns:
+    [(num, num)] of (center, width^2) pairs.
+  """
+  assert(len(k_meaned_x) > 1)
+  # ignore clusters
+  bases = [b for b, cluster in k_meaned_x]
+  # compute distances between adjancent bases
+  s_bases = bases[:]
+  s_bases.sort()
+  distances = map(lambda p: abs(p[0]-p[1]), zip(s_bases, s_bases[1:]))
+  max_d = max(distances)
+  sigma_sq = (max_d / 2**0.5)**2
+  # map to outputs 
+  response = [(b, sigma_sq) for b in bases]
+  return response
+
+
+def plot_instance(name, x, ideal_y, measured_y, trained_y, new_x, estimated_y):
+  """Plot function graph, save to file.
+  Effect: saves png file of plot to currect directory.
+  NOTE: use local graph variable
+  Args:
+    name: str of plot name, used in file name like "name.png"
+    x: [num] input vector
+    ideal_y: [num] ideal output vector
+    measured_y: [num] noisy output vector
+    trained_y: [num] trained output vector
+    new_x: [num] new input sample not used in training
+    estimated_y: [num] estimated output from trained RBN
+  """
+  # plot graph
+  pylab.rc('text', usetex=True)
+  pylab.rc('font', family='serif')
+  pylab.xlabel('$x$')
+  pylab.ylabel('$y = 0.5 + 0.4\sin(2 \pi x)$')
+  pylab.title('RBF Network: %s' % name)
+  pylab.plot(x, ideal_y, 'g', label="Ideal")
+  pylab.plot(x, measured_y, 'bo', label="Measured")
+  pylab.plot(x, trained_y, 'y', label="Trained")
+  pylab.plot(new_x, estimated_y, 'r', label="Generalized")
+  pylab.legend()
+  #  pylab.grid(True)
+  filename = name
+  filename = filename.replace(' ', '_').replace('\\', '').replace('$', '')
+  filename = filename.replace(',', '')
+  # save figure
+  pylab.savefig("%s.png" % filename)
+  # clear this figure
+  # note: use http://matplotlib.sourceforge.net/users/artists.html#artist-tutorial
+  #  in the future
+  pylab.clf()
+  pylab.cla()
+
+  
+def error(actual, expected):
+  """Return error from actual to expected.
+  Args
+    actual: [num] of sampled output
+    expected: [num] of expected ouput, ||expected|| = ||actual||
+  Returns:
+    num of average distance between actual and expected
+  """
+  sum_d = 0
+  for a, e in zip(actual, expected):
+    sum_d += abs(a-e)
+  err = sum_d / len(expected)
+  return err
+
+
+def run_test(eta, k, tests=TESTS, runs=RUNS, f_width=variance_width, graph_mod=MOD):
+  """Run an RBF training test set; plot, return errors from results.
+  Args:
+    eta: num of training rate
+    k: num of bases
+    tests: num of sample set iterations
+    runs: num of network generation iterations
+    f_width: function to generate radial widths
+    graph_mod: num of after how many iterations to plot a graph
+  Returns:
+    {str: [num]} such that n = (tests*runs) and:
+      "sample_err": [num] of n sampling errors
+      "train_err": [num] of n training errors
+      "gen_err": [num] of n estimation errors
+  """
+  
+  results = {
+    "sample_err": [],
+    "train_err": [],
+    "gen_err": [],
+    }
+
+  f_name = f_width.__name__.capitalize().split('_')[0]
+  for test in range(1,tests+1):
+
+    print "## K=%d, eta=%.2f, Test=%d" % (k, eta, test)
+
+    # compute input samples
+    input = sample(SAMPLES)
+    test_input = sample(SAMPLES)
+    # compute desired and ideal outputs
+    ideal_y = map(h, input)
+    test_ideal_y = map(h, test_input)
+    measured_y = map(noise, ideal_y)
+
+    # estimate each sample three times
+    for run in range(1,runs+1):
+      # initialize K radials
+      radials = f_width(k_means(input, k))
+      # k+1 weights, last weight is bias
+      weights = [random.uniform(-0.5, 0.5) for x in range(k+1)]
+      # train all epochs
+      for i in range(EPOCHS):
+        # train one epoch
+        for x, d in zip(input, measured_y):
+          y = output(radials, weights, x)
+          weights = update_weights(eta, weights, radials, x, y, d)
+
+      # examine results
+      trained_y = map(lambda x: output(radials, weights, x), input)
+      estimated_y = map(lambda x: output(radials, weights, x), test_input)
+      sample_err = error(measured_y, ideal_y)
+      train_err = error(trained_y, measured_y)
+      gen_err = error(estimated_y, test_ideal_y)
+      
+      # save results
+      results["sample_err"].append(sample_err)
+      results["train_err"].append(train_err)
+      results["gen_err"].append(gen_err)
+
+#      print "Run: %d, Sample: %.4f, Train: %.4f, General: %.4f" \
+#        % (run, sample_err, train_err, gen_err)
+
+      # graph some set of results
+      iteration = (test-1)*runs + run
+      if (iteration % graph_mod) == 0:
+#        print "Graphing Test=%d, Run=%d" % (test, run)
+        name = "%s $K=%d, \eta =%.2f, E=%.3f$ (%d-%d)" % \
+          (f_name, k, eta, gen_err, test, run)
+        plot_instance( \
+          name, input, ideal_y, measured_y, trained_y, test_input, estimated_y)
+  return results
+
+
+def stats(values):
+  """Return tuple of common statistical measures.
+  Returns:
+    (num, num, num, num) as (mean, std, min, max)
+   """
+  mean = sum(values) / len(values)
+  sum_sqs = reduce(lambda x, y: x + y*y, values)
+  var = sum([(mean-x)**2 for x in values]) / len(values)
+  var = (sum_sqs - len(values)*mean**2) / len(values)
+  std = var**0.5
+  min_var, max_var = min(values), max(values)
+  return (mean, std, min_var, max_var)
+
+
+def main():
+  random.seed()
+
+  # need final report
+  for f_width in (variance_width, shared_width):
+    for eta in (0.01, 0.02):
+      for k in (5, 10, 15, 20, 25):
+      
+        print ""
+        print "BEGIN PARAMETER TEST SUITE"
+        print "K=%d, eta=%.2f, f_width=%s, Tests=%d, Runs=%d" % \
+          (k, eta, f_width.__name__, TESTS, RUNS)
+        print "+++++++++++++++++++++++++++++++++++"
+        r = run_test(k=k, eta=eta, f_width=f_width)
+        print "+++++++++++++++++++++++++++++++++++"
+        print "RESULTS"
+        print "K=%d, eta=%.2f, f_width=%s, Tests=%d, Runs=%d" % \
+          (k, eta, f_width.__name__, TESTS, RUNS)
+        for name, values in r.items():
+          print name
+          print "mean=%.4f, std=%.4f, min=%.4f, max=%.4f" % \
+            stats(values)
+        print "+++++++++++++++++++++++++++++++++++"
+               
+
+if __name__ == "__main__":
+  main()
+```

From b9d42df4bef5ba1308c8f7bfcf8120504530366a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 25 May 2018 08:45:34 +0800
Subject: [PATCH 0977/1406] Update ANN.0.9.md

---
 assets/src/ANN/ANN.0.9.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.9.md b/assets/src/ANN/ANN.0.9.md
index bc3e482a..4702774a 100644
--- a/assets/src/ANN/ANN.0.9.md
+++ b/assets/src/ANN/ANN.0.9.md
@@ -40,7 +40,7 @@ RBF神经网络是一种三层前馈神经网络。第一层为输入层，由
 
 径向基神经网络中常用的径向基函数是高斯函数，因此径向基神经网络的激活函数可表示为：
 <p align="center">
-<img width="300" align="center" src="../../images/334.jpg" />
+<img width="360" align="center" src="../../images/334.jpg" />
 </p>
 
 由此可得，径向基神经网络的结构可得到网络的输出为：

From 46a56657c6b15b54f1c7b8cfd2932d778de73e76 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 25 May 2018 21:53:55 +0800
Subject: [PATCH 0978/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index f233881e..387c5a8a 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 受限玻尔兹曼机(Restricted Boltzmann Machine)
+受限玻尔兹曼机（Restricted Boltzmann Machine，RBM）是一种可用随机神经网络（stochastic neural network）来解释的概率图模型（probabilistic graphical model）。RBM是Smolensky于1986年在波尔兹曼机（Boltzmann Machine，BM）基础上提出的，所谓“随机”是指网络中的神经元是随机神经元，输出状态只有两种（未激活和激活），状态的具体取值根据概率统计法则来决定。RBM理论是Hinton在2006年提出基于RBM的（Deep Belief Network）模型，大量学者开始研究RBM的理论及其应用。
 
 受限玻尔兹曼机(Restricted Boltzmann Machine)是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。
 BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层和多个隐层组成，网络节点分为可见单元(visible unit)和隐单元(hidden unit)，用可见单元和隐单元来表达随机网络与随机环境的学习模型，通过权值表达单元之间的相关性。
@@ -21,3 +22,5 @@ BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层
 </p>
 
 Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。
+
+受限玻尔兹曼机（Restricted Boltzmann Machine，RBM）是一种可用随机神经网络（stochastic neural network）来解释的概率图模型（probabilistic graphical model）。RBM是Smolensky于1986年在波尔兹曼机（Boltzmann Machine，BM）基础上提出的，所谓“随机”是指网络中的神经元是随机神经元，输出状态只有两种（未激活和激活），状态的具体取值根据概率统计法则来决定。RBM理论是Hinton在2006年提出基于RBM的（Deep Belief Network）模型，大量学者开始研究RBM的理论及其应用。

From 450d926a202df5a359cd392edbea317d404eb43c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 25 May 2018 21:55:37 +0800
Subject: [PATCH 0979/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 387c5a8a..25675b17 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -23,4 +23,3 @@ BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层
 
 Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。
 
-受限玻尔兹曼机（Restricted Boltzmann Machine，RBM）是一种可用随机神经网络（stochastic neural network）来解释的概率图模型（probabilistic graphical model）。RBM是Smolensky于1986年在波尔兹曼机（Boltzmann Machine，BM）基础上提出的，所谓“随机”是指网络中的神经元是随机神经元，输出状态只有两种（未激活和激活），状态的具体取值根据概率统计法则来决定。RBM理论是Hinton在2006年提出基于RBM的（Deep Belief Network）模型，大量学者开始研究RBM的理论及其应用。

From ce4a99a050ae4b26c89289ab845c691f5015ac74 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 09:25:47 +0800
Subject: [PATCH 0980/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 25675b17..fa9af475 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 受限玻尔兹曼机(Restricted Boltzmann Machine)
+
 受限玻尔兹曼机（Restricted Boltzmann Machine，RBM）是一种可用随机神经网络（stochastic neural network）来解释的概率图模型（probabilistic graphical model）。RBM是Smolensky于1986年在波尔兹曼机（Boltzmann Machine，BM）基础上提出的，所谓“随机”是指网络中的神经元是随机神经元，输出状态只有两种（未激活和激活），状态的具体取值根据概率统计法则来决定。RBM理论是Hinton在2006年提出基于RBM的（Deep Belief Network）模型，大量学者开始研究RBM的理论及其应用。
 
 受限玻尔兹曼机(Restricted Boltzmann Machine)是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。

From eccdaec2ebcffdf8f304a5e05cff35e2e7c8ce48 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 16:27:46 +0800
Subject: [PATCH 0981/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index fa9af475..5f0baf9b 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -24,3 +24,7 @@ BM是一种对称耦合的随机反馈型二值单元神经网络，由可见层
 
 Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成，由于隐层神经元之间没有相互连接并且隐层神经元独立于给定的训练样本，这使直接计算依赖数据的期望值变得容易，可见层神经元之间也没有相互连接，通过从训练样本得到的隐层神经元状态上执行马尔可夫链抽样过程，来估计独立于数据的期望值，并行交替更新所有可见层神经元和隐层神经元的值。
 
+受限玻兹曼机是一种玻兹曼机的变体，但限定模型必须为二分图。模型中包含对应输入参数的输入（可见）单元和对应训练结果的隐单元，图中的每条边必须连接一个可见单元和一个隐单元。（与此相对，“无限制”玻兹曼机包含隐单元间的边，使之成为递归神经网络。）这一限定使得相比一般玻兹曼机更高效的训练算法成为可能，特别是基于梯度的对比分歧（contrastive divergence）算法。
+
+受限玻兹曼机也可被用于深度学习网络。具体地，深度信念网络可使用多个RBM堆叠而成，并可使用梯度下降法和反向传播算法进行调优
+

From 7695ee050d1d95e7e69a347aac0bd242179fee7f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 16:39:46 +0800
Subject: [PATCH 0982/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 5f0baf9b..f502511f 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -28,3 +28,5 @@ Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成
 
 受限玻兹曼机也可被用于深度学习网络。具体地，深度信念网络可使用多个RBM堆叠而成，并可使用梯度下降法和反向传播算法进行调优
 
+RBM是有两个层的浅层神经网络，它是组成深度置信网络的基础部件。RBM的第一个层称为可见层，又称输入层，而第二个层是隐藏层。
+

From 6cea9c1f5976d99ad5c03833e871f9213a06bc1e Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Sat, 26 May 2018 16:40:11 +0800
Subject: [PATCH 0983/1406] change page of images

---
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 assets/images/346.jpg | Bin 0 -> 70828 bytes
 assets/images/347.jpg | Bin 0 -> 64869 bytes
 assets/images/348.jpg | Bin 0 -> 81771 bytes
 assets/images/349.jpg | Bin 0 -> 74006 bytes
 assets/images/350.jpg | Bin 0 -> 89827 bytes
 assets/images/351.jpg | Bin 0 -> 73830 bytes
 8 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/344.jpg
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 create mode 100644 assets/images/346.jpg
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 create mode 100644 assets/images/349.jpg
 create mode 100644 assets/images/350.jpg
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From 5a5bf0e81c034a366b034fa8f309e5cd17098b92 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 16:43:13 +0800
Subject: [PATCH 0984/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index f502511f..0248f506 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -30,3 +30,22 @@ Smolensky提出的RBM由一个可见神经元层和一个隐神经元层组成
 
 RBM是有两个层的浅层神经网络，它是组成深度置信网络的基础部件。RBM的第一个层称为可见层，又称输入层，而第二个层是隐藏层。
 
+<p align="center">
+<img width="200" align="center" src="../../images/344.jpg" />
+</p>
+
+图中每个圆圈都是一个与神经元相似的单元，称为节点，运算在节点中进行。一个层中的节点与另一层中的所有节点分别连接，但与同一层中的其他节点并不相连。
+
+也就是说，层的内部不存在通信－这就是受限玻尔兹曼机被称为受限的原因。每个节点对输入进行处理和运算，判定是否继续传输输入的数据，而这种判定一开始是随机的。(“随机”（stochastic）一词在此处指与输入相乘的初始系数是随机生成的。)
+
+每个可见节点负责处理网络需要学习的数据集中一个项目的一种低层次特征。举例来说，如果处理的是一个灰度图像的数据集，则每个可见节点将接收一张图像中每个像素的像素值。（MNIST图像有784个像素，所以处理这类图像的神经网络的一个可见层必须有784个输入节点。）
+
+接着来看单个像素值x如何通过这一双层网络。在隐藏层的节点1中x与一个权重相乘，再与所谓的偏差相加。这两步运算的结果输入激活函数，得到节点的输出，即输入为x时通过节点的信号强度。
+
+```markdown
+激活函数f((权重w * 输入x) + 偏差b ) = 输出a
+```
+<p align="center">
+<img width="200" align="center" src="../../images/345.jpg" />
+</p>
+

From 1a2cbff0512a616ae28680d357d1cff47fdbbddf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 16:52:27 +0800
Subject: [PATCH 0985/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 36 +++++++++++++++++++++++++++++++++++-
 1 file changed, 35 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 0248f506..fac2d88d 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -46,6 +46,40 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 激活函数f((权重w * 输入x) + 偏差b ) = 输出a
 ```
 <p align="center">
-<img width="200" align="center" src="../../images/345.jpg" />
+<img width="300" align="center" src="../../images/345.jpg" />
 </p>
 
+一个隐藏节点如何整合多项输入。每个x分别与各自的权重相乘，乘积之和再与偏差相加，其结果同样经过激活函数运算得到节点的输出值。
+<p align="center">
+<img width="300" align="center" src="../../images/346.jpg" />
+</p>
+
+由于每个可见节点的输入都被传递至所有的隐藏节点，所以也可将RBM定义为一种对称二分图。
+
+对称指每个可见节点都与所有的隐藏节点相连接（见下图）。二分指有两个部分或层，而这里的图是指代节点网络的数学名词。
+
+在每个隐藏节点中，每一个输入x都会与其相对应的权重w相乘。也就是说，每个输入x会对应三个权重，因此总共有12个权重（4个输入节点 x 3个隐藏节点）。两层之间的权重始终都是一个行数等于输入节点数、列数等于输出节点数的矩阵。
+
+每个隐藏节点会接收四个与对应权重相乘后的输入值。这些乘积之和与一个偏差值相加（至少能强制让一部分节点激活），其结果再经过激活运算得到每个隐藏节点的输出a。
+
+<p align="center">
+<img width="300" align="center" src="../../images/347.jpg" />
+</p>
+
+如果这两个层属于一个深度神经网络，那么第一隐藏层的输出会成为第二隐藏层的输入，随后再通过任意数量的隐藏层，直至到达最终的分类层。（简单的前馈动作仅能让RBM节点实现自动编码器的功能。）
+
+<p align="center">
+<img width="300" align="center" src="../../images/348.jpg" />
+</p>
+
+第一隐藏层的激活值成为反向传递中的输入。这些输入值与同样的权重相乘，每两个相连的节点之间各有一个权重，就像正向传递中输入x的加权运算一样。这些乘积的和再与每个可见层的偏差相加，所得结果就是重构值，亦即原始输入的近似值。这一过程表示如下：
+
+<p align="center">
+<img width="300" align="center" src="../../images/349.jpg" />
+</p>
+
+由于RBM权重初始值是随机决定的，重构值与原始输入之间的差别通常很大。可以将r值与输入值之差视为重构误差，此误差值随后经由反向传播来修正RBM的权重，如此不断反复，直至误差达到最小。
+
+由此可见，RBM在正向传递中使用输入值来预测节点的激活值，亦即输入为加权的x时输出的概率：p(a|x; w)。
+
+但在反向传递时，激活值成为输入，而输出的是对于原始数据的重构值，或者说猜测值。此时RBM则是在尝试估计激活值为a时输入为x的概率，激活值的加权系数与正向传递中的权重相同。 第二个阶段可以表示为p(x|a; w)。

From a5ff608ae64f18f1f0d779c5d0022544fb0899b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 16:57:57 +0800
Subject: [PATCH 0986/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 32 +++++++++++++++++++++++++++++++-
 1 file changed, 31 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index fac2d88d..f59e6cab 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -72,7 +72,7 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 <img width="300" align="center" src="../../images/348.jpg" />
 </p>
 
-第一隐藏层的激活值成为反向传递中的输入。这些输入值与同样的权重相乘，每两个相连的节点之间各有一个权重，就像正向传递中输入x的加权运算一样。这些乘积的和再与每个可见层的偏差相加，所得结果就是重构值，亦即原始输入的近似值。这一过程表示如下：
+在重构阶段，第一隐藏层的激活值成为反向传递中的输入。这些输入值与同样的权重相乘，每两个相连的节点之间各有一个权重，就像正向传递中输入x的加权运算一样。这些乘积的和再与每个可见层的偏差相加，所得结果就是重构值，亦即原始输入的近似值。这一过程表示如下：
 
 <p align="center">
 <img width="300" align="center" src="../../images/349.jpg" />
@@ -83,3 +83,33 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 由此可见，RBM在正向传递中使用输入值来预测节点的激活值，亦即输入为加权的x时输出的概率：p(a|x; w)。
 
 但在反向传递时，激活值成为输入，而输出的是对于原始数据的重构值，或者说猜测值。此时RBM则是在尝试估计激活值为a时输入为x的概率，激活值的加权系数与正向传递中的权重相同。 第二个阶段可以表示为p(x|a; w)。
+
+上述两种预测值相结合，可以得到输入 x 和激活值 a 的联合概率分布，即p(x, a)。
+
+重构与回归、分类运算不同。回归运算根据许多输入值估测一个连续值，分类运算是猜测应当为一个特定的输入样例添加哪种具体的标签。
+
+而重构则是在猜测原始输入的概率分布，亦即同时预测许多不同的点的值。这被称为生成学习，必须和分类器所进行的判别学习区分开来，后者是将输入值映射至标签，用直线将数据点划分为不同的组。
+
+试想输入数据和重构数据是形状不同的常态曲线，两者仅有部分重叠。
+
+KL散度衡量两条曲线下方不重叠（即离散）的面积，而RBM的优化算法会尝试将这些离散部分的面积最小化，使共用权重在与第一隐藏层的激活值相乘后，可以得到与原始输入高度近似的结果。下图左半边是一组原始输入的概率分布曲线p，与之并列的是重构值的概率分布曲线q；右半边的图则显示了两条曲线之间的差异。
+
+<p align="center">
+<img width="300" align="center" src="../../images/350.jpg" />
+</p>
+
+RBM根据权重产生的误差反复调整权重，以此学习估计原始数据的近似值。可以说权重会慢慢开始反映出输入的结构，而这种结构被编码为第一个隐藏层的激活值。整个学习过程看上去像是两条概率分布曲线在逐步重合。
+
+<p align="center">
+<img width="300" align="center" src="../../images/351.jpg" />
+</p>
+
+RBM根据第一个隐藏层的激活值学习了输入数据的结构之后，数据即在网络中继续向下传递一层。第一个隐藏层的作用现在相当于可见层。激活值实际上相当于输入，在第二个隐藏层的节点中与权重相乘，得到另一组激活值。
+
+将特征分组，再将特征组分组，由此连续生成多组激活值的过程是特征层次分析的基础，神经网络用这种方法来学习更为复杂且抽象的数据表达形式。
+
+每增加一个隐藏层，其权重都会反复进行调整，直到该层能较为准确地模拟出来自前一层的输入。这是无监督的逐层贪婪预训练方法，不需要标签就可以改进网络的权重，也就是说可以采用未标记、未经人工处理的数据来训练，而现实中大部分的数据都属于这一类别。一般的规律是，算法接触的数据越多，产生的结果越准确，这正是深度学习算法十分厉害的原因之一。
+
+权重能够近似模拟出数据的特征后，也就为下一步的学习奠定了良好基础，比如可以在随后的有监督学习阶段使用深度置信网络来对图像进行分类。
+
+RBM有许多用途，其中最强的功能之一就是对权重进行合理的初始化，为之后的学习和分类做好准备。从某种意义上来说，RBM的作用与反向传播相似：让权重能够有效地模拟数据。可以认为预训练和反向传播是实现同一个目的的不同方法，二者可以相互替代。

From 0317871b8e3fee26ed8ff7e9e0a9aeb911d9cf72 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Sat, 26 May 2018 16:59:06 +0800
Subject: [PATCH 0987/1406] change ANN.0.10

---
 assets/images/352.jpg      | Bin 0 -> 60991 bytes
 assets/src/ANN/ANN.0.10.md |  17 ++++++++++-------
 2 files changed, 10 insertions(+), 7 deletions(-)
 create mode 100644 assets/images/352.jpg

diff --git a/assets/images/352.jpg b/assets/images/352.jpg
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diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index f59e6cab..0c56c930 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -46,12 +46,12 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 激活函数f((权重w * 输入x) + 偏差b ) = 输出a
 ```
 <p align="center">
-<img width="300" align="center" src="../../images/345.jpg" />
+<img width="360" align="center" src="../../images/345.jpg" />
 </p>
 
 一个隐藏节点如何整合多项输入。每个x分别与各自的权重相乘，乘积之和再与偏差相加，其结果同样经过激活函数运算得到节点的输出值。
 <p align="center">
-<img width="300" align="center" src="../../images/346.jpg" />
+<img width="360" align="center" src="../../images/346.jpg" />
 </p>
 
 由于每个可见节点的输入都被传递至所有的隐藏节点，所以也可将RBM定义为一种对称二分图。
@@ -63,19 +63,19 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 每个隐藏节点会接收四个与对应权重相乘后的输入值。这些乘积之和与一个偏差值相加（至少能强制让一部分节点激活），其结果再经过激活运算得到每个隐藏节点的输出a。
 
 <p align="center">
-<img width="300" align="center" src="../../images/347.jpg" />
+<img width="360" align="center" src="../../images/347.jpg" />
 </p>
 
 如果这两个层属于一个深度神经网络，那么第一隐藏层的输出会成为第二隐藏层的输入，随后再通过任意数量的隐藏层，直至到达最终的分类层。（简单的前馈动作仅能让RBM节点实现自动编码器的功能。）
 
 <p align="center">
-<img width="300" align="center" src="../../images/348.jpg" />
+<img width="360" align="center" src="../../images/348.jpg" />
 </p>
 
 在重构阶段，第一隐藏层的激活值成为反向传递中的输入。这些输入值与同样的权重相乘，每两个相连的节点之间各有一个权重，就像正向传递中输入x的加权运算一样。这些乘积的和再与每个可见层的偏差相加，所得结果就是重构值，亦即原始输入的近似值。这一过程表示如下：
 
 <p align="center">
-<img width="300" align="center" src="../../images/349.jpg" />
+<img width="360" align="center" src="../../images/349.jpg" />
 </p>
 
 由于RBM权重初始值是随机决定的，重构值与原始输入之间的差别通常很大。可以将r值与输入值之差视为重构误差，此误差值随后经由反向传播来修正RBM的权重，如此不断反复，直至误差达到最小。
@@ -95,13 +95,13 @@ RBM是有两个层的浅层神经网络，它是组成深度置信网络的基
 KL散度衡量两条曲线下方不重叠（即离散）的面积，而RBM的优化算法会尝试将这些离散部分的面积最小化，使共用权重在与第一隐藏层的激活值相乘后，可以得到与原始输入高度近似的结果。下图左半边是一组原始输入的概率分布曲线p，与之并列的是重构值的概率分布曲线q；右半边的图则显示了两条曲线之间的差异。
 
 <p align="center">
-<img width="300" align="center" src="../../images/350.jpg" />
+<img width="360" align="center" src="../../images/350.jpg" />
 </p>
 
 RBM根据权重产生的误差反复调整权重，以此学习估计原始数据的近似值。可以说权重会慢慢开始反映出输入的结构，而这种结构被编码为第一个隐藏层的激活值。整个学习过程看上去像是两条概率分布曲线在逐步重合。
 
 <p align="center">
-<img width="300" align="center" src="../../images/351.jpg" />
+<img width="360" align="center" src="../../images/351.jpg" />
 </p>
 
 RBM根据第一个隐藏层的激活值学习了输入数据的结构之后，数据即在网络中继续向下传递一层。第一个隐藏层的作用现在相当于可见层。激活值实际上相当于输入，在第二个隐藏层的节点中与权重相乘，得到另一组激活值。
@@ -113,3 +113,6 @@ RBM根据第一个隐藏层的激活值学习了输入数据的结构之后，
 权重能够近似模拟出数据的特征后，也就为下一步的学习奠定了良好基础，比如可以在随后的有监督学习阶段使用深度置信网络来对图像进行分类。
 
 RBM有许多用途，其中最强的功能之一就是对权重进行合理的初始化，为之后的学习和分类做好准备。从某种意义上来说，RBM的作用与反向传播相似：让权重能够有效地模拟数据。可以认为预训练和反向传播是实现同一个目的的不同方法，二者可以相互替代。
+<p align="center">
+<img width="360" align="center" src="../../images/352.jpg" />
+</p>

From 9dbd8b004c2525bd1172a32d72ece6c1d61bcc95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 May 2018 17:01:05 +0800
Subject: [PATCH 0988/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 182 +++++++++++++++++++++++++++++++++++++
 1 file changed, 182 insertions(+)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 0c56c930..89cf3ccf 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -116,3 +116,185 @@ RBM有许多用途，其中最强的功能之一就是对权重进行合理的
 <p align="center">
 <img width="360" align="center" src="../../images/352.jpg" />
 </p>
+
+这幅对称二分二向图综合显示了玻尔兹曼机的运作方式。
+
+#### 应用示例
+```python
+
+import tensorflow as tf
+import numpy as np
+import sys
+from .util import tf_xavier_init
+
+
+class RBM:
+    def __init__(self,
+                 n_visible,
+                 n_hidden,
+                 learning_rate=0.01,
+                 momentum=0.95,
+                 xavier_const=1.0,
+                 err_function='mse',
+                 use_tqdm=False,
+                 # DEPRECATED:
+                 tqdm=None):
+        if not 0.0 <= momentum <= 1.0:
+            raise ValueError('momentum should be in range [0, 1]')
+
+        if err_function not in {'mse', 'cosine'}:
+            raise ValueError('err_function should be either \'mse\' or \'cosine\'')
+
+        self._use_tqdm = use_tqdm
+        self._tqdm = None
+
+        if use_tqdm or tqdm is not None:
+            from tqdm import tqdm
+            self._tqdm = tqdm
+
+        self.n_visible = n_visible
+        self.n_hidden = n_hidden
+        self.learning_rate = learning_rate
+        self.momentum = momentum
+
+        self.x = tf.placeholder(tf.float32, [None, self.n_visible])
+        self.y = tf.placeholder(tf.float32, [None, self.n_hidden])
+
+        self.w = tf.Variable(tf_xavier_init(self.n_visible, self.n_hidden, const=xavier_const), dtype=tf.float32)
+        self.visible_bias = tf.Variable(tf.zeros([self.n_visible]), dtype=tf.float32)
+        self.hidden_bias = tf.Variable(tf.zeros([self.n_hidden]), dtype=tf.float32)
+
+        self.delta_w = tf.Variable(tf.zeros([self.n_visible, self.n_hidden]), dtype=tf.float32)
+        self.delta_visible_bias = tf.Variable(tf.zeros([self.n_visible]), dtype=tf.float32)
+        self.delta_hidden_bias = tf.Variable(tf.zeros([self.n_hidden]), dtype=tf.float32)
+
+        self.update_weights = None
+        self.update_deltas = None
+        self.compute_hidden = None
+        self.compute_visible = None
+        self.compute_visible_from_hidden = None
+
+        self._initialize_vars()
+
+        assert self.update_weights is not None
+        assert self.update_deltas is not None
+        assert self.compute_hidden is not None
+        assert self.compute_visible is not None
+        assert self.compute_visible_from_hidden is not None
+
+        if err_function == 'cosine':
+            x1_norm = tf.nn.l2_normalize(self.x, 1)
+            x2_norm = tf.nn.l2_normalize(self.compute_visible, 1)
+            cos_val = tf.reduce_mean(tf.reduce_sum(tf.mul(x1_norm, x2_norm), 1))
+            self.compute_err = tf.acos(cos_val) / tf.constant(np.pi)
+        else:
+            self.compute_err = tf.reduce_mean(tf.square(self.x - self.compute_visible))
+
+        init = tf.global_variables_initializer()
+        self.sess = tf.Session()
+        self.sess.run(init)
+
+    def _initialize_vars(self):
+        pass
+
+    def get_err(self, batch_x):
+        return self.sess.run(self.compute_err, feed_dict={self.x: batch_x})
+
+    def get_free_energy(self):
+        pass
+
+    def transform(self, batch_x):
+        return self.sess.run(self.compute_hidden, feed_dict={self.x: batch_x})
+
+    def transform_inv(self, batch_y):
+        return self.sess.run(self.compute_visible_from_hidden, feed_dict={self.y: batch_y})
+
+    def reconstruct(self, batch_x):
+        return self.sess.run(self.compute_visible, feed_dict={self.x: batch_x})
+
+    def partial_fit(self, batch_x):
+        self.sess.run(self.update_weights + self.update_deltas, feed_dict={self.x: batch_x})
+
+    def fit(self,
+            data_x,
+            n_epoches=10,
+            batch_size=10,
+            shuffle=True,
+            verbose=True):
+        assert n_epoches > 0
+
+        n_data = data_x.shape[0]
+
+        if batch_size > 0:
+            n_batches = n_data // batch_size + (0 if n_data % batch_size == 0 else 1)
+        else:
+            n_batches = 1
+
+        if shuffle:
+            data_x_cpy = data_x.copy()
+            inds = np.arange(n_data)
+        else:
+            data_x_cpy = data_x
+
+        errs = []
+
+        for e in range(n_epoches):
+            if verbose and not self._use_tqdm:
+                print('Epoch: {:d}'.format(e))
+
+            epoch_errs = np.zeros((n_batches,))
+            epoch_errs_ptr = 0
+
+            if shuffle:
+                np.random.shuffle(inds)
+                data_x_cpy = data_x_cpy[inds]
+
+            r_batches = range(n_batches)
+
+            if verbose and self._use_tqdm:
+                r_batches = self._tqdm(r_batches, desc='Epoch: {:d}'.format(e), ascii=True, file=sys.stdout)
+
+            for b in r_batches:
+                batch_x = data_x_cpy[b * batch_size:(b + 1) * batch_size]
+                self.partial_fit(batch_x)
+                batch_err = self.get_err(batch_x)
+                epoch_errs[epoch_errs_ptr] = batch_err
+                epoch_errs_ptr += 1
+
+            if verbose:
+                err_mean = epoch_errs.mean()
+                if self._use_tqdm:
+                    self._tqdm.write('Train error: {:.4f}'.format(err_mean))
+                    self._tqdm.write('')
+                else:
+                    print('Train error: {:.4f}'.format(err_mean))
+                    print('')
+                sys.stdout.flush()
+
+            errs = np.hstack([errs, epoch_errs])
+
+        return errs
+
+    def get_weights(self):
+        return self.sess.run(self.w),\
+            self.sess.run(self.visible_bias),\
+            self.sess.run(self.hidden_bias)
+
+    def save_weights(self, filename, name):
+        saver = tf.train.Saver({name + '_w': self.w,
+                                name + '_v': self.visible_bias,
+                                name + '_h': self.hidden_bias})
+        return saver.save(self.sess, filename)
+
+    def set_weights(self, w, visible_bias, hidden_bias):
+        self.sess.run(self.w.assign(w))
+        self.sess.run(self.visible_bias.assign(visible_bias))
+        self.sess.run(self.hidden_bias.assign(hidden_bias))
+
+    def load_weights(self, filename, name):
+        saver = tf.train.Saver({name + '_w': self.w,
+                                name + '_v': self.visible_bias,
+                                name + '_h': self.hidden_bias})
+        saver.restore(self.sess, filename)
+
+```

From 4d07eef9ed7b9617829ba721acd30065cde40224 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 27 May 2018 00:05:28 +0800
Subject: [PATCH 0989/1406] Update ANN.0.10.md

---
 assets/src/ANN/ANN.0.10.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.10.md b/assets/src/ANN/ANN.0.10.md
index 89cf3ccf..6e42eb57 100644
--- a/assets/src/ANN/ANN.0.10.md
+++ b/assets/src/ANN/ANN.0.10.md
@@ -12,7 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 受限玻尔兹曼机(Restricted Boltzmann Machine)
-
 受限玻尔兹曼机（Restricted Boltzmann Machine，RBM）是一种可用随机神经网络（stochastic neural network）来解释的概率图模型（probabilistic graphical model）。RBM是Smolensky于1986年在波尔兹曼机（Boltzmann Machine，BM）基础上提出的，所谓“随机”是指网络中的神经元是随机神经元，输出状态只有两种（未激活和激活），状态的具体取值根据概率统计法则来决定。RBM理论是Hinton在2006年提出基于RBM的（Deep Belief Network）模型，大量学者开始研究RBM的理论及其应用。
 
 受限玻尔兹曼机(Restricted Boltzmann Machine)是玻尔兹曼机(Boltzmann machine，BM)的一种特殊拓扑结构。BM的原理起源于统计物理学，是一种基于能量函数的建模方法，能够描述变量之间的高阶相互作用，BM的学习算法较复杂，但所建模型和学习算法有比较完备的物理解释和严格的数理统计理论作基础。

From 08dafbce8719b8ddde47df539a17795942500eef Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 27 May 2018 22:42:52 +0800
Subject: [PATCH 0990/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 1a8d4a49..eadb015c 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -13,3 +13,4 @@
 
 #### 自组织映射(Self-Organizing Map)
 
+自组织映射(Self-organizing Maps,SOM)算法是一种无导师学习方法,具有良好的自组织、可视化等特性,已经得到了广泛的应用和研究。

From cfa850d6e7e979fc1f96ff1faea45ff20e6aa320 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 27 May 2018 22:43:27 +0800
Subject: [PATCH 0991/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index eadb015c..b6cc6c34 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -13,4 +13,4 @@
 
 #### 自组织映射(Self-Organizing Map)
 
-自组织映射(Self-organizing Maps,SOM)算法是一种无导师学习方法,具有良好的自组织、可视化等特性,已经得到了广泛的应用和研究。
+自组织映射(Self-Organizing Maps, SOM)算法作为一种聚类和高维可视化的无监督学习算法, 是通过模拟人脑对信 号处理的特点而发展起来的一种人工神经网络。该模型由芬兰赫尔辛基大学教授 Teuvo Kohonen 于 1981 年提出后,现在 已成为应用最广泛的自组织神经网络方法,其中的 WTA(Winner Takes All)竞争机制反映了自组织学习最根本的特征。

From f47aa156cdd51f8633c30fe6087342d57b7612d0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:01:30 +0800
Subject: [PATCH 0992/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index b6cc6c34..639276ec 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -14,3 +14,7 @@
 #### 自组织映射(Self-Organizing Map)
 
 自组织映射(Self-Organizing Maps, SOM)算法作为一种聚类和高维可视化的无监督学习算法, 是通过模拟人脑对信 号处理的特点而发展起来的一种人工神经网络。该模型由芬兰赫尔辛基大学教授 Teuvo Kohonen 于 1981 年提出后,现在 已成为应用最广泛的自组织神经网络方法,其中的 WTA(Winner Takes All)竞争机制反映了自组织学习最根本的特征。
+
+自组织映射它的思想很简单，本质上是一种只有输入层--隐藏层的神经网络。隐藏层中的一个节点代表一个需要聚成的类。训练时采用“竞争学习”的方式，每个输入的样例在隐藏层中找到一个和它最匹配的节点，称为它的激活节点，也叫“winning neuron”。 紧接着用随机梯度下降法更新激活节点的参数。同时，和激活节点临近的点也根据它们距离激活节点的远近而适当地更新参数。
+
+所以，SOM的一个特点是，隐藏层的节点是有拓扑关系的。这个拓扑关系需要我们确定，如果想要一维的模型，那么隐藏节点依次连成一条线；如果想要二维的拓扑关系，那么就行成一个平面，如下图所示（也叫Kohonen Network）：

From 0dacbd6f693cd62515b4c0b62d61da6e48e8bfcb Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Tue, 29 May 2018 23:06:13 +0800
Subject: [PATCH 0993/1406] add image

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 assets/images/354.jpg | Bin 0 -> 4772 bytes
 assets/images/355.jpg | Bin 0 -> 6273 bytes
 assets/images/356.jpg | Bin 0 -> 6221 bytes
 4 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/353.jpg
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From 2841f6793d197514207fc822cefa2ce79e0e6f60 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:06:56 +0800
Subject: [PATCH 0994/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 639276ec..a4768c4e 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -18,3 +18,6 @@
 自组织映射它的思想很简单，本质上是一种只有输入层--隐藏层的神经网络。隐藏层中的一个节点代表一个需要聚成的类。训练时采用“竞争学习”的方式，每个输入的样例在隐藏层中找到一个和它最匹配的节点，称为它的激活节点，也叫“winning neuron”。 紧接着用随机梯度下降法更新激活节点的参数。同时，和激活节点临近的点也根据它们距离激活节点的远近而适当地更新参数。
 
 所以，SOM的一个特点是，隐藏层的节点是有拓扑关系的。这个拓扑关系需要我们确定，如果想要一维的模型，那么隐藏节点依次连成一条线；如果想要二维的拓扑关系，那么就行成一个平面，如下图所示（也叫Kohonen Network）：
+<p align="center">
+<img width="300" align="center" src="../../images/353.jpg" />
+</p>

From 2aef7b24696ecfc17e1acc80928ee2595efdd855 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:07:17 +0800
Subject: [PATCH 0995/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index a4768c4e..3f7ca5e9 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -19,5 +19,5 @@
 
 所以，SOM的一个特点是，隐藏层的节点是有拓扑关系的。这个拓扑关系需要我们确定，如果想要一维的模型，那么隐藏节点依次连成一条线；如果想要二维的拓扑关系，那么就行成一个平面，如下图所示（也叫Kohonen Network）：
 <p align="center">
-<img width="300" align="center" src="../../images/353.jpg" />
+<img width="500" align="center" src="../../images/353.jpg" />
 </p>

From 3f7f849af162779bca4930de55ecd955280c1dd2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:07:58 +0800
Subject: [PATCH 0996/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 3f7ca5e9..b465caf5 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -21,3 +21,14 @@
 <p align="center">
 <img width="500" align="center" src="../../images/353.jpg" />
 </p>
+
+既然隐藏层是有拓扑关系的，所以我们也可以说，SOM可以把任意维度的输入离散化到一维或者二维(更高维度的不常见)的离散空间上。 Computation layer里面的节点与Input layer的节点是全连接的。
+
+拓扑关系确定后，开始计算过程，大体分成几个部分：
+
+1） 初始化：每个节点随机初始化自己的参数。每个节点的参数个数与Input的维度相同。
+
+2）对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：
+<p align="center">
+<img width="380" align="center" src="../../images/354.jpg" />
+</p>

From b08ec58dcb257d8273b332bce911bac4f351d97d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:08:25 +0800
Subject: [PATCH 0997/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index b465caf5..e6926c04 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -30,5 +30,5 @@
 
 2）对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：
 <p align="center">
-<img width="380" align="center" src="../../images/354.jpg" />
+<img width="300" align="center" src="../../images/354.jpg" />
 </p>

From c68f51cb84cbaa4d9ef4033fd89c93fd7c60d633 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:09:00 +0800
Subject: [PATCH 0998/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index e6926c04..9e8325aa 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -26,9 +26,11 @@
 
 拓扑关系确定后，开始计算过程，大体分成几个部分：
 
-1） 初始化：每个节点随机初始化自己的参数。每个节点的参数个数与Input的维度相同。
+1. 初始化：每个节点随机初始化自己的参数。每个节点的参数个数与Input的维度相同。
 
-2）对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：
+2. 对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：
 <p align="center">
 <img width="300" align="center" src="../../images/354.jpg" />
 </p>
+3. 找到激活节点I(x)之后，我们也希望更新和它临近的节点。令S_ij表示节点i和j之间的距离，对于I(x)临近的节点，分配给它们一个更新权重：
+

From 2633878919538f4d307cc8ef40ed4c83b23917f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:10:39 +0800
Subject: [PATCH 0999/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 9e8325aa..e8de9688 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -33,4 +33,9 @@
 <img width="300" align="center" src="../../images/354.jpg" />
 </p>
 3. 找到激活节点I(x)之后，我们也希望更新和它临近的节点。令S_ij表示节点i和j之间的距离，对于I(x)临近的节点，分配给它们一个更新权重：
+<p align="center">
+<img width="300" align="center" src="../../images/355.jpg" />
+</p>
+简而言之就是临近的节点根据距离的远近，更新程度要会减弱。
 
+然后就是更新节点的参数了。按照梯度下降法更新：

From 78515c23fc4ebeed42ee1a37c9f775fa14b3cafc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:15:20 +0800
Subject: [PATCH 1000/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index e8de9688..948fcaeb 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -39,3 +39,7 @@
 简而言之就是临近的节点根据距离的远近，更新程度要会减弱。
 
 然后就是更新节点的参数了。按照梯度下降法更新：
+
+<p align="center">
+<img width="300" align="center" src="../../images/356.jpg" />
+</p>

From f24733d14e7c631d9fd90591d07eba9bdeb011d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:15:34 +0800
Subject: [PATCH 1001/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 948fcaeb..daa5b6e3 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -43,3 +43,6 @@
 <p align="center">
 <img width="300" align="center" src="../../images/356.jpg" />
 </p>
+
+迭代，直到收敛。
+

From a2ccc155dcace265e53b6577ece66a7d76e996c3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:17:01 +0800
Subject: [PATCH 1002/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index daa5b6e3..8d71e843 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -46,3 +46,13 @@
 
 迭代，直到收敛。
 
+与K-Means的比较
+
+同样是无监督的聚类方法，自组织映射与K-Means的不同之处：
+
+* K-Means需要事先定下类的个数，也就是K的值。 自组织映射则不用，隐藏层中的某些节点可以没有任何输入数据属于它。所以，K-Means受初始化的影响要比较大。
+
+* K-means为每个输入数据找到一个最相似的类后，只更新这个类的参数。自组织映射则会更新临近的节点。所以K-mean受noise data的影响比较大，自组织映射的准确性可能会比k-means低（因为也更新了临近节点）。
+
+* 自组织映射的可视化比较好。优雅的拓扑关系图 。
+

From cf4207fc1aeccf49aae100dff1f0a2c03b6ac231 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:20:05 +0800
Subject: [PATCH 1003/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 128 +++++++++++++++++++++++++++++++++++++
 1 file changed, 128 insertions(+)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 8d71e843..8f465f04 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -56,3 +56,131 @@
 
 * 自组织映射的可视化比较好。优雅的拓扑关系图 。
 
+#### 应用示例
+
+```python
+import numpy
+from sklearn.decomposition import RandomizedPCA
+
+
+class SOM():
+    def __init__(self, x, y):        
+        self.map = []
+        self.n_neurons = x*y
+        self.sigma = x
+        self.template = numpy.arange(x*y).reshape(self.n_neurons,1)
+        self.alpha = 0.6
+        self.alpha_final = 0.1
+        self.shape = [x,y]
+        self.epoch = 0
+        
+    def train(self, X, iter, batch_size=1):
+        if len(self.map) == 0:
+            x,y = self.shape
+            # first we initialize the map
+            self.map = numpy.zeros((self.n_neurons, len(X[0])))
+            
+            # then we the pricipal components of the input data
+            eigen = RandomizedPCA(10).fit_transform(X.T).T
+            
+            # then we set different point on the map equal to principal components to force diversification
+            self.map[0] = eigen[0]
+            self.map[y-1] = eigen[1]
+            self.map[(x-1)*y] = eigen[2]
+            self.map[x*y - 1] = eigen[3]
+            for i in range(4, 10):
+                self.map[numpy.random.randint(1, self.n_neurons)] = eigen[i]
+                
+        self.total = iter
+        
+        # coefficient of decay for learning rate alpha
+        self.alpha_decay = (self.alpha_final/self.alpha)**(1.0/self.total)
+        
+        # coefficient of decay for gaussian smoothing
+        self.sigma_decay = (numpy.sqrt(self.shape[0])/(4*self.sigma))**(1.0/self.total)
+        
+        samples = numpy.arange(len(X))
+        numpy.random.shuffle(samples)
+    
+        for i in xrange(iter):
+            idx = samples[i:i + batch_size]
+            self.iterate(X[idx])
+    
+    def transform(self, X):
+        # We simply compute the dot product of the input with the transpose of the map to get the new input vectors
+        res = numpy.dot(numpy.exp(X),numpy.exp(self.map.T))/numpy.sum(numpy.exp(self.map), axis=1)
+        res = res / (numpy.exp(numpy.max(res)) + 1e-8)
+        return res
+     
+    def iterate(self, vector):  
+        x, y = self.shape
+        
+        delta = self.map - vector
+        
+        # Euclidian distance of each neurons with the example
+        dists = numpy.sum((delta)**2, axis=1).reshape(x,y)
+        
+        # Best maching unit
+        idx = numpy.argmin(dists)
+        print "Epoch ", self.epoch, ": ", (idx/x, idx%y), "; Sigma: ", self.sigma, "; alpha: ", self.alpha
+        
+        # Linearly reducing the width of Gaussian Kernel
+        self.sigma = self.sigma*self.sigma_decay
+        dist_map = self.template.reshape(x,y)     
+        
+        # Distance of each neurons in the map from the best matching neuron
+        dists = numpy.sqrt((dist_map/x - idx/x)**2 + (numpy.mod(dist_map,x) - idx%y)**2).reshape(self.n_neurons, 1)
+        #dists = self.template - idx
+        
+        # Applying Gaussian smoothing to distances of neurons from best matching neuron
+        h = numpy.exp(-(dists/self.sigma)**2)      
+         
+        # Updating neurons in the map
+        self.map -= self.alpha*h*delta
+       
+        # Decreasing alpha
+        self.alpha = self.alpha*self.alpha_decay
+        
+        self.epoch = self.epoch + 1 
+        
+        
+##################################################### 
+#       EXAMPLE: TRAINING SOM ON MNIST DATA         #
+#####################################################       
+    
+from PIL import Image
+from tools import make_tile
+import gzip
+import cPickle
+
+def load_mnist():   
+    f = gzip.open("mnist/mnist.pkl.gz", 'rb')
+    train, valid, test = cPickle.load(f)
+    f.close()  
+    return train[0][:20000],train[1][:20000]
+    
+def demo():
+    # Get data
+    X, y = load_mnist()
+    cl = SOM(20, 20)
+    cl.train(X, 2000)  
+    
+    # Plotting hidden units
+    W = cl.map
+    W = make_tile(W, img_shape= (28,28), tile_shape=(20,20))
+    img = Image.fromarray(W)
+    img.save("som_results.png")
+    
+    
+    # creating new inputs
+    X = cl.transform(X)
+   
+    # we can plot "landscape" 3d to view the map in 3d
+    landscape = cl.transform(numpy.ones((1,28**2)))
+    return cl.map, X, y,landscape
+    
+    
+if __name__ == '__main__':
+    demo()
+
+```

From bb05e4f3efaa4c3efb94cb0842bab16ad9cb4236 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 May 2018 23:21:35 +0800
Subject: [PATCH 1004/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index 8f465f04..aade86a5 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -142,12 +142,12 @@ class SOM():
         self.alpha = self.alpha*self.alpha_decay
         
         self.epoch = self.epoch + 1 
+
+```
+
+```python
         
-        
-##################################################### 
-#       EXAMPLE: TRAINING SOM ON MNIST DATA         #
-#####################################################       
-    
+           
 from PIL import Image
 from tools import make_tile
 import gzip

From f50f030c7003439f5e2fd80856a9614411d6ad11 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 May 2018 08:44:12 +0800
Subject: [PATCH 1005/1406] Update ANN.0.11.md

---
 assets/src/ANN/ANN.0.11.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.11.md b/assets/src/ANN/ANN.0.11.md
index aade86a5..774fb7fb 100644
--- a/assets/src/ANN/ANN.0.11.md
+++ b/assets/src/ANN/ANN.0.11.md
@@ -30,7 +30,7 @@
 
 2. 对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：
 <p align="center">
-<img width="300" align="center" src="../../images/354.jpg" />
+<img width="200" align="center" src="../../images/354.jpg" />
 </p>
 3. 找到激活节点I(x)之后，我们也希望更新和它临近的节点。令S_ij表示节点i和j之间的距离，对于I(x)临近的节点，分配给它们一个更新权重：
 <p align="center">

From bbcc8d53b1a9e11ee6212ebbc450894ac60dc242 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 May 2018 11:28:50 +0800
Subject: [PATCH 1006/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index cc04305f..c62df1a7 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -11,5 +11,5 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
-#### 尖峰神经网络(Spiking Neural Network)
+#### 脉冲神经网络(Spiking Neural Network)
 

From 8dc26c6666448cb67fac2b3217dc33288ef409b8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 May 2018 11:29:13 +0800
Subject: [PATCH 1007/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 11bdcf53..1fe4c561 100644
--- a/README.md
+++ b/README.md
@@ -129,7 +129,7 @@
      * [径向基函数网络(Radial Basis Function Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.9.md) 
      * [受限玻尔兹曼机(Restricted Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.10.md) 
      * [自组织映射(Self-Organizing Map)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.11.md) 
-     * [尖峰神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
+     * [脉冲神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
  * [深度学习(Deep Learning)]() 
      * [深度信念网络(Deep Belief Machines)]() 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 

From f9e79b14d2338d412a25da8f73c1b8cc6c1a2c83 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 May 2018 12:00:17 +0800
Subject: [PATCH 1008/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index c62df1a7..d0446518 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -12,4 +12,5 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 脉冲神经网络(Spiking Neural Network)
-
+脉冲神经网络 （SNN-Spiking Neuron Networks) 经常被誉为第三代人工神经网络。其模拟神经元更加接近实际，除此之外，它把时间信息的影响也考虑其中。
+思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。

From 2c7f3d00ca0eec94e6e392a9c6f49eb950b23133 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 31 May 2018 22:18:45 +0800
Subject: [PATCH 1009/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index d0446518..ba49ffe9 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -12,5 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 脉冲神经网络(Spiking Neural Network)
-脉冲神经网络 （SNN-Spiking Neuron Networks) 经常被誉为第三代人工神经网络。其模拟神经元更加接近实际，除此之外，它把时间信息的影响也考虑其中。
-思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。
+脉冲神经网络Spiking neuralnetworks (SNNs)是第三代神经网络模型，其模拟神经元更加接近实际，除此之外，把时间信息的影响也考虑其中。思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。
+
+在脉冲神经网络中，神经元的当前激活水平（被建模成某种微分方程）通常被认为是当前状态，一个输入脉冲会使当前这个值升高，持续一段时间，然后逐渐衰退。出现了很多编码方式把这些输出脉冲序列解释为一个实际的数字，这些编码方式会同时考虑到脉冲频率和脉冲间隔时间。

From 3ed1c74fa68a9cb1f77430fb3ac847f906ac9ba8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 31 May 2018 22:19:13 +0800
Subject: [PATCH 1010/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index ba49ffe9..f75d1a3e 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -15,3 +15,7 @@
 脉冲神经网络Spiking neuralnetworks (SNNs)是第三代神经网络模型，其模拟神经元更加接近实际，除此之外，把时间信息的影响也考虑其中。思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。
 
 在脉冲神经网络中，神经元的当前激活水平（被建模成某种微分方程）通常被认为是当前状态，一个输入脉冲会使当前这个值升高，持续一段时间，然后逐渐衰退。出现了很多编码方式把这些输出脉冲序列解释为一个实际的数字，这些编码方式会同时考虑到脉冲频率和脉冲间隔时间。
+
+Alan Lloyd Hodgkin 和 Andrew Huxley在1952年提出了第一个脉冲神经网络模型，这个模型描述了动作电位是怎样产生并传播的。但是，脉冲并不是在神经元之间直接传播的，它需要在突触间隙间交换一种叫“神经递质”的化学物质。这种生物体的复杂性和可变性导致了许多不同的神经元模型的产生。
+
+从信息论的观点来看，找到一种可以解释脉冲，也就是动作电位的模型是个问题。所以，神经科学的一个基本问题就是确定神经元是否通过时间编码来交流。时间编码表明单一的神经元可以取代上百个S型隐藏层节点。

From 9ddb894ad712d78d91915d34b5acde41954773dc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 31 May 2018 22:49:29 +0800
Subject: [PATCH 1011/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index f75d1a3e..44699acb 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -19,3 +19,8 @@
 Alan Lloyd Hodgkin 和 Andrew Huxley在1952年提出了第一个脉冲神经网络模型，这个模型描述了动作电位是怎样产生并传播的。但是，脉冲并不是在神经元之间直接传播的，它需要在突触间隙间交换一种叫“神经递质”的化学物质。这种生物体的复杂性和可变性导致了许多不同的神经元模型的产生。
 
 从信息论的观点来看，找到一种可以解释脉冲，也就是动作电位的模型是个问题。所以，神经科学的一个基本问题就是确定神经元是否通过时间编码来交流。时间编码表明单一的神经元可以取代上百个S型隐藏层节点。
+
+
+这种神经网络大体上可以和传统的人工神经网络一样被用在信息处理中，而且脉冲神经网络可以对一个虚拟昆虫寻找食物的问题建模，而不需要环境的先验知识。并且，由于它更加接近现实的性能，使它可以用来学习生物神经系统的工作，电生理学的脉冲和脉冲神经网络在电脑上的模拟输出相比，确定了拓扑学和生物神经学的假说的可能性。
+
+在实践中脉冲神经网络和已被证明的理论之间还存在一个主要的不同点。脉冲神经网络已被证明在神经科学系统中有作用，而在工程学中还无建树，一些大规模的神经网络已经被设计来利用脉冲神经网络中发现的脉冲编码，这些网络根据储备池计算的原则，但是现实中，大规模的脉冲神经网络计算由于所需计算资源多而产能小，发展受限，造成了只有很少的大规模脉冲神经网络被用来解决复杂的计算问题，而这些之前都是由第二代神经网络解决的。第二代神经网络模型中难以加入时间，脉冲神经网络（特别当算法定义为离散时间时）相当容易观察其动力学特征。我们很难建立一个具有稳定行为的模型来实现一个特定功能。

From 4741bf906b87d5c60965bc64da34df2e305d44b8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 31 May 2018 22:50:27 +0800
Subject: [PATCH 1012/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index 44699acb..28637725 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -14,8 +14,11 @@
 #### 脉冲神经网络(Spiking Neural Network)
 脉冲神经网络Spiking neuralnetworks (SNNs)是第三代神经网络模型，其模拟神经元更加接近实际，除此之外，把时间信息的影响也考虑其中。思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。
 
+脉冲神经网络，其模拟神经元更加接近实际，除此之外，把时间信息的影响也考虑其中。思路是这样的，动态神经网络中的神经元不是在每一次迭代传播中都被激活（而在典型的多层感知机网络中却是），而是在它的膜电位达到某一个特定值才被激活。当一个神经元被激活，它会产生一个信号传递给其他神经元，提高或降低其膜电位。
 在脉冲神经网络中，神经元的当前激活水平（被建模成某种微分方程）通常被认为是当前状态，一个输入脉冲会使当前这个值升高，持续一段时间，然后逐渐衰退。出现了很多编码方式把这些输出脉冲序列解释为一个实际的数字，这些编码方式会同时考虑到脉冲频率和脉冲间隔时间。
 
+借助于神经科学的研究，人们可以精确的建立基于脉冲产生时间神经网络模型。这种新型的神经网络采用脉冲编码(spike coding)，通过获得脉冲发生的精确时间，这种新型的神经网络可以进行获得更多的信息和更强的计算能力。
+
 Alan Lloyd Hodgkin 和 Andrew Huxley在1952年提出了第一个脉冲神经网络模型，这个模型描述了动作电位是怎样产生并传播的。但是，脉冲并不是在神经元之间直接传播的，它需要在突触间隙间交换一种叫“神经递质”的化学物质。这种生物体的复杂性和可变性导致了许多不同的神经元模型的产生。
 
 从信息论的观点来看，找到一种可以解释脉冲，也就是动作电位的模型是个问题。所以，神经科学的一个基本问题就是确定神经元是否通过时间编码来交流。时间编码表明单一的神经元可以取代上百个S型隐藏层节点。

From f5a4b77111d58216b5f2534d2568142b19ea62e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 09:05:02 +0800
Subject: [PATCH 1013/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index 28637725..c3922717 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -27,3 +27,6 @@ Alan Lloyd Hodgkin 和 Andrew Huxley在1952年提出了第一个脉冲神经网
 这种神经网络大体上可以和传统的人工神经网络一样被用在信息处理中，而且脉冲神经网络可以对一个虚拟昆虫寻找食物的问题建模，而不需要环境的先验知识。并且，由于它更加接近现实的性能，使它可以用来学习生物神经系统的工作，电生理学的脉冲和脉冲神经网络在电脑上的模拟输出相比，确定了拓扑学和生物神经学的假说的可能性。
 
 在实践中脉冲神经网络和已被证明的理论之间还存在一个主要的不同点。脉冲神经网络已被证明在神经科学系统中有作用，而在工程学中还无建树，一些大规模的神经网络已经被设计来利用脉冲神经网络中发现的脉冲编码，这些网络根据储备池计算的原则，但是现实中，大规模的脉冲神经网络计算由于所需计算资源多而产能小，发展受限，造成了只有很少的大规模脉冲神经网络被用来解决复杂的计算问题，而这些之前都是由第二代神经网络解决的。第二代神经网络模型中难以加入时间，脉冲神经网络（特别当算法定义为离散时间时）相当容易观察其动力学特征。我们很难建立一个具有稳定行为的模型来实现一个特定功能。
+
+#### 应用示例
+

From b59625802654c398baacdcbb46f6eb7ecac56f34 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 09:05:27 +0800
Subject: [PATCH 1014/1406] Update ANN.0.12.md

---
 assets/src/ANN/ANN.0.12.md | 66 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)

diff --git a/assets/src/ANN/ANN.0.12.md b/assets/src/ANN/ANN.0.12.md
index c3922717..1abed500 100644
--- a/assets/src/ANN/ANN.0.12.md
+++ b/assets/src/ANN/ANN.0.12.md
@@ -29,4 +29,70 @@ Alan Lloyd Hodgkin 和 Andrew Huxley在1952年提出了第一个脉冲神经网
 在实践中脉冲神经网络和已被证明的理论之间还存在一个主要的不同点。脉冲神经网络已被证明在神经科学系统中有作用，而在工程学中还无建树，一些大规模的神经网络已经被设计来利用脉冲神经网络中发现的脉冲编码，这些网络根据储备池计算的原则，但是现实中，大规模的脉冲神经网络计算由于所需计算资源多而产能小，发展受限，造成了只有很少的大规模脉冲神经网络被用来解决复杂的计算问题，而这些之前都是由第二代神经网络解决的。第二代神经网络模型中难以加入时间，脉冲神经网络（特别当算法定义为离散时间时）相当容易观察其动力学特征。我们很难建立一个具有稳定行为的模型来实现一个特定功能。
 
 #### 应用示例
+```python
+import chainer, math
+import numpy as np
+from chainer import cuda
+from chainer import function
+from chainer.utils import type_check
 
+class SELU(function.Function):
+	def __init__(self, alpha, lam):
+		self.alpha = float(alpha)
+		self.lam = float(lam)
+
+	def check_type_forward(self, in_types):
+		type_check.expect(in_types.size() == 1)
+		x_type, = in_types
+		type_check.expect(x_type.dtype.kind == 'f')
+
+	def forward_cpu(self, x):
+		y = x[0].copy()
+		neg_indices = x[0] <= 0
+		y[neg_indices] = self.alpha * (np.exp(y[neg_indices]) - 1)
+		y *= self.lam
+		return y,
+
+	def forward_gpu(self, x):
+		y = cuda.elementwise(
+			'T x, T alpha, T lam', 'T y',
+			'y = x > 0 ? (T)(lam * x) : (T)(lam * alpha * (exp(x) - 1))',
+			'elu_fwd')(x[0], self.alpha, self.lam)
+		return y,
+
+	def backward_cpu(self, x, gy):
+		gx = gy[0].copy()
+		neg_indices = x[0] <= 0
+		gx[neg_indices] *= self.alpha * np.exp(x[0][neg_indices])
+		gx *= self.lam
+		return gx,
+
+	def backward_gpu(self, x, gy):
+		gx = cuda.elementwise(
+			'T x, T gy, T alpha, T lam', 'T gx',
+			'gx = x > 0 ? (T)(lam * gy) : (T)(lam * gy * alpha * exp(x))',
+			'elu_bwd')(
+				x[0], gy[0], self.alpha, self.lam)
+		return gx,
+
+
+def selu(x, alpha=1.6732632423543772848170429916717, lam=1.0507009873554804934193349852946):
+	return SELU(alpha, lam)(x)
+
+def dropout_selu(x, ratio=0.1, alpha=-1.7580993408473766):
+	if chainer.config.train == False:
+		return x
+
+	q = 1.0 - ratio
+
+	xp = cuda.get_array_module(*x)
+	if xp == np:
+		d = np.random.rand(*x[0].shape) >= ratio
+	else:
+		d = xp.random.rand(*x[0].shape, dtype=np.float32) >= ratio
+
+	a = math.pow(q + alpha ** 2 * q * (1 - q), -0.5)
+	b = -a * (1 - q) * alpha
+
+	return a * (x * d + alpha * (1 - d)) + b
+```

From aa87466f49d49def422fa024e7ab929bb5c19802 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Fri, 1 Jun 2018 11:45:08 +0800
Subject: [PATCH 1015/1406] add DL

---
 assets/src/DL/DL.0.1.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 assets/src/DL/DL.0.1.md

diff --git a/assets/src/DL/DL.0.1.md b/assets/src/DL/DL.0.1.md
new file mode 100644
index 00000000..f286864f
--- /dev/null
+++ b/assets/src/DL/DL.0.1.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 深度学习(Deep Learning)

From ed9c576c01b6c40adbdce7c80303c777fe2f4fa4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 11:48:01 +0800
Subject: [PATCH 1016/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1fe4c561..1898545f 100644
--- a/README.md
+++ b/README.md
@@ -130,7 +130,7 @@
      * [受限玻尔兹曼机(Restricted Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.10.md) 
      * [自组织映射(Self-Organizing Map)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.11.md) 
      * [脉冲神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
- * [深度学习(Deep Learning)]() 
+ * [深度学习(Deep Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.1.md) 
      * [深度信念网络(Deep Belief Machines)]() 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
      * [深度递归神经网络(Deep Recurrent Neural Networks)]() 

From 67e09373daaa1bc407fd5e86b5d060691837c30f Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Fri, 1 Jun 2018 11:50:30 +0800
Subject: [PATCH 1017/1406] change page of readme

---
 README.md               | 2 +-
 assets/src/DL/DL.0.2.md | 5 +++++
 2 files changed, 6 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/DL/DL.0.2.md

diff --git a/README.md b/README.md
index 1898545f..4a1bd428 100644
--- a/README.md
+++ b/README.md
@@ -131,7 +131,7 @@
      * [自组织映射(Self-Organizing Map)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.11.md) 
      * [脉冲神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
  * [深度学习(Deep Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.1.md) 
-     * [深度信念网络(Deep Belief Machines)]() 
+     * [深度信念网络(Deep Belief Machines)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.2.md) 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
      * [深度递归神经网络(Deep Recurrent Neural Networks)]() 
      * [分层时间记忆(Hierarchical Temporal Memory)]() 
diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
new file mode 100644
index 00000000..1bcc52b5
--- /dev/null
+++ b/assets/src/DL/DL.0.2.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 深度信念网络(Deep Belief Machines)

From 83120e362f2e9c166ca953a3cc3140dd0e6b9c24 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 1 Jun 2018 22:16:30 +0800
Subject: [PATCH 1018/1406] change page of DL

---
 assets/src/DL/DL.0.1.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/assets/src/DL/DL.0.1.md b/assets/src/DL/DL.0.1.md
index f286864f..3e6eaf7c 100644
--- a/assets/src/DL/DL.0.1.md
+++ b/assets/src/DL/DL.0.1.md
@@ -3,3 +3,18 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度学习(Deep Learning)
+深度学习是机器学习研究中的一个新的领域，其动机在于建立、模拟人脑进行分析学习的神经网络，它模仿人脑的机制来解释数据，例如图像，声音和文本。深度学习是无监督学习的一种。
+
+深度学习的概念源于人工神经网络的研究。含多隐层的多层感知器就是一种深度学习结构。深度学习通过组合低层特征形成更加抽象的高层表示属性类别或特征，以发现数据的分布式特征表示。
+
+Deep learning本身算是machine learning的一个分支，简单可以理解为neural network的发展。大约二三十年前，neural network曾经是ML领域特别火热的一个方向，但是后来确慢慢淡出了，原因包括以下几个方面：
+
+(1)比较容易过拟合，参数比较难tune，而且需要不少trick；
+
+(2)训练速度比较慢，在层次比较少（小于等于3）的情况下效果并不比其它方法更优；
+
+所以中间有大约20多年的时间，神经网络被关注很少，这段时间基本上是SVM和boosting算法的天下。但是，一个痴心的老先生Hinton，他坚持了下来，并最终（和其它人一起Bengio、Yann.lecun等）提成了一个实际可行的deep learning框架。
+
+Deep learning与传统的神经网络之间有相同的地方也有很多不同。
+
+二者的相同在于deep learning采用了神经网络相似的分层结构，系统由包括输入层、隐层（多层）、输出层组成的多层网络，只有相邻层节点之间有连接，同一层以及跨层节点之间相互无连接，每一层可以看作是一个logistic regression模型；这种分层结构，是比较接近人类大脑的结构的。
\ No newline at end of file

From b68ab3c1905cc44ceffc6794353ab55af0570be4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 22:18:39 +0800
Subject: [PATCH 1019/1406] Update DL.0.1.md

---
 assets/src/DL/DL.0.1.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.1.md b/assets/src/DL/DL.0.1.md
index 3e6eaf7c..e32a6759 100644
--- a/assets/src/DL/DL.0.1.md
+++ b/assets/src/DL/DL.0.1.md
@@ -3,6 +3,10 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度学习(Deep Learning)
+深度学习的概念源于人工神经网络的研究。含多隐层的多层感知器就是一种深度学习结构。深度学习通过组合低层特征形成更加抽象的高层表示属性类别或特征，以发现数据的分布式特征表示。 
+
+深度学习的概念由Hinton等人于2006年提出。基于深度置信网络(DBN)提出非监督贪心逐层训练算法，为解决深层结构相关的优化难题带来希望，随后提出多层自动编码器深层结构。此外Lecun等人提出的卷积神经网络是第一个真正多层结构学习算法，它利用空间相对关系减少参数数目以提高训练性能。
+
 深度学习是机器学习研究中的一个新的领域，其动机在于建立、模拟人脑进行分析学习的神经网络，它模仿人脑的机制来解释数据，例如图像，声音和文本。深度学习是无监督学习的一种。
 
 深度学习的概念源于人工神经网络的研究。含多隐层的多层感知器就是一种深度学习结构。深度学习通过组合低层特征形成更加抽象的高层表示属性类别或特征，以发现数据的分布式特征表示。
@@ -17,4 +21,5 @@ Deep learning本身算是machine learning的一个分支，简单可以理解为
 
 Deep learning与传统的神经网络之间有相同的地方也有很多不同。
 
-二者的相同在于deep learning采用了神经网络相似的分层结构，系统由包括输入层、隐层（多层）、输出层组成的多层网络，只有相邻层节点之间有连接，同一层以及跨层节点之间相互无连接，每一层可以看作是一个logistic regression模型；这种分层结构，是比较接近人类大脑的结构的。
\ No newline at end of file
+二者的相同在于deep learning采用了神经网络相似的分层结构，系统由包括输入层、隐层（多层）、输出层组成的多层网络，只有相邻层节点之间有连接，同一层以及跨层节点之间相互无连接，每一层可以看作是一个logistic regression模型；这种分层结构，是比较接近人类大脑的结构的。
+

From e19df73c0c4e3a901337030a7b9bce751e10688f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 22:19:15 +0800
Subject: [PATCH 1020/1406] Update DL.0.1.md

---
 assets/src/DL/DL.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.1.md b/assets/src/DL/DL.0.1.md
index e32a6759..0b99c544 100644
--- a/assets/src/DL/DL.0.1.md
+++ b/assets/src/DL/DL.0.1.md
@@ -23,3 +23,5 @@ Deep learning与传统的神经网络之间有相同的地方也有很多不同
 
 二者的相同在于deep learning采用了神经网络相似的分层结构，系统由包括输入层、隐层（多层）、输出层组成的多层网络，只有相邻层节点之间有连接，同一层以及跨层节点之间相互无连接，每一层可以看作是一个logistic regression模型；这种分层结构，是比较接近人类大脑的结构的。
 
+深度学习(Deep Learning)的应用算法有：
+

From 1f5636d948def05741cd2e70102b1fcaba9682c9 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 1 Jun 2018 22:22:07 +0800
Subject: [PATCH 1021/1406] change page of DL

---
 assets/src/DL/DL.0.1.md | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.1.md b/assets/src/DL/DL.0.1.md
index 0b99c544..f4e9aa74 100644
--- a/assets/src/DL/DL.0.1.md
+++ b/assets/src/DL/DL.0.1.md
@@ -24,4 +24,10 @@ Deep learning与传统的神经网络之间有相同的地方也有很多不同
 二者的相同在于deep learning采用了神经网络相似的分层结构，系统由包括输入层、隐层（多层）、输出层组成的多层网络，只有相邻层节点之间有连接，同一层以及跨层节点之间相互无连接，每一层可以看作是一个logistic regression模型；这种分层结构，是比较接近人类大脑的结构的。
 
 深度学习(Deep Learning)的应用算法有：
-
+* 深度信念网络(Deep Belief Machines)
+* 深度卷积神经网络(Deep Convolutional Neural Networks)
+* 深度递归神经网络(Deep Recurrent Neural Networks)
+* 分层时间记忆(Hierarchical Temporal Memory)
+* 深度玻尔兹曼机(Deep Boltzmann Machine)
+* 堆叠自动编码器(Stacked Boltzmann Machine)
+* 生成式对抗网络(Generative Adversarial Networks)

From d0a8fb47376d41438782cdb26a41d3800dc3a00e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Fri, 1 Jun 2018 22:26:58 +0800
Subject: [PATCH 1022/1406] change page of DL

---
 assets/src/DL/DL.0.3.md | 5 +++++
 assets/src/DL/DL.0.4.md | 5 +++++
 assets/src/DL/DL.0.5.md | 5 +++++
 assets/src/DL/DL.0.6.md | 5 +++++
 assets/src/DL/DL.0.7.md | 5 +++++
 assets/src/DL/DL.0.8.md | 5 +++++
 6 files changed, 30 insertions(+)
 create mode 100644 assets/src/DL/DL.0.3.md
 create mode 100644 assets/src/DL/DL.0.4.md
 create mode 100644 assets/src/DL/DL.0.5.md
 create mode 100644 assets/src/DL/DL.0.6.md
 create mode 100644 assets/src/DL/DL.0.7.md
 create mode 100644 assets/src/DL/DL.0.8.md

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
new file mode 100644
index 00000000..eb5f7a52
--- /dev/null
+++ b/assets/src/DL/DL.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 深度卷积神经网络(Deep Convolutional Neural Networks)
diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
new file mode 100644
index 00000000..3bfb9a83
--- /dev/null
+++ b/assets/src/DL/DL.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 深度递归神经网络(Deep Recurrent Neural Networks)
diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
new file mode 100644
index 00000000..e476e1d9
--- /dev/null
+++ b/assets/src/DL/DL.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 分层时间记忆(Hierarchical Temporal Memory)
diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
new file mode 100644
index 00000000..ea82cdab
--- /dev/null
+++ b/assets/src/DL/DL.0.6.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 深度玻尔兹曼机(Deep Boltzmann Machine)
diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
new file mode 100644
index 00000000..b7771af9
--- /dev/null
+++ b/assets/src/DL/DL.0.7.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 堆叠自动编码器(Stacked Boltzmann Machine)
diff --git a/assets/src/DL/DL.0.8.md b/assets/src/DL/DL.0.8.md
new file mode 100644
index 00000000..a8f3f1c3
--- /dev/null
+++ b/assets/src/DL/DL.0.8.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 生成式对抗网络(Generative Adversarial Networks)

From 4658c8996ac28a4b99dbfa62959cd8e564ed65d1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 22:32:36 +0800
Subject: [PATCH 1023/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 4a1bd428..9b539922 100644
--- a/README.md
+++ b/README.md
@@ -132,7 +132,7 @@
      * [脉冲神经网络(Spiking Neural Network)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ANN/ANN.0.12.md) 
  * [深度学习(Deep Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.1.md) 
      * [深度信念网络(Deep Belief Machines)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.2.md) 
-     * [深度卷积神经网络(Deep Convolutional Neural Networks)]() 
+     * [深度卷积神经网络(Deep Convolutional Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.3.md) 
      * [深度递归神经网络(Deep Recurrent Neural Networks)]() 
      * [分层时间记忆(Hierarchical Temporal Memory)]() 
      * [深度玻尔兹曼机(Deep Boltzmann Machine)]() 

From c7d0409c6a49320ba20ec74e1b1bae4369de0d81 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Jun 2018 23:17:19 +0800
Subject: [PATCH 1024/1406] Update README.md

---
 README.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index 9b539922..9ae70038 100644
--- a/README.md
+++ b/README.md
@@ -133,11 +133,11 @@
  * [深度学习(Deep Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.1.md) 
      * [深度信念网络(Deep Belief Machines)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.2.md) 
      * [深度卷积神经网络(Deep Convolutional Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.3.md) 
-     * [深度递归神经网络(Deep Recurrent Neural Networks)]() 
-     * [分层时间记忆(Hierarchical Temporal Memory)]() 
-     * [深度玻尔兹曼机(Deep Boltzmann Machine)]() 
-     * [堆叠自动编码器(Stacked Boltzmann Machine)]() 
-     * [生成式对抗网络(Generative Adversarial Networks)]()
+     * [深度递归神经网络(Deep Recurrent Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.4.md) 
+     * [分层时间记忆(Hierarchical Temporal Memory)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.5.md) 
+     * [深度玻尔兹曼机(Deep Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
+     * [堆叠自动编码器(Stacked Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md) 
+     * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.8.md)
  * [降维算法]()
      * [主成分分析法（PCA）]()
      * [主成分回归（PCR）]()

From 99645210d6498c05f75660ff965f4a6d7ee34a65 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 3 Jun 2018 07:38:39 +0800
Subject: [PATCH 1025/1406] Update README.md

---
 README.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/README.md b/README.md
index 9ae70038..b86c64e1 100644
--- a/README.md
+++ b/README.md
@@ -30,7 +30,6 @@
  * [机器学习的框架](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.03.md)
  * [机器学习的应用案例]()
 
-
 #### 深度学习
 * 深度学习：深度学习是基于机器学习延伸出来的一个新的领域，由以人大脑结构为启发的神经网络算法为起源加之模型结构深度的增加发展，并伴随大数据和计算能力的提高而产生的一系列新的算法。
 * 深度学习的方向：被应用在图像处理与计算机视觉，自然语言处理以及语音识别等领域。 
@@ -40,7 +39,6 @@
  * [深度学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Neural%20Network/NNK.03.md)
  * [深度学习的应用案例]()
 
-
 #### 机器学习算法概览
 <p align="center">
 <img width="100%" align="center" src="assets/images/overview.png" />

From 7e82d717b3688dcb0d289216d21b66c410d99e74 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 5 Jun 2018 11:58:38 +0800
Subject: [PATCH 1026/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 1bcc52b5..a67bfa67 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度信念网络(Deep Belief Machines)
+

From 0b06a340b310608da2a0d67b982df805df698bc5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 6 Jun 2018 10:30:02 +0800
Subject: [PATCH 1027/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index a67bfa67..bb5f7827 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -4,3 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度信念网络(Deep Belief Machines)
 
+深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。

From 7292157e4dc9707dd3cfc257579333cd6c7ca7f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 6 Jun 2018 22:49:32 +0800
Subject: [PATCH 1028/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index bb5f7827..751d4cfb 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -3,5 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度信念网络(Deep Belief Machines)
-
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。

From 4528034341c6ad3aca627a59604b3b0c8a7b51e5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 7 Jun 2018 08:53:38 +0800
Subject: [PATCH 1029/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 751d4cfb..bb5f7827 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -3,4 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度信念网络(Deep Belief Machines)
+
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。

From cbab75105c0d5ab28834398bfa66791736a7701d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 10 Jun 2018 16:29:07 +0800
Subject: [PATCH 1030/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index bb5f7827..e20421e1 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -5,3 +5,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 深度信念网络(Deep Belief Machines)
 
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
+
+DBN 由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
+DBN 的组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。

From 7e8363d5688d882ceff2876b5ed26f8022adf96d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 10 Jun 2018 16:31:07 +0800
Subject: [PATCH 1031/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index e20421e1..cf699236 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -6,5 +6,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
 
-DBN 由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
+深度信念网络 由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 DBN 的组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。

From a98a64be95b713f21abec1a0e9715ed5ea51f2d1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 10 Jun 2018 16:31:51 +0800
Subject: [PATCH 1032/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index cf699236..21ec62ab 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -6,5 +6,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
 
-深度信念网络 由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
+深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 DBN 的组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。

From 37be5123af44d21a76ad90cde8ee83e7ce4d29d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 11 Jun 2018 08:49:23 +0800
Subject: [PATCH 1033/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 21ec62ab..5cd037fe 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -7,4 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
 
 深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
-DBN 的组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
+
+深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。

From 03ffc8309486a30aee5ef4a84abb6b1738df08aa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 11 Jun 2018 08:53:42 +0800
Subject: [PATCH 1034/1406] Update BIR.md

---
 assets/src/BIR/BIR.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BIR/BIR.md b/assets/src/BIR/BIR.md
index 370d12f5..4365c431 100644
--- a/assets/src/BIR/BIR.md
+++ b/assets/src/BIR/BIR.md
@@ -11,7 +11,6 @@
 
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
-
 #### BIRCH
 1 算法摘要
 

From c5d9529f74caee67dc08c21096bd12e962d754c7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 12 Jun 2018 08:48:02 +0800
Subject: [PATCH 1035/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 5cd037fe..79677a0c 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -5,7 +5,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 深度信念网络(Deep Belief Machines)
 
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
-
 深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。

From 05e5cc09648d1479f57a635256615c274fb478eb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 15 Jun 2018 14:48:42 +0800
Subject: [PATCH 1036/1406] Update README.md

---
 README.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/README.md b/README.md
index b86c64e1..3805dae0 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 最近以来一直在学习机器学习和算法，然后自己就在不断总结和写笔记，记录下自己的学习AI与算法历程。
 机器学习(Machine Learning, ML)是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。专门研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。
 
@@ -6,6 +7,12 @@
 <img width="100%" align="center" src="assets/images/global.png" />
 </p>
 
+<p align='center'>
+<img src="https://img.shields.io/badge/build-passing-brightgreen.svg">
+<a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>
+<a href="https://www.zhihu.com/people/sencoed.com/activities"><img src="https://img.shields.io/badge/%E7%9F%A5%E4%B9%8E-keke-green.svg?style=flat&colorA=009df2"></a>
+</p>
+
 * 机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。
 * 机器学习：多领域交叉学科，涉及概率论统计学，逼近论，凸分析，算法复杂度理论等多门学科。
 * 机器学习的应用：语音识别，自动驾驶，语言翻译，计算机视觉，推荐系统，无人机，识别垃圾邮件，人脸识别，电商推荐系统。

From e39654efec40cededfd170188242a7a72f2555e5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 15 Jun 2018 14:49:43 +0800
Subject: [PATCH 1037/1406] Update README.md

---
 README.md | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index 3805dae0..baaa3103 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,9 @@
 ### Deeplearning Algorithms tutorial
-
+<p align='left'>
+<img src="https://img.shields.io/badge/build-passing-brightgreen.svg">
+<a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>
+<a href="https://www.zhihu.com/people/sencoed.com/activities"><img src="https://img.shields.io/badge/%E7%9F%A5%E4%B9%8E-keke-green.svg?style=flat&colorA=009df2"></a>
+</p>
 最近以来一直在学习机器学习和算法，然后自己就在不断总结和写笔记，记录下自己的学习AI与算法历程。
 机器学习(Machine Learning, ML)是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。专门研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。
 
@@ -7,12 +11,6 @@
 <img width="100%" align="center" src="assets/images/global.png" />
 </p>
 
-<p align='center'>
-<img src="https://img.shields.io/badge/build-passing-brightgreen.svg">
-<a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>
-<a href="https://www.zhihu.com/people/sencoed.com/activities"><img src="https://img.shields.io/badge/%E7%9F%A5%E4%B9%8E-keke-green.svg?style=flat&colorA=009df2"></a>
-</p>
-
 * 机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。
 * 机器学习：多领域交叉学科，涉及概率论统计学，逼近论，凸分析，算法复杂度理论等多门学科。
 * 机器学习的应用：语音识别，自动驾驶，语言翻译，计算机视觉，推荐系统，无人机，识别垃圾邮件，人脸识别，电商推荐系统。

From 59b46f20dd45db42fc5ec13c20d727226ab7e606 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 08:47:04 +0800
Subject: [PATCH 1038/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 79677a0c..3d535b5f 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度信念网络(Deep Belief Machines)
-
 深度信念网络 (Deep Belief Network, DBN) 由 Geoffrey Hinton 在 2006 年提出。它是一种生成模型，通过训练其神经元间的权重，我们可以让整个神经网络按照最大概率来生成训练数据。我们不仅可以使用 DBN 识别特征、分类数据，还可以用它来生成数据。
 深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 

From 60484f889708a2845a4527b6b42db65d66c662ec Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 21 Jun 2018 08:52:19 +0800
Subject: [PATCH 1039/1406] add images

---
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 assets/images/358.jpg | Bin 0 -> 87433 bytes
 assets/images/359.jpg | Bin 0 -> 137822 bytes
 3 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/357.jpg
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From cf50a6b2c71508abc270ab5d842b739c7fe9b930 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 08:54:17 +0800
Subject: [PATCH 1040/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 3d535b5f..8e079796 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -7,3 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
+<p align="center">
+<img width="300" align="center" src="../../images/357.jpg" />
+</p>

From d62ad502fb0bfbb6172cd133ae55424485f3cbb0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 08:56:22 +0800
Subject: [PATCH 1041/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 8e079796..3c6ed1ea 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -8,5 +8,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
 <p align="center">
-<img width="300" align="center" src="../../images/357.jpg" />
+<img width="400" align="center" src="../../images/357.jpg" />
 </p>

From 45330d30d9187b0d6a4e4d7bd859cbe4745be343 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 08:58:14 +0800
Subject: [PATCH 1042/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 3c6ed1ea..fb80dab5 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -7,6 +7,17 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 深度信念网络(Deep Belief Network, DBN)由多层神经元构成，这些神经元又分为显性神经元和隐性神经元（以下简称显元和隐元）。显元用于接受输入，隐元用于提取特征。因此隐元也有个别名，叫特征检测器 (feature detectors)。最顶上的两层间的连接是无向的，组成联合内存 (associative memory)。较低的其他层之间有连接上下的有向连接。最底层代表了数据向量 (data vectors)，每一个神经元代表数据向量的一维。 
 
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
+
 <p align="center">
 <img width="400" align="center" src="../../images/357.jpg" />
 </p>
+
+如上图所示用两个限制玻尔兹曼机堆叠起来，构成深度信念网络(Deep Belief Nets, 简称DBN)。
+
+* 利用输入，生成第一个限制玻尔兹曼机，得到输入的特征。
+* 利上面得到的输入的特征，生成每二个限制玻尔兹曼机，得到特征的特征。
+* 以次循环，可以得到多个限制玻尔兹曼机。
+* 把得到次序到多个限制玻尔兹曼机堆叠起来，构成一个DBN。
+* 以上是一种贪婪的训练堆叠方式，对网络的预训练非常好。 
+
+这样得到的效果跟autoencoder的堆叠一致。

From 6faa653ba5f31c3eee041dbabbc46e747b84630e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 09:03:11 +0800
Subject: [PATCH 1043/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index fb80dab5..946d68e4 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -15,8 +15,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 如上图所示用两个限制玻尔兹曼机堆叠起来，构成深度信念网络(Deep Belief Nets, 简称DBN)。
 
 * 利用输入，生成第一个限制玻尔兹曼机，得到输入的特征。
-* 利上面得到的输入的特征，生成每二个限制玻尔兹曼机，得到特征的特征。
-* 以次循环，可以得到多个限制玻尔兹曼机。
+* 利用上面得到的输入的特征，生成每二个限制玻尔兹曼机，得到特征的特征。
+* 依次循环，可以得到多个限制玻尔兹曼机。
 * 把得到次序到多个限制玻尔兹曼机堆叠起来，构成一个DBN。
 * 以上是一种贪婪的训练堆叠方式，对网络的预训练非常好。 
 

From d2dba6c1b1aaf4f78708f5343ea819630940899c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 09:09:05 +0800
Subject: [PATCH 1044/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 17 ++++++++++++++++-
 1 file changed, 16 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 946d68e4..a5848ad8 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -9,7 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
 
 <p align="center">
-<img width="400" align="center" src="../../images/357.jpg" />
+<img width="500" align="center" src="../../images/357.jpg" />
 </p>
 
 如上图所示用两个限制玻尔兹曼机堆叠起来，构成深度信念网络(Deep Belief Nets, 简称DBN)。
@@ -21,3 +21,18 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 以上是一种贪婪的训练堆叠方式，对网络的预训练非常好。 
 
 这样得到的效果跟autoencoder的堆叠一致。
+
+wake-sleep算法：在分类问题中，DBN的最底层可以是已知的label层，如下图:
+<p align="center">
+<img width="500" align="center" src="../../images/358.jpg" />
+</p>
+
+上图是MNIST数字识别的一个任务，输入是28*28的图片，输出是0到9的数字。
+
+在经过上面提到的贪婪地堆叠训练后，再加上一层label层进行训练。然后再利用wake-sleep算法进行调优:
+* wake: 认知过程，通过外界的特征和向上的权重 (认知权重) 产生每一层的抽象表示 (结点状态) ，并且使用梯度下降修改层间的下行权重 (生成权重) 。自底向上，进行训练
+* sleep: 生成过程，通过顶层表示 (醒时学得的概念) 和向下权重，生成底层的状态，同时修改层间向上的权重。自项向下，进行训练
+
+在上面的训练完成后，如果对最上的两层进行随机的Gibbs采样，然后再逐渐从顶到底，生成的图像就是0到9中的一个图像。 
+感觉这个跟人回忆、画画、做梦的过程非常像。
+

From 956c07610fc72851a6cda4be327357d3ea69fc5c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 09:09:32 +0800
Subject: [PATCH 1045/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index a5848ad8..389ca33d 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -9,7 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 深度信念网络(Deep Belief Network, DBN)组成元件是受限玻尔兹曼机 (Restricted Boltzmann Machines, RBM)。训练 DBN 的过程是一层一层地进行的。在每一层中，用数据向量来推断隐层，再把这一隐层当作下一层 (高一层) 的数据向量。
 
 <p align="center">
-<img width="500" align="center" src="../../images/357.jpg" />
+<img width="400" align="center" src="../../images/357.jpg" />
 </p>
 
 如上图所示用两个限制玻尔兹曼机堆叠起来，构成深度信念网络(Deep Belief Nets, 简称DBN)。
@@ -24,7 +24,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 wake-sleep算法：在分类问题中，DBN的最底层可以是已知的label层，如下图:
 <p align="center">
-<img width="500" align="center" src="../../images/358.jpg" />
+<img width="400" align="center" src="../../images/358.jpg" />
 </p>
 
 上图是MNIST数字识别的一个任务，输入是28*28的图片，输出是0到9的数字。

From 722b2dc05fd00c795c9126c69b1e03d4b38f743b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 09:10:31 +0800
Subject: [PATCH 1046/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 389ca33d..98c1be16 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -35,4 +35,7 @@ wake-sleep算法：在分类问题中，DBN的最底层可以是已知的label
 
 在上面的训练完成后，如果对最上的两层进行随机的Gibbs采样，然后再逐渐从顶到底，生成的图像就是0到9中的一个图像。 
 感觉这个跟人回忆、画画、做梦的过程非常像。
-
+<p align="center">
+<img width="400" align="center" src="../../images/359.jpg" />
+</p>
+由stuff、image、label的构成，是右边这种模式，而非左边那种。所以，一个更好的方式是直接从image，进行非监督还原成stuff，然后再学习stuff与label的关系。这也就是非监督的预训练有效的原因。

From 9fedf8850bce9b18d4af74bfe35c2de4894cfc18 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 21 Jun 2018 09:12:36 +0800
Subject: [PATCH 1047/1406] Update DL.0.2.md

---
 assets/src/DL/DL.0.2.md | 39 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 39 insertions(+)

diff --git a/assets/src/DL/DL.0.2.md b/assets/src/DL/DL.0.2.md
index 98c1be16..55386c8d 100644
--- a/assets/src/DL/DL.0.2.md
+++ b/assets/src/DL/DL.0.2.md
@@ -39,3 +39,42 @@ wake-sleep算法：在分类问题中，DBN的最底层可以是已知的label
 <img width="400" align="center" src="../../images/359.jpg" />
 </p>
 由stuff、image、label的构成，是右边这种模式，而非左边那种。所以，一个更好的方式是直接从image，进行非监督还原成stuff，然后再学习stuff与label的关系。这也就是非监督的预训练有效的原因。
+
+#### 应用示例
+```python
+import numpy as np
+from rbm import *
+class dbn:
+    def __init__(self,sizes = [],learning_rate = 0.01,numepochs = 1):
+        print 'dbn init ,sizes:',sizes,', numepochs:',numepochs
+        self.sizes = sizes
+        self.rbms = []
+        self.learning_rate = learning_rate
+        self.numepochs = numepochs
+
+        for i in range(len(self.sizes)-1):
+            self.rbms.append(rbm(sizes[i:i+2],self.learning_rate,self.numepochs))
+
+    def train(self,X):
+        #for i in range(self.numepochs):
+      for j in range(len(self.sizes)-1):
+            self.rbms[j].train(X)
+            X = self.rbms[j].v2h(X)
+
+    def v2h(self,X):
+        for j in range(len(self.sizes)-1):
+            X = self.rbms[j].v2h(X)
+        return X
+
+    def h2v(self,X):
+        for j in range(len(self.sizes)-1):
+            if j == len(self.sizes)-2:
+                X = self.rbms[len(self.sizes)-j-2].h2v(X,False);
+            else:
+                X = self.rbms[len(self.sizes)-j-2].h2v(X)
+        return X
+
+    def predict(self, X):
+        return self.h2v(self.v2h(X))
+
+```

From b7e59a5f273693f110afe3a08955023b8f54933c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 25 Jun 2018 08:51:10 +0800
Subject: [PATCH 1048/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index eb5f7a52..ac5c51f2 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,3 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
+卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
+
+卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。

From dca0893f3d97b4d15717130cd6f916721c638aca Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 29 Jun 2018 09:09:55 +0800
Subject: [PATCH 1049/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index ac5c51f2..586dfb37 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
+
 卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
 
 卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。

From 483bd8eb91514f6f26cf55d8c8156e9501a20fc8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 30 Jun 2018 08:05:15 +0800
Subject: [PATCH 1050/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 586dfb37..ac5c51f2 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
-
 卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
 
 卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。

From 39acc54118524cf45f5dd72d71a8d81f6b505a7e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 30 Jun 2018 08:05:21 +0800
Subject: [PATCH 1051/1406] Update DL.0.3.md


From 0414e6c1ceb0fdf99cab1cd8e35e1de005152238 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 08:38:45 +0800
Subject: [PATCH 1052/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index ac5c51f2..586dfb37 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
+
 卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
 
 卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。

From 43771ba74b61ece5e8a4c74b15478fea64e9a2ac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 08:39:45 +0800
Subject: [PATCH 1053/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 586dfb37..0f555f1f 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -7,3 +7,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
 
 卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。
+
+卷积层（Convolutional layer），卷积神经网络中每层卷积层由若干卷积单元组成，每个卷积单元的参数都是通过反向传播算法最佳化得到的。卷积运算的目的是提取输入的不同特征，第一层卷积层可能只能提取一些低级的特征如边缘、线条和角等层级，更多层的网路能从低级特征中迭代提取更复杂的特征。
+
+线性整流层（Rectified Linear Units layer, ReLU layer）使用线性整流（Rectified Linear Units, ReLU） {\displaystyle f(x)=\max(0,x)} {\displaystyle f(x)=\max(0,x)}作为这一层神经的激励函数（Activation function）。它可以增强判定函数和整个神经网络的非线性特性，而本身并不会改变卷积层。
+
+事实上，其他的一些函数也可以用于增强网络的非线性特性，如双曲正切函数 {\displaystyle f(x)=\tanh(x)} {\displaystyle f(x)=\tanh(x)}, {\displaystyle f(x)=|\tanh(x)|} {\displaystyle f(x)=|\tanh(x)|}，或者Sigmoid函数 {\displaystyle f(x)=(1+e^{-x})^{-1}} {\displaystyle f(x)=(1+e^{-x})^{-1}}。相比其它函数来说，ReLU函数更受青睐，这是因为它可以将神经网络的训练速度提升数倍[3]，而并不会对模型的泛化准确度造成显著影响。

From 7e4f2d612d17460ae45f90187913ff3b0a94311a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 08:40:15 +0800
Subject: [PATCH 1054/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 0f555f1f..5ad8c5e6 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -13,3 +13,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 线性整流层（Rectified Linear Units layer, ReLU layer）使用线性整流（Rectified Linear Units, ReLU） {\displaystyle f(x)=\max(0,x)} {\displaystyle f(x)=\max(0,x)}作为这一层神经的激励函数（Activation function）。它可以增强判定函数和整个神经网络的非线性特性，而本身并不会改变卷积层。
 
 事实上，其他的一些函数也可以用于增强网络的非线性特性，如双曲正切函数 {\displaystyle f(x)=\tanh(x)} {\displaystyle f(x)=\tanh(x)}, {\displaystyle f(x)=|\tanh(x)|} {\displaystyle f(x)=|\tanh(x)|}，或者Sigmoid函数 {\displaystyle f(x)=(1+e^{-x})^{-1}} {\displaystyle f(x)=(1+e^{-x})^{-1}}。相比其它函数来说，ReLU函数更受青睐，这是因为它可以将神经网络的训练速度提升数倍[3]，而并不会对模型的泛化准确度造成显著影响。
+
+池化（Pooling）是卷积神经网络中另一个重要的概念，它实际上是一种形式的降采样。有多种不同形式的非线性池化函数，而其中“最大池化（Max pooling）”是最为常见的。它是将输入的图像划分为若干个矩形区域，对每个子区域输出最大值。直觉上，这种机制能够有效地原因在于，在发现一个特征之后，它的精确位置远不及它和其他特征的相对位置的关系重要。池化层会不断地减小数据的空间大小，因此参数的数量和计算量也会下降，这在一定程度上也控制了过拟合。通常来说，CNN的卷积层之间都会周期性地插入池化层。
+
+池化层通常会分别作用于每个输入的特征并减小其大小。目前最常用形式的池化层是每隔2个元素从图像划分出 {\displaystyle 2\times 2} 2\times 2的区块，然后对每个区块中的4个数取最大值。这将会减少75%的数据量。
+
+除了最大池化之外，池化层也可以使用其他池化函数，例如“平均池化”甚至“L2-范数池化”等。过去，平均池化的使用曾经较为广泛，但是最近由于最大池化在实践中的表现更好，平均池化已经不太常用。
+
+由于池化层过快地减少了数据的大小，目前文献中的趋势是使用较小的池化滤镜，[4]甚至不再使用池化层。

From 5abed9b359202f1b366c4932b55bf566b669d253 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Mon, 2 Jul 2018 08:43:11 +0800
Subject: [PATCH 1055/1406] change page of DL

---
 assets/images/360.jpg   | Bin 0 -> 13503 bytes
 assets/src/DL/DL.0.3.md |   4 ++++
 2 files changed, 4 insertions(+)
 create mode 100644 assets/images/360.jpg

diff --git a/assets/images/360.jpg b/assets/images/360.jpg
new file mode 100644
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diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 5ad8c5e6..84bdcc2d 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -21,3 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 除了最大池化之外，池化层也可以使用其他池化函数，例如“平均池化”甚至“L2-范数池化”等。过去，平均池化的使用曾经较为广泛，但是最近由于最大池化在实践中的表现更好，平均池化已经不太常用。
 
 由于池化层过快地减少了数据的大小，目前文献中的趋势是使用较小的池化滤镜，[4]甚至不再使用池化层。
+
+<p align="center">
+<img width="400" align="center" src="../../images/360.jpg" />
+</p>

From bf70eda3055bb1e9e62ae13b35f726588b893c18 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 08:44:51 +0800
Subject: [PATCH 1056/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 84bdcc2d..5bd0b80d 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -12,7 +12,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性整流层（Rectified Linear Units layer, ReLU layer）使用线性整流（Rectified Linear Units, ReLU） {\displaystyle f(x)=\max(0,x)} {\displaystyle f(x)=\max(0,x)}作为这一层神经的激励函数（Activation function）。它可以增强判定函数和整个神经网络的非线性特性，而本身并不会改变卷积层。
 
-事实上，其他的一些函数也可以用于增强网络的非线性特性，如双曲正切函数 {\displaystyle f(x)=\tanh(x)} {\displaystyle f(x)=\tanh(x)}, {\displaystyle f(x)=|\tanh(x)|} {\displaystyle f(x)=|\tanh(x)|}，或者Sigmoid函数 {\displaystyle f(x)=(1+e^{-x})^{-1}} {\displaystyle f(x)=(1+e^{-x})^{-1}}。相比其它函数来说，ReLU函数更受青睐，这是因为它可以将神经网络的训练速度提升数倍[3]，而并不会对模型的泛化准确度造成显著影响。
+事实上，其他的一些函数也可以用于增强网络的非线性特性，如双曲正切函数 {\displaystyle f(x)=\tanh(x)} {\displaystyle f(x)=\tanh(x)}, {\displaystyle f(x)=|\tanh(x)|} {\displaystyle f(x)=|\tanh(x)|}，或者Sigmoid函数 {\displaystyle f(x)=(1+e^{-x})^{-1}} {\displaystyle f(x)=(1+e^{-x})^{-1}}。相比其它函数来说，ReLU函数更受青睐，这是因为它可以将神经网络的训练速度提升数倍，而并不会对模型的泛化准确度造成显著影响。
 
 池化（Pooling）是卷积神经网络中另一个重要的概念，它实际上是一种形式的降采样。有多种不同形式的非线性池化函数，而其中“最大池化（Max pooling）”是最为常见的。它是将输入的图像划分为若干个矩形区域，对每个子区域输出最大值。直觉上，这种机制能够有效地原因在于，在发现一个特征之后，它的精确位置远不及它和其他特征的相对位置的关系重要。池化层会不断地减小数据的空间大小，因此参数的数量和计算量也会下降，这在一定程度上也控制了过拟合。通常来说，CNN的卷积层之间都会周期性地插入池化层。
 
@@ -20,7 +20,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 除了最大池化之外，池化层也可以使用其他池化函数，例如“平均池化”甚至“L2-范数池化”等。过去，平均池化的使用曾经较为广泛，但是最近由于最大池化在实践中的表现更好，平均池化已经不太常用。
 
-由于池化层过快地减少了数据的大小，目前文献中的趋势是使用较小的池化滤镜，[4]甚至不再使用池化层。
+由于池化层过快地减少了数据的大小，目前文献中的趋势是使用较小的池化滤镜，甚至不再使用池化层。
 
 <p align="center">
 <img width="400" align="center" src="../../images/360.jpg" />

From d57b516650edcd00821798b4fa74eee6749b4c59 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 08:45:46 +0800
Subject: [PATCH 1057/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 5bd0b80d..202b7ab9 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -25,3 +25,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="400" align="center" src="../../images/360.jpg" />
 </p>
+
+#### 应用领域
+卷积神经网络通常在影像辨识别系统中使用，也常被用于自然语言处理。 CNN的模型被证明可以有效的处理各种自然语言处理的问题，如语义分析、搜索结果提取、句子建模、分类、预测、和其他传统的NLP任务
+
+
+

From cfaf80583a82c161d885f61af85d0dd0c8e6c163 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 21:19:28 +0800
Subject: [PATCH 1058/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 28 ----------------------------
 1 file changed, 28 deletions(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 202b7ab9..eb5f7a52 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,31 +3,3 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
-
-卷积神经网络（Convolutional Neural Network, CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。
-
-卷积神经网络由一个或多个卷积层和顶端的全连通层（对应经典的神经网络）组成，同时也包括关联权重和池化层（pooling layer）。这一结构使得卷积神经网络能够利用输入数据的二维结构。与其他深度学习结构相比，卷积神经网络在图像和语音识别方面能够给出更好的结果。这一模型也可以使用反向传播算法进行训练。相比较其他深度、前馈神经网络，卷积神经网络需要考量的参数更少，使之成为一种颇具吸引力的深度学习结构。
-
-卷积层（Convolutional layer），卷积神经网络中每层卷积层由若干卷积单元组成，每个卷积单元的参数都是通过反向传播算法最佳化得到的。卷积运算的目的是提取输入的不同特征，第一层卷积层可能只能提取一些低级的特征如边缘、线条和角等层级，更多层的网路能从低级特征中迭代提取更复杂的特征。
-
-线性整流层（Rectified Linear Units layer, ReLU layer）使用线性整流（Rectified Linear Units, ReLU） {\displaystyle f(x)=\max(0,x)} {\displaystyle f(x)=\max(0,x)}作为这一层神经的激励函数（Activation function）。它可以增强判定函数和整个神经网络的非线性特性，而本身并不会改变卷积层。
-
-事实上，其他的一些函数也可以用于增强网络的非线性特性，如双曲正切函数 {\displaystyle f(x)=\tanh(x)} {\displaystyle f(x)=\tanh(x)}, {\displaystyle f(x)=|\tanh(x)|} {\displaystyle f(x)=|\tanh(x)|}，或者Sigmoid函数 {\displaystyle f(x)=(1+e^{-x})^{-1}} {\displaystyle f(x)=(1+e^{-x})^{-1}}。相比其它函数来说，ReLU函数更受青睐，这是因为它可以将神经网络的训练速度提升数倍，而并不会对模型的泛化准确度造成显著影响。
-
-池化（Pooling）是卷积神经网络中另一个重要的概念，它实际上是一种形式的降采样。有多种不同形式的非线性池化函数，而其中“最大池化（Max pooling）”是最为常见的。它是将输入的图像划分为若干个矩形区域，对每个子区域输出最大值。直觉上，这种机制能够有效地原因在于，在发现一个特征之后，它的精确位置远不及它和其他特征的相对位置的关系重要。池化层会不断地减小数据的空间大小，因此参数的数量和计算量也会下降，这在一定程度上也控制了过拟合。通常来说，CNN的卷积层之间都会周期性地插入池化层。
-
-池化层通常会分别作用于每个输入的特征并减小其大小。目前最常用形式的池化层是每隔2个元素从图像划分出 {\displaystyle 2\times 2} 2\times 2的区块，然后对每个区块中的4个数取最大值。这将会减少75%的数据量。
-
-除了最大池化之外，池化层也可以使用其他池化函数，例如“平均池化”甚至“L2-范数池化”等。过去，平均池化的使用曾经较为广泛，但是最近由于最大池化在实践中的表现更好，平均池化已经不太常用。
-
-由于池化层过快地减少了数据的大小，目前文献中的趋势是使用较小的池化滤镜，甚至不再使用池化层。
-
-<p align="center">
-<img width="400" align="center" src="../../images/360.jpg" />
-</p>
-
-#### 应用领域
-卷积神经网络通常在影像辨识别系统中使用，也常被用于自然语言处理。 CNN的模型被证明可以有效的处理各种自然语言处理的问题，如语义分析、搜索结果提取、句子建模、分类、预测、和其他传统的NLP任务
-
-
-

From 6949cd7604d3cc33c564668de28fe46dc6ef0d8e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Mon, 2 Jul 2018 21:21:31 +0800
Subject: [PATCH 1059/1406] change page of DL

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D05B|o


From b26d2e20f25894e94244c737deab30da9179b025 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 2 Jul 2018 21:48:40 +0800
Subject: [PATCH 1060/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index eb5f7a52..61aa72f5 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,3 +3,15 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
+卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
+
+卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。
+
+CNN的基本结构包括两层，其一为特征提取层，每个神经元的输入与前一层的局部接受域相连，并提取该局部的特征。一旦该局部特征被提取后，它与其它特征间的位置关系也随之确定下来；其二是特征映射层，网络的每个计算层由多个特征映射组成，每个特征映射是一个平面，平面上所有神经元的权值相等。特征映射结构采用影响函数核小的sigmoid函数作为卷积网络的激活函数，使得特征映射具有位移不变性。此外，由于一个映射面上的神经元共享权值，因而减少了网络自由参数的个数。卷积神经网络中的每一个卷积层都紧跟着一个用来求局部平均与二次提取的计算层，这种特有的两次特征提取结构减小了特征分辨率。
+
+CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
+
+<p align="center">
+<img width="300" align="center" src="../../images/1.jpg" />
+</p>
+

From bbea9471d9c15023c9b048cdaf87531a69d45557 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:47:11 +0800
Subject: [PATCH 1061/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 61aa72f5..255e3d3e 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
+
 卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。

From 2748924f6002cdb711057461169cf23f88781b06 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:49:03 +0800
Subject: [PATCH 1062/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 255e3d3e..c62d4c76 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -4,7 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
 
-卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
+深度卷积神经网络（DCNN）在特征识别相关任务中取得的效果，远比传统方法好。因此，DCNN常用于图像识别、语音识别等。但是，因为DCNN结构庞大，一般都会包含几十个神经层，每一层，又有数百至数千个神经元；同时，DCNN任意两层之间神经元的相互影响错综复杂。这两个主要的因素，导致DCNN难以理解、分析。为此，用户很难从失败或成功的例子中学习到如何设计一个好的卷积神经网络。因此，设计一个效果好的神经网络，往往需要依靠大量的尝试。
+
+而卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。
 

From a2ac0ea3a6aad8fbc8dcb9a150c614a8e5fe0f86 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:52:13 +0800
Subject: [PATCH 1063/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index c62d4c76..3cf18f26 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -18,3 +18,4 @@ CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图
 <img width="300" align="center" src="../../images/1.jpg" />
 </p>
 
+一个典型的卷积神经网络包含两个卷积层（convolution layer），两个池化层（pooling layer）和一个全连接层（fully connected layer）。

From 3a2ae551317252e220b75d141baf16f2a2d26f0a Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Tue, 3 Jul 2018 08:53:40 +0800
Subject: [PATCH 1064/1406] change page of DL

---
 assets/images/360.jpg | Bin 0 -> 138298 bytes
 assets/images/361.jpg | Bin 0 -> 38401 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/360.jpg
 create mode 100644 assets/images/361.jpg

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HcmV?d00001


From 5840456eda90d86e22e52e50f6c74ff598898b57 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Tue, 3 Jul 2018 08:55:14 +0800
Subject: [PATCH 1065/1406] change page of DL

---
 assets/src/DL/DL.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 3cf18f26..a0fdef17 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -19,3 +19,6 @@ CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图
 </p>
 
 一个典型的卷积神经网络包含两个卷积层（convolution layer），两个池化层（pooling layer）和一个全连接层（fully connected layer）。
+<p align="center">
+<img width="300" align="center" src="../../images/360.jpg" />
+</p>

From a149db0dcc6b1f9d1cb01563154913fa20c0c65e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:55:54 +0800
Subject: [PATCH 1066/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index a0fdef17..9c67d61d 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -10,9 +10,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。
 
-CNN的基本结构包括两层，其一为特征提取层，每个神经元的输入与前一层的局部接受域相连，并提取该局部的特征。一旦该局部特征被提取后，它与其它特征间的位置关系也随之确定下来；其二是特征映射层，网络的每个计算层由多个特征映射组成，每个特征映射是一个平面，平面上所有神经元的权值相等。特征映射结构采用影响函数核小的sigmoid函数作为卷积网络的激活函数，使得特征映射具有位移不变性。此外，由于一个映射面上的神经元共享权值，因而减少了网络自由参数的个数。卷积神经网络中的每一个卷积层都紧跟着一个用来求局部平均与二次提取的计算层，这种特有的两次特征提取结构减小了特征分辨率。
+卷积神经网络的基本结构包括两层，其一为特征提取层，每个神经元的输入与前一层的局部接受域相连，并提取该局部的特征。一旦该局部特征被提取后，它与其它特征间的位置关系也随之确定下来；其二是特征映射层，网络的每个计算层由多个特征映射组成，每个特征映射是一个平面，平面上所有神经元的权值相等。特征映射结构采用影响函数核小的sigmoid函数作为卷积网络的激活函数，使得特征映射具有位移不变性。此外，由于一个映射面上的神经元共享权值，因而减少了网络自由参数的个数。卷积神经网络中的每一个卷积层都紧跟着一个用来求局部平均与二次提取的计算层，这种特有的两次特征提取结构减小了特征分辨率。
 
-CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
+卷积神经网络主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 
 <p align="center">
 <img width="300" align="center" src="../../images/1.jpg" />
@@ -22,3 +22,5 @@ CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图
 <p align="center">
 <img width="300" align="center" src="../../images/360.jpg" />
 </p>
+
+卷积层，采用各种卷积核对输入图片进行卷积处理，基本卷积过程如图2所示。卷积操作具有平移不变性。因而，能够支持神经元学习到鲁棒性比较高的特征。

From f91c504a18f4e833ea7fee5f2b047c370f742d9d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:56:21 +0800
Subject: [PATCH 1067/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 9c67d61d..c55e24d5 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -24,3 +24,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 卷积层，采用各种卷积核对输入图片进行卷积处理，基本卷积过程如图2所示。卷积操作具有平移不变性。因而，能够支持神经元学习到鲁棒性比较高的特征。
+
+<p align="center">
+<img width="300" align="center" src="../../images/361.jpg" />
+</p>
+池化层的操作，是一种降采样操作。该操作是在一个小区域内，采取一个特定的值作为输出值。比如图3，在每个特定的小区域内，我们选取最大值作为输出值。池化层的操作可以达到一定的空间不变性效果。
+
+卷积神经网络中的激励函数，根据一系列的输入值，神经元之间连接的权值以及激励规则，刺激神经元。
+
+卷积神经网络中的损失函数，在训练阶段，用于评估网络输出结果与实际值的差异。然后用损失函数的值更新每个神经元之间的权重值。卷积神经网络的训练目的就是最小化损失函数值。

From 841efa9ef6edef8593840574388a66fdd44393d8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 08:58:26 +0800
Subject: [PATCH 1068/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 184 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 184 insertions(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index c55e24d5..0ea2a3d5 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -33,3 +33,187 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 卷积神经网络中的激励函数，根据一系列的输入值，神经元之间连接的权值以及激励规则，刺激神经元。
 
 卷积神经网络中的损失函数，在训练阶段，用于评估网络输出结果与实际值的差异。然后用损失函数的值更新每个神经元之间的权重值。卷积神经网络的训练目的就是最小化损失函数值。
+
+
+#### 应用示例
+```python
+import argparse
+import os
+
+import matplotlib
+matplotlib.use('AGG')
+import matplotlib.pyplot as plt
+import numpy as np
+from keras.datasets import cifar10
+from keras.layers import (Activation, Conv3D, Dense, Dropout, Flatten,
+                          MaxPooling3D)
+from keras.layers.advanced_activations import LeakyReLU
+from keras.losses import categorical_crossentropy
+from keras.models import Sequential
+from keras.optimizers import Adam
+from keras.utils import np_utils
+from keras.utils.vis_utils import plot_model
+from sklearn.model_selection import train_test_split
+
+import videoto3d
+from tqdm import tqdm
+
+
+def plot_history(history, result_dir):
+    plt.plot(history.history['acc'], marker='.')
+    plt.plot(history.history['val_acc'], marker='.')
+    plt.title('model accuracy')
+    plt.xlabel('epoch')
+    plt.ylabel('accuracy')
+    plt.grid()
+    plt.legend(['acc', 'val_acc'], loc='lower right')
+    plt.savefig(os.path.join(result_dir, 'model_accuracy.png'))
+    plt.close()
+
+    plt.plot(history.history['loss'], marker='.')
+    plt.plot(history.history['val_loss'], marker='.')
+    plt.title('model loss')
+    plt.xlabel('epoch')
+    plt.ylabel('loss')
+    plt.grid()
+    plt.legend(['loss', 'val_loss'], loc='upper right')
+    plt.savefig(os.path.join(result_dir, 'model_loss.png'))
+    plt.close()
+
+
+def save_history(history, result_dir):
+    loss = history.history['loss']
+    acc = history.history['acc']
+    val_loss = history.history['val_loss']
+    val_acc = history.history['val_acc']
+    nb_epoch = len(acc)
+
+    with open(os.path.join(result_dir, 'result.txt'), 'w') as fp:
+        fp.write('epoch\tloss\tacc\tval_loss\tval_acc\n')
+        for i in range(nb_epoch):
+            fp.write('{}\t{}\t{}\t{}\t{}\n'.format(
+                i, loss[i], acc[i], val_loss[i], val_acc[i]))
+
+
+def loaddata(video_dir, vid3d, nclass, result_dir, color=False, skip=True):
+    files = os.listdir(video_dir)
+    X = []
+    labels = []
+    labellist = []
+
+    pbar = tqdm(total=len(files))
+
+    for filename in files:
+        pbar.update(1)
+        if filename == '.DS_Store':
+            continue
+        name = os.path.join(video_dir, filename)
+        label = vid3d.get_UCF_classname(filename)
+        if label not in labellist:
+            if len(labellist) >= nclass:
+                continue
+            labellist.append(label)
+        labels.append(label)
+        X.append(vid3d.video3d(name, color=color, skip=skip))
+
+    pbar.close()
+    with open(os.path.join(result_dir, 'classes.txt'), 'w') as fp:
+        for i in range(len(labellist)):
+            fp.write('{}\n'.format(labellist[i]))
+
+    for num, label in enumerate(labellist):
+        for i in range(len(labels)):
+            if label == labels[i]:
+                labels[i] = num
+    if color:
+        return np.array(X).transpose((0, 2, 3, 4, 1)), labels
+    else:
+        return np.array(X).transpose((0, 2, 3, 1)), labels
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description='simple 3D convolution for action recognition')
+    parser.add_argument('--batch', type=int, default=128)
+    parser.add_argument('--epoch', type=int, default=100)
+    parser.add_argument('--videos', type=str, default='UCF101',
+                        help='directory where videos are stored')
+    parser.add_argument('--nclass', type=int, default=101)
+    parser.add_argument('--output', type=str, required=True)
+    parser.add_argument('--color', type=bool, default=False)
+    parser.add_argument('--skip', type=bool, default=True)
+    parser.add_argument('--depth', type=int, default=10)
+    args = parser.parse_args()
+
+    img_rows, img_cols, frames = 32, 32, args.depth
+    channel = 3 if args.color else 1
+    fname_npz = 'dataset_{}_{}_{}.npz'.format(
+        args.nclass, args.depth, args.skip)
+
+    vid3d = videoto3d.Videoto3D(img_rows, img_cols, frames)
+    nb_classes = args.nclass
+    if os.path.exists(fname_npz):
+        loadeddata = np.load(fname_npz)
+        X, Y = loadeddata["X"], loadeddata["Y"]
+    else:
+        x, y = loaddata(args.videos, vid3d, args.nclass,
+                        args.output, args.color, args.skip)
+        X = x.reshape((x.shape[0], img_rows, img_cols, frames, channel))
+        Y = np_utils.to_categorical(y, nb_classes)
+
+        X = X.astype('float32')
+        np.savez(fname_npz, X=X, Y=Y)
+        print('Saved dataset to dataset.npz.')
+    print('X_shape:{}\nY_shape:{}'.format(X.shape, Y.shape))
+
+    # Define model
+    model = Sequential()
+    model.add(Conv3D(32, kernel_size=(3, 3, 3), input_shape=(
+        X.shape[1:]), border_mode='same'))
+    model.add(Activation('relu'))
+    model.add(Conv3D(32, kernel_size=(3, 3, 3), border_mode='same'))
+    model.add(Activation('softmax'))
+    model.add(MaxPooling3D(pool_size=(3, 3, 3), border_mode='same'))
+    model.add(Dropout(0.25))
+
+    model.add(Conv3D(64, kernel_size=(3, 3, 3), border_mode='same'))
+    model.add(Activation('relu'))
+    model.add(Conv3D(64, kernel_size=(3, 3, 3), border_mode='same'))
+    model.add(Activation('softmax'))
+    model.add(MaxPooling3D(pool_size=(3, 3, 3), border_mode='same'))
+    model.add(Dropout(0.25))
+
+    model.add(Flatten())
+    model.add(Dense(512, activation='sigmoid'))
+    model.add(Dropout(0.5))
+    model.add(Dense(nb_classes, activation='softmax'))
+
+    model.compile(loss=categorical_crossentropy,
+                  optimizer=Adam(), metrics=['accuracy'])
+    model.summary()
+    plot_model(model, show_shapes=True,
+               to_file=os.path.join(args.output, 'model.png'))
+
+    X_train, X_test, Y_train, Y_test = train_test_split(
+        X, Y, test_size=0.2, random_state=43)
+
+    history = model.fit(X_train, Y_train, validation_data=(X_test, Y_test), batch_size=args.batch,
+                        epochs=args.epoch, verbose=1, shuffle=True)
+    model.evaluate(X_test, Y_test, verbose=0)
+    model_json = model.to_json()
+    if not os.path.isdir(args.output):
+        os.makedirs(args.output)
+    with open(os.path.join(args.output, 'ucf101_3dcnnmodel.json'), 'w') as json_file:
+        json_file.write(model_json)
+    model.save_weights(os.path.join(args.output, 'ucf101_3dcnnmodel.hd5'))
+
+    loss, acc = model.evaluate(X_test, Y_test, verbose=0)
+    print('Test loss:', loss)
+    print('Test accuracy:', acc)
+    plot_history(history, args.output)
+    save_history(history, args.output)
+
+
+if __name__ == '__main__':
+    main()
+```

From 244117c3b297dc76ab8b8374b4487d2b6c0cdb80 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 09:04:09 +0800
Subject: [PATCH 1069/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 0ea2a3d5..476f57ad 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度卷积神经网络(Deep Convolutional Neural Networks)
 
-深度卷积神经网络（DCNN）在特征识别相关任务中取得的效果，远比传统方法好。因此，DCNN常用于图像识别、语音识别等。但是，因为DCNN结构庞大，一般都会包含几十个神经层，每一层，又有数百至数千个神经元；同时，DCNN任意两层之间神经元的相互影响错综复杂。这两个主要的因素，导致DCNN难以理解、分析。为此，用户很难从失败或成功的例子中学习到如何设计一个好的卷积神经网络。因此，设计一个效果好的神经网络，往往需要依靠大量的尝试。
+深度卷积神经网络（DCNN）在特征识别相关任务中取得的效果，远比传统方法好。因此，DCNN常用于图像识别、语音识别等。但是，因为深度卷积神经网络结构庞大，一般都会包含几十个神经层，每一层，又有数百至数千个神经元；同时，DCNN任意两层之间神经元的相互影响错综复杂。这两个主要的因素，导致DCNN难以理解、分析。为此，用户很难从失败或成功的例子中学习到如何设计一个好的卷积神经网络。因此，设计一个效果好的神经网络，往往需要依靠大量的尝试。
 
 而卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
@@ -34,6 +34,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 卷积神经网络中的损失函数，在训练阶段，用于评估网络输出结果与实际值的差异。然后用损失函数的值更新每个神经元之间的权重值。卷积神经网络的训练目的就是最小化损失函数值。
 
+深度卷积神经网络在许多模式识别任务上较传统的方法而言已经展示了很大的提升，比如语音识别，图像分类和视频分类。
+
 
 #### 应用示例
 ```python

From 716cc04e092740953a7ac0284c0f8b7d144218f7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 3 Jul 2018 09:07:31 +0800
Subject: [PATCH 1070/1406] Update DL.0.3.md

---
 assets/src/DL/DL.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.3.md b/assets/src/DL/DL.0.3.md
index 476f57ad..08e6668d 100644
--- a/assets/src/DL/DL.0.3.md
+++ b/assets/src/DL/DL.0.3.md
@@ -19,6 +19,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 一个典型的卷积神经网络包含两个卷积层（convolution layer），两个池化层（pooling layer）和一个全连接层（fully connected layer）。
+
 <p align="center">
 <img width="300" align="center" src="../../images/360.jpg" />
 </p>

From d0a352e88ac4c3190b4e463fc4935442f429c3fd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 4 Jul 2018 08:41:39 +0800
Subject: [PATCH 1071/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 3bfb9a83..0d72002e 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
+
+递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。

From 937f9ca25aaa4d49e02f40973a0e233a5ae4ccd2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 4 Jul 2018 08:44:51 +0800
Subject: [PATCH 1072/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 0d72002e..9507bde4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
 
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
+
+时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果

From 22a589099193e4e87cd09b09be91778084ef73f4 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Wed, 11 Jul 2018 09:09:18 +0800
Subject: [PATCH 1073/1406] change page of readme

---
 README.md | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index baaa3103..15d08543 100644
--- a/README.md
+++ b/README.md
@@ -4,6 +4,7 @@
 <a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>
 <a href="https://www.zhihu.com/people/sencoed.com/activities"><img src="https://img.shields.io/badge/%E7%9F%A5%E4%B9%8E-keke-green.svg?style=flat&colorA=009df2"></a>
 </p>
+
 最近以来一直在学习机器学习和算法，然后自己就在不断总结和写笔记，记录下自己的学习AI与算法历程。
 机器学习(Machine Learning, ML)是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。专门研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。
 
@@ -193,11 +194,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信,加入我们的交流群一起交流机器学习！
-
-<p style="left">
-  <img src="https://github.com/KeKe-Li/book/blob/master/images/1.jpg" width="260">
-</p>
+觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信**Sen0676**,加入我们的交流群一起交流机器学习！
 
 ### License
 This is free software distributed under the terms of the MIT license

From 4259798226c16ddea3294af36f16d7b983932f2c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 13 Jul 2018 09:16:06 +0800
Subject: [PATCH 1074/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 9507bde4..29b03788 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
-
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果

From c5e5ad8a6326089d04260f6d04925f3833ba1e01 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 17 Jul 2018 18:45:03 +0800
Subject: [PATCH 1075/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index e711c852..45f66244 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -6,7 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
 
-k-means算法属于非监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点
+k-means算法属于无监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点
 
 聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。相异度计算方法：欧几里得距离,曼哈顿距离,闵可夫斯基距离,皮尔逊相关系数.
 

From 86f2a447319892f06ca8efa29274e4961c664d70 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 23 Jul 2018 08:35:53 +0800
Subject: [PATCH 1076/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 29b03788..9507bde4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
+
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果

From 981c2ccd14e2c03e6e6361d2dc999b767483da2f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Jul 2018 08:46:11 +0800
Subject: [PATCH 1077/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 9507bde4..f58e10d9 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -7,3 +7,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果
+
+RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。

From 6a96f2fc0068ecdeba089d749cf76cb2bd121c65 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 27 Jul 2018 08:48:31 +0800
Subject: [PATCH 1078/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index f58e10d9..9507bde4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -7,5 +7,3 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果
-
-RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。

From 5920929e5e5b612ac07500f344127770d0a212ae Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 30 Jul 2018 08:46:39 +0800
Subject: [PATCH 1079/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 9507bde4..29b03788 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
-
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果

From 8b20272b9e1a992efce5f09f60db2a809720a25b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 30 Jul 2018 08:50:36 +0800
Subject: [PATCH 1080/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 29b03788..73612b22 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,6 +3,8 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
-递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（recurrent neural network），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
+递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（Recurrent Neural Networks,RNN），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果
+
+循环神经网络不同于传统的FNNs(Feed-forward Neural Networks，前向反馈神经网络)，循环神经网络引入了定向循环，能够处理那些输入之间前后关联的问题。

From 6e3aac10cc63897d072783f419235f1687bcfedc Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Mon, 30 Jul 2018 08:54:36 +0800
Subject: [PATCH 1081/1406] change page of DL

---
 assets/images/362.jpg   | Bin 0 -> 26040 bytes
 assets/images/363.jpg   | Bin 0 -> 165133 bytes
 assets/images/364.jpg   | Bin 0 -> 44320 bytes
 assets/images/365.jpg   | Bin 0 -> 180021 bytes
 assets/images/366.jpg   | Bin 0 -> 539494 bytes
 assets/src/DL/DL.0.4.md |   3 +++
 6 files changed, 3 insertions(+)
 create mode 100644 assets/images/362.jpg
 create mode 100644 assets/images/363.jpg
 create mode 100644 assets/images/364.jpg
 create mode 100644 assets/images/365.jpg
 create mode 100644 assets/images/366.jpg

diff --git a/assets/images/362.jpg b/assets/images/362.jpg
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diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 73612b22..66cd3cdc 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -8,3 +8,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果
 
 循环神经网络不同于传统的FNNs(Feed-forward Neural Networks，前向反馈神经网络)，循环神经网络引入了定向循环，能够处理那些输入之间前后关联的问题。
+<p align="center">
+<img width="500" align="center" src="../../images/362.jpg" />
+</p>
\ No newline at end of file

From 1f87ca69180a585a0a585f89e116bda6db5835b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 30 Jul 2018 09:08:02 +0800
Subject: [PATCH 1082/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 66cd3cdc..15cacfee 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -10,4 +10,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 循环神经网络不同于传统的FNNs(Feed-forward Neural Networks，前向反馈神经网络)，循环神经网络引入了定向循环，能够处理那些输入之间前后关联的问题。
 <p align="center">
 <img width="500" align="center" src="../../images/362.jpg" />
-</p>
\ No newline at end of file
+</p>
+
+循环神经网络的目的是用来处理序列数据的问题。通常在传统的神经网络模型中，是从输入层到隐含层再到输出层，层与层之间是全连接的，每层之间的节点是无连接的。但是这种普通的神经网络对于很多问题却是无法解决的。比如你需要要预测一个句子的下一个单词是什么，一般需要用到前面的单词，因为一个句子中前后单词并不是独立的。RNNs之所以称为循环神经网路，即一个序列当前的输出与前面的输出也有关。对应的表现形式为网络会对前面的信息进行记忆并应用于当前输出的计算中，即隐藏层之间的节点不再无连接而是有连接的，并且隐藏层的输入不仅包括输入层的输出还包括上一时刻隐藏层的输出。理论上，RNNs能够对任何长度的序列数据进行处理。
+<p align="center">
+<img width="500" align="center" src="../../images/363.jpg" />
+</p>

From 6775a5425930e5f4c3ccee1f8e5690712015dfce Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 30 Jul 2018 09:08:47 +0800
Subject: [PATCH 1083/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 15cacfee..4a0f15b4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -16,3 +16,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/363.jpg" />
 </p>
+
+<p align="center">
+<img width="500" align="center" src="../../images/364.jpg" />
+</p>

From aa8ba1b5fb1451942e7a8af5ac7c9c850c14a752 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 Jul 2018 21:11:11 +0800
Subject: [PATCH 1084/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 4a0f15b4..99af36e4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度递归神经网络(Deep Recurrent Neural Networks)
+
 递归神经网络（RNN）是两种人工神经网络的总称。一种是时间递归神经网络（Recurrent Neural Networks,RNN），又名循环神经网络，另一种是结构递归神经网络（recursive neural network）。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络利用相似的神经网络结构递归构造更为复杂的深度网络。RNN一般指代时间递归神经网络。单纯递归神经网络因为无法处理随着递归，权重指数级爆炸或消失的问题（Vanishing gradient problem），难以捕捉长期时间关联；而结合不同的LSTM可以很好解决这个问题。
 
 时间递归神经网络可以描述动态时间行为，因为和前馈神经网络（feedforward neural network）接受较特定结构的输入不同，RNN将状态在自身网络中循环传递，因此可以接受更广泛的时间序列结构输入。手写识别是最早成功利用RNN的研究结果

From ecb98356698107f8aaec5c72493fe76f194ef49f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 Jul 2018 23:05:05 +0800
Subject: [PATCH 1085/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 99af36e4..6b4b0ddf 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -21,3 +21,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/364.jpg" />
 </p>
+
+时间递归神经网络包含输入单元(Input units)，输入集标记为，而输出单元(Output units)的输出集则被标记为。RNNs还包含隐藏单元(Hidden units)，我们将其输出集标记为，这些隐藏单元完成了最为主要的工作。你会发现，在图中：有一条单向流动的信息流是从输入单元到达隐藏单元的，与此同时另一条单向流动的信息流从隐藏单元到达输出单元。在某些情况下，RNNs会打破后者的限制，引导信息从输出单元返回隐藏单元，这些被称为“Back Projections”，并且隐藏层的输入还包括上一隐藏层的状态，即隐藏层内的节点可以自连也可以互连。 

From b0d8533444458f05e8d999f1547aa40cfe04dca4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 Jul 2018 23:15:55 +0800
Subject: [PATCH 1086/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 6b4b0ddf..48729825 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -21,5 +21,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/364.jpg" />
 </p>
+图中是循环神经网络进行展开成一个全神经网络的过程
 
 时间递归神经网络包含输入单元(Input units)，输入集标记为，而输出单元(Output units)的输出集则被标记为。RNNs还包含隐藏单元(Hidden units)，我们将其输出集标记为，这些隐藏单元完成了最为主要的工作。你会发现，在图中：有一条单向流动的信息流是从输入单元到达隐藏单元的，与此同时另一条单向流动的信息流从隐藏单元到达输出单元。在某些情况下，RNNs会打破后者的限制，引导信息从输出单元返回隐藏单元，这些被称为“Back Projections”，并且隐藏层的输入还包括上一隐藏层的状态，即隐藏层内的节点可以自连也可以互连。 

From 7cc2917b75c4c5dd08d606e98ea65780e287aa13 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 Jul 2018 23:23:17 +0800
Subject: [PATCH 1087/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 48729825..7f81dc2e 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -24,3 +24,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 图中是循环神经网络进行展开成一个全神经网络的过程
 
 时间递归神经网络包含输入单元(Input units)，输入集标记为，而输出单元(Output units)的输出集则被标记为。RNNs还包含隐藏单元(Hidden units)，我们将其输出集标记为，这些隐藏单元完成了最为主要的工作。你会发现，在图中：有一条单向流动的信息流是从输入单元到达隐藏单元的，与此同时另一条单向流动的信息流从隐藏单元到达输出单元。在某些情况下，RNNs会打破后者的限制，引导信息从输出单元返回隐藏单元，这些被称为“Back Projections”，并且隐藏层的输入还包括上一隐藏层的状态，即隐藏层内的节点可以自连也可以互连。 
+
+在深度递归神经网络中，如果对一个包含5个单词的语句，那么展开的网络便是一个五层的神经网络，每一层代表一个单词。对于该网络该如何操作呢？
+
+

From b551d39db7015a5b60672866ef598d0c9909b5f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 22:52:23 +0800
Subject: [PATCH 1088/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 7f81dc2e..abdd6a11 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -25,6 +25,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 时间递归神经网络包含输入单元(Input units)，输入集标记为，而输出单元(Output units)的输出集则被标记为。RNNs还包含隐藏单元(Hidden units)，我们将其输出集标记为，这些隐藏单元完成了最为主要的工作。你会发现，在图中：有一条单向流动的信息流是从输入单元到达隐藏单元的，与此同时另一条单向流动的信息流从隐藏单元到达输出单元。在某些情况下，RNNs会打破后者的限制，引导信息从输出单元返回隐藏单元，这些被称为“Back Projections”，并且隐藏层的输入还包括上一隐藏层的状态，即隐藏层内的节点可以自连也可以互连。 
 
-在深度递归神经网络中，如果对一个包含5个单词的语句，那么展开的网络便是一个五层的神经网络，每一层代表一个单词。对于该网络该如何操作呢？
-
+在深度递归神经网络中，它的主要作用是做什么呢？
 
+ 时间递归神经网络已经被在实践中证明对NLP是非常成功的。如词向量表达、语句合法性检查、词性标注等。在时间递归神经网络中，目前使用最广泛最成功的模型便是LSTMs(Long Short-Term Memory，长短时记忆模型)模型，该模型通常比vanilla RNNs能够更好地对长短时依赖进行表达，该模型相对于一般的RNNs，只是在隐藏层做了手脚。
+ 

From 2fb85d3897fe6a6647e3e9909899e114f2d873b3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 22:52:37 +0800
Subject: [PATCH 1089/1406] Update DL.0.4.md


From 4d6ca45db1d6399a96aa1b686c41c5d851f26e81 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 23:01:51 +0800
Subject: [PATCH 1090/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index abdd6a11..1bcecbfd 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -27,5 +27,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在深度递归神经网络中，它的主要作用是做什么呢？
 
- 时间递归神经网络已经被在实践中证明对NLP是非常成功的。如词向量表达、语句合法性检查、词性标注等。在时间递归神经网络中，目前使用最广泛最成功的模型便是LSTMs(Long Short-Term Memory，长短时记忆模型)模型，该模型通常比vanilla RNNs能够更好地对长短时依赖进行表达，该模型相对于一般的RNNs，只是在隐藏层做了手脚。
+ 时间递归神经网络已经被在实践中证明对NLP是非常成功的。如词向量表达、语句合法性检查、词性标注、机器翻译、图像描述生成等。在时间递归神经网络中，目前使用最广泛最成功的模型便是LSTMs(Long Short-Term Memory，长短时记忆模型)模型，该模型通常比vanilla RNNs能够更好地对长短时依赖进行表达，该模型相对于一般的RNNs，只是在隐藏层做了改变。
+ 
+ 
+ 那么我们应该怎么训练时间递归神经网络呢？
+ 
+ 对于递归神经网络的训练和对传统的人工神经网络训练一样。同样使用BP误差反向传播算法，不过这里有点区别。如果将RNNs进行网络展开，那么参数是共享的，而传统神经网络不是这样的。所以使用梯度下降算法中，每一步的输出不仅依赖当前步的网络，而且还依赖前面操作的网络的状态。该学习算法称为Backpropagation Through Time (BPTT).这里我们需要了解到的是，在vanilla RNNs训练中，BPTT无法解决长时依赖问题(即当前的输出与前面很长的一段序列有关，一般超过十步就无能为力了)，因为BPTT会带来所谓的梯度消失或梯度爆炸问题(the vanishing/exploding gradient problem)。当然，有很多方法去解决这个问题，如LSTMs便是专门应对这种问题的。
+ 
+ 
+ 接下来我们需要对RNNs进行扩展和模型改进.
  

From cde55538058537dce779886189dc5b9ce3dca78d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 1 Aug 2018 23:10:07 +0800
Subject: [PATCH 1091/1406] change page of images

---
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 assets/images/368.jpg | Bin 0 -> 31693 bytes
 assets/images/369.jpg | Bin 0 -> 56160 bytes
 assets/images/370.jpg | Bin 0 -> 42380 bytes
 assets/images/371.jpg | Bin 0 -> 27692 bytes
 assets/images/372.jpg | Bin 0 -> 71016 bytes
 assets/images/373.jpg | Bin 0 -> 52212 bytes
 7 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/367.jpg
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From 9e76fb152d52f936d8596bdec5e132d87212c530 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 1 Aug 2018 23:14:04 +0800
Subject: [PATCH 1092/1406] change page of images

---
 assets/images/365.jpg | Bin 180021 -> 26799 bytes
 assets/images/366.jpg | Bin 539494 -> 31693 bytes
 assets/images/367.jpg | Bin 26799 -> 56160 bytes
 assets/images/368.jpg | Bin 31693 -> 42380 bytes
 assets/images/369.jpg | Bin 56160 -> 27692 bytes
 assets/images/370.jpg | Bin 42380 -> 71016 bytes
 assets/images/371.jpg | Bin 27692 -> 52212 bytes
 assets/images/372.jpg | Bin 71016 -> 0 bytes
 assets/images/373.jpg | Bin 52212 -> 0 bytes
 9 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 assets/images/372.jpg
 delete mode 100644 assets/images/373.jpg

diff --git a/assets/images/365.jpg b/assets/images/365.jpg
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diff --git a/assets/images/367.jpg b/assets/images/367.jpg
index e2e78647be974a0e5736d949dddb26ab970d0391..39190102ecc801b8bb13f108021dd30403de5863 100644
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From ef21a224b8a54facd1ac783bf589cf19d31e08bb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 23:15:30 +0800
Subject: [PATCH 1093/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 1bcecbfd..1770d89f 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -37,3 +37,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
  
  接下来我们需要对RNNs进行扩展和模型改进.
  
+* 第一种: Simple RNNs(SRNs)
+
+SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐藏层增加了上下文单元，下图中的便是隐藏层，便是上下文单元。上下文单元节点与隐藏层中的节点的连接是固定的，并且权值也是固定的(值是多少)，其实是一个上下文节点与隐藏层节点一一对应，并且值是确定的。在每一步中，使用标准的前向反馈进行传播，然后使用学习算法进行学习。上下文每一个节点保存其连接的隐藏层节点的上一步的输出，即保存上文，并作用于当前步对应的隐藏层节点的状态，即隐藏层的输入由输入层的输出与上一步的自己的状态所决定的。因此SRNs能够解决标准的多层感知机(MLP)无法解决的对序列数据进行预测的任务。
+
+<p align="center">
+<img width="500" align="center" src="../../images/365.jpg" />
+</p>
+

From 3b87a7df78f77ce50f7a862cbd51ebeb460bb8b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 23:21:22 +0800
Subject: [PATCH 1094/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 51 +++++++++++++++++++++++++++++++++++++++--
 1 file changed, 49 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 1770d89f..fef726a4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -37,11 +37,58 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
  
  接下来我们需要对RNNs进行扩展和模型改进.
  
-* 第一种: Simple RNNs(SRNs)
+* 第一种:Simple RNNs(SRNs)
 
 SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐藏层增加了上下文单元，下图中的便是隐藏层，便是上下文单元。上下文单元节点与隐藏层中的节点的连接是固定的，并且权值也是固定的(值是多少)，其实是一个上下文节点与隐藏层节点一一对应，并且值是确定的。在每一步中，使用标准的前向反馈进行传播，然后使用学习算法进行学习。上下文每一个节点保存其连接的隐藏层节点的上一步的输出，即保存上文，并作用于当前步对应的隐藏层节点的状态，即隐藏层的输入由输入层的输出与上一步的自己的状态所决定的。因此SRNs能够解决标准的多层感知机(MLP)无法解决的对序列数据进行预测的任务。
 
 <p align="center">
-<img width="500" align="center" src="../../images/365.jpg" />
+<img width="300" align="center" src="../../images/365.jpg" />
 </p>
 
+* 第二种:Bidirectional RNNs
+
+ Bidirectional RNNs双向网络改进之处，假设当前的输出(第步的输出)不仅仅与前面的序列有关，并且还与后面的序列有关。例如：预测一个语句中缺失的词语那么就需要根据上下文来进行预测。Bidirectional RNNs是一个相对较简单的RNNs，是由两个RNNs上下叠加在一起组成的。输出由这两个RNNs的隐藏层的状态决定的。
+ 
+ 
+<p align="center">
+<img width="300" align="center" src="../../images/366.jpg" />
+</p>
+
+* 第三种: Deep(Bidirectional)RNNs
+
+Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输入有多层网络。该网络便有更强大的表达与学习能力，但是复杂性也提高了，同时需要更多的训练数据。
+
+<p align="center">
+<img width="300" align="center" src="../../images/367.jpg" />
+</p>
+
+* 第四种:Echo State Networks
+
+ ESNs(回声状态网络)也是一种RNNs，但是它与传统的RNNs相差很大。回声状态网络具有三个特点：
+
+* 它的核心结构时一个随机生成、且保持不变的储备池(Reservoir)，储备池是大规模的、随机生成的、稀疏连接(SD通常保持1%～5%，SD表示储备池中互相连接的神经元占总的神经元个数N的比例)的循环结构；
+* 它的储备池到输出层的权值矩阵是唯一需要调整的部分；
+* 通过简单的线性回归就可完成网络的训练。
+
+回声状态网络是一种特殊类型的循环神经网络，其基本思想是：使用大规模随机连接的循环网络取代经典神经网络中的中间层，从而简化网络的训练过程。因此ESNs的关键是中间的储备池。网络中的参数包括：为储备池中节点的连接权值矩阵，为输入层到储备池之间的连接权值矩阵，表明储备池中的神经元之间是连接的，为输出层到储备池之间的反馈连接权值矩阵，表明储备池会有输出层来的反馈，为输入层、储备池、输出层到输出层的连接权值矩阵，表明输出层不仅与储备池连接，还与输入层和自己连接。表示输出层的偏置项。
+
+ 对于ESNs，关键是储备池的四个参数，如储备池内部连接权谱半径SR(，只有SR <1时，ESNs才能具有回声状态属性)、储备池规模N(即储备池中神经元的个数)、储备池输入单元尺度IS(IS为储备池的输入信号连接到储备池内部神经元之前需要相乘的一个尺度因子)、储备池稀疏程度SD(即为储备池中互相连接的神经元个数占储备池神经元总个数的比例)。对于IS，如果需要处理的任务的非线性越强，那么输入单元尺度越大。该原则的本质就是通过输入单元尺度IS，将输入变换到神经元激活函数相应的范围(神经元激活函数的不同输入范围，其非线性程度不同)。
+ <p align="center">
+<img width="300" align="center" src="../../images/368.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/369.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/370.jpg" />
+</p>
+
+* 第五种:Gated Recurrent Unit Recurrent Neural Networks
+
+ GRUs也是一般的RNNs的改良版本，主要是体现在两个方面。一是，序列中不同的位置处的单词(已单词举例)对当前的隐藏层的状态的影响不同，越前面的影响越小，即每个前面状态对当前的影响进行了距离加权，距离越远，权值越小。二是，在产生误差error时，误差可能是由某一个或者几个单词而引发的，所以应当仅仅对对应的单词weight进行更新。GRUs的结构如下图所示。GRUs首先根据当前输入单词向量word vector已经前一个隐藏层的状态hidden state计算出update gate和reset gate。再根据reset gate、当前word vector以及前一个hidden state计算新的记忆单元内容(new memory content)。当reset gate为1的时候，new memory content忽略之前的所有memory content，最终的memory是之前的hidden state与new memory content的结合。
+ <p align="center">
+<img width="300" align="center" src="../../images/371.jpg" />
+</p>
+ 

From d91052957edd67df77c9c3347c8567c40e000d3d Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 1 Aug 2018 23:23:56 +0800
Subject: [PATCH 1095/1406] change page of DL04

---
 assets/src/DL/DL.0.4.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index fef726a4..1b7c2f65 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -42,7 +42,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐藏层增加了上下文单元，下图中的便是隐藏层，便是上下文单元。上下文单元节点与隐藏层中的节点的连接是固定的，并且权值也是固定的(值是多少)，其实是一个上下文节点与隐藏层节点一一对应，并且值是确定的。在每一步中，使用标准的前向反馈进行传播，然后使用学习算法进行学习。上下文每一个节点保存其连接的隐藏层节点的上一步的输出，即保存上文，并作用于当前步对应的隐藏层节点的状态，即隐藏层的输入由输入层的输出与上一步的自己的状态所决定的。因此SRNs能够解决标准的多层感知机(MLP)无法解决的对序列数据进行预测的任务。
 
 <p align="center">
-<img width="300" align="center" src="../../images/365.jpg" />
+<img width="470" align="center" src="../../images/365.jpg" />
 </p>
 
 * 第二种:Bidirectional RNNs
@@ -51,7 +51,7 @@ SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐
  
  
 <p align="center">
-<img width="300" align="center" src="../../images/366.jpg" />
+<img width="470" align="center" src="../../images/366.jpg" />
 </p>
 
 * 第三种: Deep(Bidirectional)RNNs
@@ -59,7 +59,7 @@ SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐
 Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输入有多层网络。该网络便有更强大的表达与学习能力，但是复杂性也提高了，同时需要更多的训练数据。
 
 <p align="center">
-<img width="300" align="center" src="../../images/367.jpg" />
+<img width="470" align="center" src="../../images/367.jpg" />
 </p>
 
 * 第四种:Echo State Networks
@@ -74,7 +74,7 @@ Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输
 
  对于ESNs，关键是储备池的四个参数，如储备池内部连接权谱半径SR(，只有SR <1时，ESNs才能具有回声状态属性)、储备池规模N(即储备池中神经元的个数)、储备池输入单元尺度IS(IS为储备池的输入信号连接到储备池内部神经元之前需要相乘的一个尺度因子)、储备池稀疏程度SD(即为储备池中互相连接的神经元个数占储备池神经元总个数的比例)。对于IS，如果需要处理的任务的非线性越强，那么输入单元尺度越大。该原则的本质就是通过输入单元尺度IS，将输入变换到神经元激活函数相应的范围(神经元激活函数的不同输入范围，其非线性程度不同)。
  <p align="center">
-<img width="300" align="center" src="../../images/368.jpg" />
+<img width="470" align="center" src="../../images/368.jpg" />
 </p>
 
 <p align="center">

From 83275820d8330bedf754b80a63937f7c1e8874cf Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 1 Aug 2018 23:27:04 +0800
Subject: [PATCH 1096/1406] change page

---
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From 23e7862c9ad10f487a636568c6eb0c0ffe9d8d6e Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Wed, 1 Aug 2018 23:30:16 +0800
Subject: [PATCH 1097/1406] add images

---
 assets/images/365.jpg | Bin 0 -> 26799 bytes
 assets/images/366.jpg | Bin 0 -> 31693 bytes
 assets/images/367.jpg | Bin 0 -> 56160 bytes
 assets/images/368.jpg | Bin 0 -> 42380 bytes
 assets/images/370.jpg | Bin 0 -> 71016 bytes
 assets/images/371.jpg | Bin 0 -> 52212 bytes
 6 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/365.jpg
 create mode 100644 assets/images/366.jpg
 create mode 100644 assets/images/367.jpg
 create mode 100644 assets/images/368.jpg
 create mode 100644 assets/images/370.jpg
 create mode 100644 assets/images/371.jpg

diff --git a/assets/images/365.jpg b/assets/images/365.jpg
new file mode 100644
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From dc3b3310a48be4a3cf31ba41cf665cdfed0d92dd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 23:31:08 +0800
Subject: [PATCH 1098/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 1b7c2f65..fef726a4 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -42,7 +42,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐藏层增加了上下文单元，下图中的便是隐藏层，便是上下文单元。上下文单元节点与隐藏层中的节点的连接是固定的，并且权值也是固定的(值是多少)，其实是一个上下文节点与隐藏层节点一一对应，并且值是确定的。在每一步中，使用标准的前向反馈进行传播，然后使用学习算法进行学习。上下文每一个节点保存其连接的隐藏层节点的上一步的输出，即保存上文，并作用于当前步对应的隐藏层节点的状态，即隐藏层的输入由输入层的输出与上一步的自己的状态所决定的。因此SRNs能够解决标准的多层感知机(MLP)无法解决的对序列数据进行预测的任务。
 
 <p align="center">
-<img width="470" align="center" src="../../images/365.jpg" />
+<img width="300" align="center" src="../../images/365.jpg" />
 </p>
 
 * 第二种:Bidirectional RNNs
@@ -51,7 +51,7 @@ SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐
  
  
 <p align="center">
-<img width="470" align="center" src="../../images/366.jpg" />
+<img width="300" align="center" src="../../images/366.jpg" />
 </p>
 
 * 第三种: Deep(Bidirectional)RNNs
@@ -59,7 +59,7 @@ SRNs是RNNs的一种特例，它是一个由三层网络组成的，并且在隐
 Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输入有多层网络。该网络便有更强大的表达与学习能力，但是复杂性也提高了，同时需要更多的训练数据。
 
 <p align="center">
-<img width="470" align="center" src="../../images/367.jpg" />
+<img width="300" align="center" src="../../images/367.jpg" />
 </p>
 
 * 第四种:Echo State Networks
@@ -74,7 +74,7 @@ Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输
 
  对于ESNs，关键是储备池的四个参数，如储备池内部连接权谱半径SR(，只有SR <1时，ESNs才能具有回声状态属性)、储备池规模N(即储备池中神经元的个数)、储备池输入单元尺度IS(IS为储备池的输入信号连接到储备池内部神经元之前需要相乘的一个尺度因子)、储备池稀疏程度SD(即为储备池中互相连接的神经元个数占储备池神经元总个数的比例)。对于IS，如果需要处理的任务的非线性越强，那么输入单元尺度越大。该原则的本质就是通过输入单元尺度IS，将输入变换到神经元激活函数相应的范围(神经元激活函数的不同输入范围，其非线性程度不同)。
  <p align="center">
-<img width="470" align="center" src="../../images/368.jpg" />
+<img width="300" align="center" src="../../images/368.jpg" />
 </p>
 
 <p align="center">

From dbca29608d7b511275114e1e3764a09e673c1ba3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Aug 2018 23:32:50 +0800
Subject: [PATCH 1099/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 204 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 204 insertions(+)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index fef726a4..336a26db 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -92,3 +92,207 @@ Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输
 <img width="300" align="center" src="../../images/371.jpg" />
 </p>
  
+#### 应用示例
+```python
+
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+
+from __future__ import print_function
+
+import os
+import sys
+import time
+from datetime import timedelta
+
+import numpy as np
+import tensorflow as tf
+from sklearn import metrics
+
+from cnn_model import TCNNConfig, TextCNN
+from data.cnews_loader import read_vocab, read_category, batch_iter, process_file, build_vocab
+
+base_dir = 'data/cnews'
+train_dir = os.path.join(base_dir, 'cnews.train.txt')
+test_dir = os.path.join(base_dir, 'cnews.test.txt')
+val_dir = os.path.join(base_dir, 'cnews.val.txt')
+vocab_dir = os.path.join(base_dir, 'cnews.vocab.txt')
+
+save_dir = 'checkpoints/textcnn'
+save_path = os.path.join(save_dir, 'best_validation')  # 最佳验证结果保存路径
+
+
+def get_time_dif(start_time):
+    """获取已使用时间"""
+    end_time = time.time()
+    time_dif = end_time - start_time
+    return timedelta(seconds=int(round(time_dif)))
+
+
+def feed_data(x_batch, y_batch, keep_prob):
+    feed_dict = {
+        model.input_x: x_batch,
+        model.input_y: y_batch,
+        model.keep_prob: keep_prob
+    }
+    return feed_dict
+
+
+def evaluate(sess, x_, y_):
+    """评估在某一数据上的准确率和损失"""
+    data_len = len(x_)
+    batch_eval = batch_iter(x_, y_, 128)
+    total_loss = 0.0
+    total_acc = 0.0
+    for x_batch, y_batch in batch_eval:
+        batch_len = len(x_batch)
+        feed_dict = feed_data(x_batch, y_batch, 1.0)
+        loss, acc = sess.run([model.loss, model.acc], feed_dict=feed_dict)
+        total_loss += loss * batch_len
+        total_acc += acc * batch_len
+
+    return total_loss / data_len, total_acc / data_len
+
+
+def train():
+    print("Configuring TensorBoard and Saver...")
+    # 配置 Tensorboard，重新训练时，请将tensorboard文件夹删除，不然图会覆盖
+    tensorboard_dir = 'tensorboard/textcnn'
+    if not os.path.exists(tensorboard_dir):
+        os.makedirs(tensorboard_dir)
+
+    tf.summary.scalar("loss", model.loss)
+    tf.summary.scalar("accuracy", model.acc)
+    merged_summary = tf.summary.merge_all()
+    writer = tf.summary.FileWriter(tensorboard_dir)
+
+    # 配置 Saver
+    saver = tf.train.Saver()
+    if not os.path.exists(save_dir):
+        os.makedirs(save_dir)
+
+    print("Loading training and validation data...")
+    # 载入训练集与验证集
+    start_time = time.time()
+    x_train, y_train = process_file(train_dir, word_to_id, cat_to_id, config.seq_length)
+    x_val, y_val = process_file(val_dir, word_to_id, cat_to_id, config.seq_length)
+    time_dif = get_time_dif(start_time)
+    print("Time usage:", time_dif)
+
+    # 创建session
+    session = tf.Session()
+    session.run(tf.global_variables_initializer())
+    writer.add_graph(session.graph)
+
+    print('Training and evaluating...')
+    start_time = time.time()
+    total_batch = 0  # 总批次
+    best_acc_val = 0.0  # 最佳验证集准确率
+    last_improved = 0  # 记录上一次提升批次
+    require_improvement = 1000  # 如果超过1000轮未提升，提前结束训练
+
+    flag = False
+    for epoch in range(config.num_epochs):
+        print('Epoch:', epoch + 1)
+        batch_train = batch_iter(x_train, y_train, config.batch_size)
+        for x_batch, y_batch in batch_train:
+            feed_dict = feed_data(x_batch, y_batch, config.dropout_keep_prob)
+
+            if total_batch % config.save_per_batch == 0:
+                # 每多少轮次将训练结果写入tensorboard scalar
+                s = session.run(merged_summary, feed_dict=feed_dict)
+                writer.add_summary(s, total_batch)
+
+            if total_batch % config.print_per_batch == 0:
+                # 每多少轮次输出在训练集和验证集上的性能
+                feed_dict[model.keep_prob] = 1.0
+                loss_train, acc_train = session.run([model.loss, model.acc], feed_dict=feed_dict)
+                loss_val, acc_val = evaluate(session, x_val, y_val)  # todo
+
+                if acc_val > best_acc_val:
+                    # 保存最好结果
+                    best_acc_val = acc_val
+                    last_improved = total_batch
+                    saver.save(sess=session, save_path=save_path)
+                    improved_str = '*'
+                else:
+                    improved_str = ''
+
+                time_dif = get_time_dif(start_time)
+                msg = 'Iter: {0:>6}, Train Loss: {1:>6.2}, Train Acc: {2:>7.2%},' \
+                      + ' Val Loss: {3:>6.2}, Val Acc: {4:>7.2%}, Time: {5} {6}'
+                print(msg.format(total_batch, loss_train, acc_train, loss_val, acc_val, time_dif, improved_str))
+
+            session.run(model.optim, feed_dict=feed_dict)  # 运行优化
+            total_batch += 1
+
+            if total_batch - last_improved > require_improvement:
+                # 验证集正确率长期不提升，提前结束训练
+                print("No optimization for a long time, auto-stopping...")
+                flag = True
+                break  # 跳出循环
+        if flag:  # 同上
+            break
+
+
+def test():
+    print("Loading test data...")
+    start_time = time.time()
+    x_test, y_test = process_file(test_dir, word_to_id, cat_to_id, config.seq_length)
+
+    session = tf.Session()
+    session.run(tf.global_variables_initializer())
+    saver = tf.train.Saver()
+    saver.restore(sess=session, save_path=save_path)  # 读取保存的模型
+
+    print('Testing...')
+    loss_test, acc_test = evaluate(session, x_test, y_test)
+    msg = 'Test Loss: {0:>6.2}, Test Acc: {1:>7.2%}'
+    print(msg.format(loss_test, acc_test))
+
+    batch_size = 128
+    data_len = len(x_test)
+    num_batch = int((data_len - 1) / batch_size) + 1
+
+    y_test_cls = np.argmax(y_test, 1)
+    y_pred_cls = np.zeros(shape=len(x_test), dtype=np.int32)  # 保存预测结果
+    for i in range(num_batch):  # 逐批次处理
+        start_id = i * batch_size
+        end_id = min((i + 1) * batch_size, data_len)
+        feed_dict = {
+            model.input_x: x_test[start_id:end_id],
+            model.keep_prob: 1.0
+        }
+        y_pred_cls[start_id:end_id] = session.run(model.y_pred_cls, feed_dict=feed_dict)
+
+    # 评估
+    print("Precision, Recall and F1-Score...")
+    print(metrics.classification_report(y_test_cls, y_pred_cls, target_names=categories))
+
+    # 混淆矩阵
+    print("Confusion Matrix...")
+    cm = metrics.confusion_matrix(y_test_cls, y_pred_cls)
+    print(cm)
+
+    time_dif = get_time_dif(start_time)
+    print("Time usage:", time_dif)
+
+
+if __name__ == '__main__':
+    if len(sys.argv) != 2 or sys.argv[1] not in ['train', 'test']:
+        raise ValueError("""usage: python run_cnn.py [train / test]""")
+
+    print('Configuring CNN model...')
+    config = TCNNConfig()
+    if not os.path.exists(vocab_dir):  # 如果不存在词汇表，重建
+        build_vocab(train_dir, vocab_dir, config.vocab_size)
+    categories, cat_to_id = read_category()
+    words, word_to_id = read_vocab(vocab_dir)
+    config.vocab_size = len(words)
+    model = TextCNN(config)
+
+    if sys.argv[1] == 'train':
+        train()
+    else:
+        test()
+```

From 7b306a861f0f6d0a4cf9afe37850e8191aba6bf9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 08:44:39 +0800
Subject: [PATCH 1100/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index e476e1d9..73cb10cb 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -3,3 +3,9 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 分层时间记忆(Hierarchical Temporal Memory)
+分层时间记忆算法(Hierarchical Temporal Memory)，全称HTM Cortical Learning Algorithms是由《人工智能的未来》(On Intelligence)一书作者Jeff Hawkins创建的Numenta公司发表的新一代人工智能算法。HTM算法旨在模拟新大脑皮层的工作原理，将复杂的问题转化为模式匹配与预测。正如它的名字HTM一样，该算法与普通的神经网络算法有诸多的不同之处。HTM强调对“神经元”进行分层级，强调信息模式的空间特性与时间特性。目前Numenta公司已经推出基于HTM算法的python平台和可进行视觉识别的软件工具箱。
+
+传统的人工智能算法大多是针对特定的任务目标而设计的。HTM算法与之不同 ，它注重先把问题转化成模式匹配与预测的问题再解决。这使提出人工智能的“统一理论”成为可能。HTM算法是建立在大量解剖学和神经科学的基础上的。HTM算法认为人类之所以具有智能，新大脑皮层是不可缺少的必要条件，并且由其承担高级脑活动。我们的大脑的运行机制是将接受到的各种模式与记忆中模式进行匹配，并对下一刻将会接收到的信息作出预测及反应，如此循环往复。这正是其时效性(Temporal)的体现。
+HTM算法表面上与神经网络算法有相似之处，其实质是完全不同的。这就好比一般电路与门电路的区别。将模拟“神经元”按照新大脑皮层的结构连接之后就会产生与一般神经网路完全不同的效果。一般的神经网络注重前馈，而HTM算法更注重信息的双向交流，这也是由于神经解剖学发现反馈突触数量不亚于前馈的原因。而反馈并不能得到大多数人的重视。
+
+HTM算法也是一种拥有记忆性和可学习性的算法。它相对于其他学习算法更注重对神经网络的训练而不是架构。HTM算法认为只要经过合理的训练，该算法适用于解决大多数人工智能问题。对于不同的任务目标实验者需要将数据先空间化和时间化再对HTM网络进行训练即可。

From 5e60ce2e00c6240aebffc68f462f916035b61ca6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 08:47:08 +0800
Subject: [PATCH 1101/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index 73cb10cb..203ec68e 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 分层时间记忆(Hierarchical Temporal Memory)
+
 分层时间记忆算法(Hierarchical Temporal Memory)，全称HTM Cortical Learning Algorithms是由《人工智能的未来》(On Intelligence)一书作者Jeff Hawkins创建的Numenta公司发表的新一代人工智能算法。HTM算法旨在模拟新大脑皮层的工作原理，将复杂的问题转化为模式匹配与预测。正如它的名字HTM一样，该算法与普通的神经网络算法有诸多的不同之处。HTM强调对“神经元”进行分层级，强调信息模式的空间特性与时间特性。目前Numenta公司已经推出基于HTM算法的python平台和可进行视觉识别的软件工具箱。
 
 传统的人工智能算法大多是针对特定的任务目标而设计的。HTM算法与之不同 ，它注重先把问题转化成模式匹配与预测的问题再解决。这使提出人工智能的“统一理论”成为可能。HTM算法是建立在大量解剖学和神经科学的基础上的。HTM算法认为人类之所以具有智能，新大脑皮层是不可缺少的必要条件，并且由其承担高级脑活动。我们的大脑的运行机制是将接受到的各种模式与记忆中模式进行匹配，并对下一刻将会接收到的信息作出预测及反应，如此循环往复。这正是其时效性(Temporal)的体现。

From 21401b66eb0786120a280a28f058c4ef0caf2386 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 08:58:43 +0800
Subject: [PATCH 1102/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index 203ec68e..f2b93460 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -10,3 +10,16 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 HTM算法表面上与神经网络算法有相似之处，其实质是完全不同的。这就好比一般电路与门电路的区别。将模拟“神经元”按照新大脑皮层的结构连接之后就会产生与一般神经网路完全不同的效果。一般的神经网络注重前馈，而HTM算法更注重信息的双向交流，这也是由于神经解剖学发现反馈突触数量不亚于前馈的原因。而反馈并不能得到大多数人的重视。
 
 HTM算法也是一种拥有记忆性和可学习性的算法。它相对于其他学习算法更注重对神经网络的训练而不是架构。HTM算法认为只要经过合理的训练，该算法适用于解决大多数人工智能问题。对于不同的任务目标实验者需要将数据先空间化和时间化再对HTM网络进行训练即可。
+
+其实HTM算法是源于生物学理论，意味着它来自神经解剖学和神经生理学，是解释生物学的新皮质如何运作的。我们有时说HTM 理论是“约束于生物学”，和“启发于生物学”相反，后者是机器学习领域常用的说法。HTM 理论必须与新皮质的生物学细节相容，并且不能依赖生物组织中不可能实现的原理。比如，考虑锥体细胞，这是新皮质中最常见的神经元类型。锥体细胞有称作树突的树状延伸，通过数千个突触连接。神经学家知道树突是激活的处理单元，通过突触的交流是动态的、内在随机的过程。锥体细胞是新皮质的核心信息处理元件，突触是记忆的基础。所以，为了理解新皮质是如何运作的，我们需要一种适应神经元和突触的本质特征的理论。人工神经网络（ANN）一般是对没有树突并且只有很少的高度精确的突触和特征的神经元建模，真实的神经元并非如此。这种人工神经元与生物神经元不相容，因此不可能发展成与脑的运作原理相同的网络。这个评论不是说 ANN 没用，只是它们的运作原理和生物神经网络的不同。你将会看到，HTM 理论解释了为什么神经元有数千个突触和激活树突。我们认为，这些和很多其他生物学特征对智能系统来说是必不可少、无法忽视的。
+
+
+HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布表征，简称 SDR。SDR 是包含数千比特的向量。在任何时候，一小部分比特置 1，其余的置 0。HTM 理论会解释为什么在 SDR 中，总是有一小部分零散的比特置 1，以及这些置 1 的比特的比重必须小，通常小于 2%。SDR 中的比特对应着新皮质中的神经元。稀疏分布表征有一些意义重大并且不可思议的特性。为了方便比较，考虑在可编程计算机中的表征方法。单词存储在计算机中的含义不是单词内在的。如果给你看计算机内存中某处的 64 比特，你并不能知道它表示什么。在程序运行的某一时刻，这些比特可能是表示一个意思，在另一时刻，可能又表示别的意思。无论是哪种情况，只能依赖物理地址，
+而非比特本身。对于 SDR，表征的比特编码了自身的语义特征，即表达和含义是一致的。如果两个 SDR 有相同的比特位置 1，它们就共有某种语义特征。如果两个 SDR 有越多相同的比特位置 1，它们在语义上就越相似。SDR 解释了人脑是如何做语义归纳的，它正是这种表征方法的内在特性。另一个展示稀疏表征的特有能力的例子是，一组神经元可以同时激活多种表征并且不引起混乱。这就好比在计算机内存中的某处，不仅仅只能容纳一个值，而是同时容纳二十个值，并且不引起混乱。我们称这种独一无二的特性为“联合性”。在 HTM 理论中它被用来同时做多个预测。稀疏分布表征的运用是 HTM 理论的关键所在。我们认为，所有真正的智能系统必须要运用稀疏分布表征。为了轻松理解 HTM 理论，你需要培养一种面向 SDR 的数学特性和表征特性的直觉。
+
+
+
+每个 HTM 系统都需要“感知器官”，我们称之为“编码器”。每种编码器负责把某类数据（数字、事件、温度、图像或者 GPS 坐标）转化成一个稀疏分布表征，以便 HTM 学习算法进一步处理。每种编码器都是为明确的数据类型专门设计的，往往有很多途径可以把输入信息转化为 SDR，就如同哺乳动物们的视网膜构造五花八门。只要感知信息被编码成适当的 SDR，HTM 学习算法就可以处理了。
+
+基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
+

From 003ef012a1a3af2dbb87215bb8c5a328e1d79e93 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 08:59:29 +0800
Subject: [PATCH 1103/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index f2b93460..e3dccec6 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -23,3 +23,7 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
 
+
+每个 HTM 系统都需要“感知器官”，我们称之为“编码器”。每种编码器负责把某类数据（数字、事件、温度、图像或者 GPS 坐标）转化成一个稀疏分布表征，以便 HTM 学习算法进一步处理。每种编码器都是为明确的数据类型专门设计的，往往有很多途径可以把输入信息转化为 SDR，就如同哺乳动物们的视网膜构造五花八门。只要感知信息被编码成适当的 SDR，HTM 学习算法就可以处理了。
+
+基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。

From dad7702f03c2d51fcc0000f371d16fe4caa8649d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:02:09 +0800
Subject: [PATCH 1104/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 167 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 167 insertions(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index e3dccec6..dc5e222a 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -27,3 +27,170 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 每个 HTM 系统都需要“感知器官”，我们称之为“编码器”。每种编码器负责把某类数据（数字、事件、温度、图像或者 GPS 坐标）转化成一个稀疏分布表征，以便 HTM 学习算法进一步处理。每种编码器都是为明确的数据类型专门设计的，往往有很多途径可以把输入信息转化为 SDR，就如同哺乳动物们的视网膜构造五花八门。只要感知信息被编码成适当的 SDR，HTM 学习算法就可以处理了。
 
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
+
+#### 应用示例
+```python
+
+from carver.htm.config import config
+from carver.htm.synapse import CONNECTED_CUTOFF
+from carver.htm.segment import Segment
+
+#one column out of n should fire:
+desiredLocalActivity = config.getint('constants','desiredLocalActivity')
+
+def pool_spatial(htm):
+    '''
+    A couple notable deviations:
+    *column overlap boost and cutoff are swapped from pseudocode, details inline
+        see _spatial_overlap
+    *time and inputData removed from code - used a data producer model, linked to htm 
+    *getBestMatchingSegment now takes an argument for whether it is a nextStep segment or a sequence one
+        inspired by binarybarry on http://www.numenta.com/phpBB2/viewtopic.php?t=1403
+    '''
+    
+    _spatial_overlap(htm)
+    
+    activeColumns = _spatial_inhibition(htm)
+            
+    inhibitionRadius = _spatial_learning(htm, activeColumns)
+    
+    htm.inhibitionRadius = inhibitionRadius
+
+def pool_temporal(htm, updateSegments, learning=True):
+    updateSegments = _temporal_phase1(htm, learning, updateSegments)
+            
+    updateSegments = _temporal_phase2(htm, updateSegments, learning)
+    
+    if learning:
+        updateSegments = _temporal_phase3(htm, updateSegments)
+    
+    return updateSegments
+    
+def _spatial_overlap(htm):
+    'Overlap, p 35'
+    
+    for col in htm.columns:
+        col.overlap = len(col.old_firing_synapses())
+            
+        #The paper has conflicting information in the following lines.
+        #The text implies boost before cutoff, the code: cutoff then boost. I 
+        #chose boost first because I think the boost should help a column 
+        #overcome the cutoff.
+        col.overlap *= col.boost
+        
+        if col.overlap < col.MIN_OVERLAP:
+            col.overlap = 0
+    
+def _spatial_inhibition(htm):
+    'Inhibition, p 35'
+    activeColumns = []
+    for col in htm.columns:
+        kthNeighbor = col.kth_neighbor(desiredLocalActivity)
+        minLocalActivity = kthNeighbor.overlap
+        
+        if col.overlap > 0 and col.overlap >= minLocalActivity:
+            activeColumns.append(col)
+            col.active = True
+        else:
+            col.active = False
+    
+    return activeColumns
+
+def _spatial_learning(htm, activeColumns):
+    'Learning, p 36'
+    for col in activeColumns:
+        for s in col.synapses:
+            if s.was_firing():
+                s.permanence_increment()
+            else:
+                s.permanence_decrement()
+            
+    for col in htm.columns:
+        col.dutyCycleMin = 0.01 * col.neighbor_duty_cycle_max()
+        col.dutyCycleActive = col.get_duty_cycle_active()
+        col.boost = col.next_boost()
+        
+        col.dutyCycleOverlap = col.get_duty_cycle_overlap()
+        if col.dutyCycleOverlap < col.dutyCycleMin:
+            col.increase_permanences(0.1 * CONNECTED_CUTOFF)
+        
+    return htm.average_receptive_field_size()
+
+def _temporal_phase1(htm, learning, updateSegments):
+    '''
+    Phase 1, p40
+    @param htm: htm network object
+    @param learning: boolean describing whether the network is learning now
+    @param updateSegments: hash from cell to a list of segments to update when cell becomes active
+    '''
+    
+    for col in htm.columns_active():
+        buPredicted = False
+        learningCellChosen = False
+        for cell in col.cells:
+            if cell.predicted:
+                seg = cell.findSegmentWasActive(nextStep=True)
+                
+                #distal dendrite segments = sequence memory
+                if seg and seg.distal:
+                    buPredicted = True
+                    cell.active = True
+                    
+                    #Learning Phase 1, p 41
+                    if learning and seg.wasActiveFromLearningCells:
+                        learningCellChosen = True
+                        cell.learning = True
+                    
+        if not buPredicted:
+            for cell in col.cells:
+                cell.active = True
+                
+        #Learning Phase 1, p41
+        if learning and not learningCellChosen:
+            cell, seg = col.bestCell(nextStep=True)
+            cell.learning = True
+            
+            if seg is None:
+                seg = cell.create_segment(htm, nextStep=True)
+                
+            updateSegments.add(cell, seg, timeDelta=-1)
+            
+    return updateSegments
+            
+def _temporal_phase2(htm, updateSegments, learning):
+    'Phase 2, p40'
+    for cell in htm.cells:
+        for seg in cell.segments:
+            if seg.active:
+                cell.predicting = True
+                
+                if learning:
+                    updateSegments.add(cell, seg, timeDelta=0)
+            
+        #for each cell, grab the best segment. right now, this does not prevent 
+        #duplication of learning on the best segment
+        if learning and cell.predicting:
+            bestSeg = cell.bestMatchingSegment(nextStep=False)
+            if bestSeg is None:
+                bestSeg = cell.create_segment(htm, nextStep=False)
+                
+            bestSeg.round_out_synapses(htm)
+            
+            updateSegments.add(cell, bestSeg, timeDelta=-1)
+    
+    return updateSegments
+
+def _temporal_phase3(htm, updateSegments):
+    'Phase 3, p42'
+    for cell in htm.cells:
+        if cell.learning:
+            for synapseStates in updateSegments[cell]:
+                Segment.adapt_up(synapseStates)
+            updateSegments.reset(cell)
+        elif not cell.predicting and cell.predicted:
+            for synapseStates in updateSegments[cell]:
+                Segment.adapt_down(synapseStates)
+            updateSegments.reset(cell)
+            
+    return updateSegments
+```

From 1898705ef9275d84d062ff6b27becf838c946f5f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:05:39 +0800
Subject: [PATCH 1105/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index dc5e222a..b2bb983e 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -28,6 +28,9 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
 
+
+因而HTM算法应用与传统的算法应用是不同的。传统上每一个程序解决一个具体问题例如处理电邮或是分析数据。与此相反，HTM算法可以被训练来解决不领域不同类型的问题。一个HTM系统，相比之下，是在训练，而不是编程。 HTM通过感知的数据流以人类认知世界的方式来学习世界中的对象。通过模拟人类大脑的模式发现机制，HTM提供一种在杂乱 、大型、现实世界的数据集中进行模式识别和预测的方法。其应用领域很广，比如图像和声音识别，复杂系统的故障预测，网络点击预测，欺诈检测系统预测，文本的语义分析等 。HTM底层的学习算法并不局限于特定的应用领域。
+
 #### 应用示例
 ```python
 

From e61abfa3aca560ee046c3a95b6cf18c4a9486e63 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 2 Aug 2018 09:08:31 +0800
Subject: [PATCH 1106/1406] add images

---
 assets/images/372.jpg | Bin 0 -> 42260 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/372.jpg

diff --git a/assets/images/372.jpg b/assets/images/372.jpg
new file mode 100644
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From 2460d58df77abb0cd22a5715dda3ba7199b7802f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:09:56 +0800
Subject: [PATCH 1107/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index b2bb983e..cb9f9d65 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -18,7 +18,6 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 而非比特本身。对于 SDR，表征的比特编码了自身的语义特征，即表达和含义是一致的。如果两个 SDR 有相同的比特位置 1，它们就共有某种语义特征。如果两个 SDR 有越多相同的比特位置 1，它们在语义上就越相似。SDR 解释了人脑是如何做语义归纳的，它正是这种表征方法的内在特性。另一个展示稀疏表征的特有能力的例子是，一组神经元可以同时激活多种表征并且不引起混乱。这就好比在计算机内存中的某处，不仅仅只能容纳一个值，而是同时容纳二十个值，并且不引起混乱。我们称这种独一无二的特性为“联合性”。在 HTM 理论中它被用来同时做多个预测。稀疏分布表征的运用是 HTM 理论的关键所在。我们认为，所有真正的智能系统必须要运用稀疏分布表征。为了轻松理解 HTM 理论，你需要培养一种面向 SDR 的数学特性和表征特性的直觉。
 
 
-
 每个 HTM 系统都需要“感知器官”，我们称之为“编码器”。每种编码器负责把某类数据（数字、事件、温度、图像或者 GPS 坐标）转化成一个稀疏分布表征，以便 HTM 学习算法进一步处理。每种编码器都是为明确的数据类型专门设计的，往往有很多途径可以把输入信息转化为 SDR，就如同哺乳动物们的视网膜构造五花八门。只要感知信息被编码成适当的 SDR，HTM 学习算法就可以处理了。
 
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
@@ -28,6 +27,11 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
 
+<p align="center">
+<img width="300" align="center" src="../../images/360.jpg" />
+</p>
+HTM 算法在图像识别中的应用
+
 
 因而HTM算法应用与传统的算法应用是不同的。传统上每一个程序解决一个具体问题例如处理电邮或是分析数据。与此相反，HTM算法可以被训练来解决不领域不同类型的问题。一个HTM系统，相比之下，是在训练，而不是编程。 HTM通过感知的数据流以人类认知世界的方式来学习世界中的对象。通过模拟人类大脑的模式发现机制，HTM提供一种在杂乱 、大型、现实世界的数据集中进行模式识别和预测的方法。其应用领域很广，比如图像和声音识别，复杂系统的故障预测，网络点击预测，欺诈检测系统预测，文本的语义分析等 。HTM底层的学习算法并不局限于特定的应用领域。
 

From 87d34f6f54cc3bd6f5849b8b148f20900a510194 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:10:20 +0800
Subject: [PATCH 1108/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index cb9f9d65..1b5b1dd5 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -28,7 +28,7 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 基于 HTM 理论的机器智能令人兴奋的一个方面是，我们可以创造一些生物学上不存在的具有类似功能的编码器。比如，我们可以创造接收 GPS 坐标的编码器并把数据转化成 SDR。这种编码器允许 HTM 系统直接通过空间位置检测运动。HTM 系统可以进一步对运动分类，预测未来的位置，侦查运动中的异常。能够运用非人类感官的能力启发了智能机器可能的发展方向。智能机器不仅仅在人类事务上表现出优越性，还将处理那些人类难以感知或者无能为力的问题。
 
 <p align="center">
-<img width="300" align="center" src="../../images/360.jpg" />
+<img width="500" align="center" src="../../images/372.jpg" />
 </p>
 HTM 算法在图像识别中的应用
 

From 80ec355fef7b739ff322b53c3127e172937d57dc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:11:04 +0800
Subject: [PATCH 1109/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index 1b5b1dd5..fadca5c2 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -29,8 +29,9 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 <p align="center">
 <img width="500" align="center" src="../../images/372.jpg" />
+<span>HTM 算法在图像识别中的应用</span>
 </p>
-HTM 算法在图像识别中的应用
+
 
 
 因而HTM算法应用与传统的算法应用是不同的。传统上每一个程序解决一个具体问题例如处理电邮或是分析数据。与此相反，HTM算法可以被训练来解决不领域不同类型的问题。一个HTM系统，相比之下，是在训练，而不是编程。 HTM通过感知的数据流以人类认知世界的方式来学习世界中的对象。通过模拟人类大脑的模式发现机制，HTM提供一种在杂乱 、大型、现实世界的数据集中进行模式识别和预测的方法。其应用领域很广，比如图像和声音识别，复杂系统的故障预测，网络点击预测，欺诈检测系统预测，文本的语义分析等 。HTM底层的学习算法并不局限于特定的应用领域。

From 4a6c649b6dc90a2eb2ac6fb7ff35db170afe8bbe Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:11:29 +0800
Subject: [PATCH 1110/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index fadca5c2..ece3d71d 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -29,7 +29,7 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 <p align="center">
 <img width="500" align="center" src="../../images/372.jpg" />
-<span>HTM 算法在图像识别中的应用</span>
+<p>HTM 算法在图像识别中的应用</p>
 </p>
 
 

From 48eb53d05cb20b9ae89131e331c543216a33adc3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:11:57 +0800
Subject: [PATCH 1111/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index ece3d71d..cddee0fb 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -29,10 +29,8 @@ HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布
 
 <p align="center">
 <img width="500" align="center" src="../../images/372.jpg" />
-<p>HTM 算法在图像识别中的应用</p>
 </p>
-
-
+<p align="center">HTM 算法在图像识别中的应用</p>
 
 因而HTM算法应用与传统的算法应用是不同的。传统上每一个程序解决一个具体问题例如处理电邮或是分析数据。与此相反，HTM算法可以被训练来解决不领域不同类型的问题。一个HTM系统，相比之下，是在训练，而不是编程。 HTM通过感知的数据流以人类认知世界的方式来学习世界中的对象。通过模拟人类大脑的模式发现机制，HTM提供一种在杂乱 、大型、现实世界的数据集中进行模式识别和预测的方法。其应用领域很广，比如图像和声音识别，复杂系统的故障预测，网络点击预测，欺诈检测系统预测，文本的语义分析等 。HTM底层的学习算法并不局限于特定的应用领域。
 

From d3efcad7af7fe7cc6f5bfdfc930b51b443639873 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 2 Aug 2018 09:12:51 +0800
Subject: [PATCH 1112/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index 336a26db..eab8e525 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -21,7 +21,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/364.jpg" />
 </p>
-图中是循环神经网络进行展开成一个全神经网络的过程
+<p align="center">循环神经网络进行展开成一个全神经网络的过程</p>
+
 
 时间递归神经网络包含输入单元(Input units)，输入集标记为，而输出单元(Output units)的输出集则被标记为。RNNs还包含隐藏单元(Hidden units)，我们将其输出集标记为，这些隐藏单元完成了最为主要的工作。你会发现，在图中：有一条单向流动的信息流是从输入单元到达隐藏单元的，与此同时另一条单向流动的信息流从隐藏单元到达输出单元。在某些情况下，RNNs会打破后者的限制，引导信息从输出单元返回隐藏单元，这些被称为“Back Projections”，并且隐藏层的输入还包括上一隐藏层的状态，即隐藏层内的节点可以自连也可以互连。 
 

From c4b5eb4fb8019d27a9892ae2bfb08849e8f32f99 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 08:43:54 +0800
Subject: [PATCH 1113/1406] Update README.md

---
 README.md | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index 15d08543..1897302a 100644
--- a/README.md
+++ b/README.md
@@ -139,9 +139,8 @@
      * [深度卷积神经网络(Deep Convolutional Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.3.md) 
      * [深度递归神经网络(Deep Recurrent Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.4.md) 
      * [分层时间记忆(Hierarchical Temporal Memory)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.5.md) 
-     * [深度玻尔兹曼机(Deep Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
-     * [堆叠自动编码器(Stacked Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md) 
-     * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.8.md)
+     * [堆叠自动编码器(Stacked Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
+     * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
  * [降维算法]()
      * [主成分分析法（PCA）]()
      * [主成分回归（PCR）]()

From fc311b6830e7b6d1f85ccf85d54b59ab4b4b5d06 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Fri, 3 Aug 2018 08:45:59 +0800
Subject: [PATCH 1114/1406] change page of DL

---
 assets/src/DL/DL.0.8.md | 5 -----
 1 file changed, 5 deletions(-)
 delete mode 100644 assets/src/DL/DL.0.8.md

diff --git a/assets/src/DL/DL.0.8.md b/assets/src/DL/DL.0.8.md
deleted file mode 100644
index a8f3f1c3..00000000
--- a/assets/src/DL/DL.0.8.md
+++ /dev/null
@@ -1,5 +0,0 @@
-### Deeplearning Algorithms tutorial
-谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
-AI的开发离不开算法那我们就接下来开始学习算法吧！
-
-#### 生成式对抗网络(Generative Adversarial Networks)

From f8cd94fd48819a8f589a6634752a4ea3dd8a0143 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 08:47:29 +0800
Subject: [PATCH 1115/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ea82cdab..b7771af9 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 深度玻尔兹曼机(Deep Boltzmann Machine)
+#### 堆叠自动编码器(Stacked Boltzmann Machine)

From 13f394b7003b2017fb80e8417f2632d0367d41d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 08:47:51 +0800
Subject: [PATCH 1116/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index b7771af9..a8f3f1c3 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 堆叠自动编码器(Stacked Boltzmann Machine)
+#### 生成式对抗网络(Generative Adversarial Networks)

From c220b13c0e3dd6cc19b182b412e2e65662a85ccf Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 08:58:31 +0800
Subject: [PATCH 1117/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1897302a..6e6ee1d9 100644
--- a/README.md
+++ b/README.md
@@ -139,7 +139,7 @@
      * [深度卷积神经网络(Deep Convolutional Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.3.md) 
      * [深度递归神经网络(Deep Recurrent Neural Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.4.md) 
      * [分层时间记忆(Hierarchical Temporal Memory)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.5.md) 
-     * [堆叠自动编码器(Stacked Boltzmann Machine)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
+     * [堆叠自动编码器(Stacked AutoEncoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
  * [降维算法]()
      * [主成分分析法（PCA）]()

From 2dc9bb5b8482f8fdc0fafb16e5a6a2fe14098990 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 08:58:53 +0800
Subject: [PATCH 1118/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index b7771af9..c0d6aa3c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 堆叠自动编码器(Stacked Boltzmann Machine)
+#### 堆叠自动编码器(Stacked AutoEncoder)

From 3c1a57c7bb72bc3cb1719c302cf2097d5e9c2be4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 3 Aug 2018 09:04:43 +0800
Subject: [PATCH 1119/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index c0d6aa3c..3cf6989c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -3,3 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 堆叠自动编码器(Stacked AutoEncoder)
+自动编码器（AutoEncoder，AE）就是一种尽可能复现输入信号的神经网络，其输出向量与输入向量同维，常按照输入向量的某种形式，通过隐层学习一个数据的表示或对原始数据进行有效编码。值得注意的是，这种自编码器是一种不利用类标签的非线性特征提取方法， 就方法本身而言， 这种特征提取的目的在于保留和获得更好的信息表示， 而不是执行分类任务，尽管有时这两个目标是相关的。
+
+

From 1012d9a5dbce4a65bab1f54857ddd248ffe3eaa4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 5 Aug 2018 10:46:26 +0800
Subject: [PATCH 1120/1406] Update DL.0.5.md

---
 assets/src/DL/DL.0.5.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/DL/DL.0.5.md b/assets/src/DL/DL.0.5.md
index cddee0fb..bc9bc8ed 100644
--- a/assets/src/DL/DL.0.5.md
+++ b/assets/src/DL/DL.0.5.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 分层时间记忆(Hierarchical Temporal Memory)
-
 分层时间记忆算法(Hierarchical Temporal Memory)，全称HTM Cortical Learning Algorithms是由《人工智能的未来》(On Intelligence)一书作者Jeff Hawkins创建的Numenta公司发表的新一代人工智能算法。HTM算法旨在模拟新大脑皮层的工作原理，将复杂的问题转化为模式匹配与预测。正如它的名字HTM一样，该算法与普通的神经网络算法有诸多的不同之处。HTM强调对“神经元”进行分层级，强调信息模式的空间特性与时间特性。目前Numenta公司已经推出基于HTM算法的python平台和可进行视觉识别的软件工具箱。
 
 传统的人工智能算法大多是针对特定的任务目标而设计的。HTM算法与之不同 ，它注重先把问题转化成模式匹配与预测的问题再解决。这使提出人工智能的“统一理论”成为可能。HTM算法是建立在大量解剖学和神经科学的基础上的。HTM算法认为人类之所以具有智能，新大脑皮层是不可缺少的必要条件，并且由其承担高级脑活动。我们的大脑的运行机制是将接受到的各种模式与记忆中模式进行匹配，并对下一刻将会接收到的信息作出预测及反应，如此循环往复。这正是其时效性(Temporal)的体现。
@@ -13,7 +12,6 @@ HTM算法也是一种拥有记忆性和可学习性的算法。它相对于其
 
 其实HTM算法是源于生物学理论，意味着它来自神经解剖学和神经生理学，是解释生物学的新皮质如何运作的。我们有时说HTM 理论是“约束于生物学”，和“启发于生物学”相反，后者是机器学习领域常用的说法。HTM 理论必须与新皮质的生物学细节相容，并且不能依赖生物组织中不可能实现的原理。比如，考虑锥体细胞，这是新皮质中最常见的神经元类型。锥体细胞有称作树突的树状延伸，通过数千个突触连接。神经学家知道树突是激活的处理单元，通过突触的交流是动态的、内在随机的过程。锥体细胞是新皮质的核心信息处理元件，突触是记忆的基础。所以，为了理解新皮质是如何运作的，我们需要一种适应神经元和突触的本质特征的理论。人工神经网络（ANN）一般是对没有树突并且只有很少的高度精确的突触和特征的神经元建模，真实的神经元并非如此。这种人工神经元与生物神经元不相容，因此不可能发展成与脑的运作原理相同的网络。这个评论不是说 ANN 没用，只是它们的运作原理和生物神经网络的不同。你将会看到，HTM 理论解释了为什么神经元有数千个突触和激活树突。我们认为，这些和很多其他生物学特征对智能系统来说是必不可少、无法忽视的。
 
-
 HTM的原理：稀疏分布表征理论,运用的表征方法称作稀疏分布表征，简称 SDR。SDR 是包含数千比特的向量。在任何时候，一小部分比特置 1，其余的置 0。HTM 理论会解释为什么在 SDR 中，总是有一小部分零散的比特置 1，以及这些置 1 的比特的比重必须小，通常小于 2%。SDR 中的比特对应着新皮质中的神经元。稀疏分布表征有一些意义重大并且不可思议的特性。为了方便比较，考虑在可编程计算机中的表征方法。单词存储在计算机中的含义不是单词内在的。如果给你看计算机内存中某处的 64 比特，你并不能知道它表示什么。在程序运行的某一时刻，这些比特可能是表示一个意思，在另一时刻，可能又表示别的意思。无论是哪种情况，只能依赖物理地址，
 而非比特本身。对于 SDR，表征的比特编码了自身的语义特征，即表达和含义是一致的。如果两个 SDR 有相同的比特位置 1，它们就共有某种语义特征。如果两个 SDR 有越多相同的比特位置 1，它们在语义上就越相似。SDR 解释了人脑是如何做语义归纳的，它正是这种表征方法的内在特性。另一个展示稀疏表征的特有能力的例子是，一组神经元可以同时激活多种表征并且不引起混乱。这就好比在计算机内存中的某处，不仅仅只能容纳一个值，而是同时容纳二十个值，并且不引起混乱。我们称这种独一无二的特性为“联合性”。在 HTM 理论中它被用来同时做多个预测。稀疏分布表征的运用是 HTM 理论的关键所在。我们认为，所有真正的智能系统必须要运用稀疏分布表征。为了轻松理解 HTM 理论，你需要培养一种面向 SDR 的数学特性和表征特性的直觉。
 

From b24b6ec4acc2f4c4cb0359049f784dcad9650743 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 5 Aug 2018 10:50:44 +0800
Subject: [PATCH 1121/1406] change page of readme

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From be37d59b7863b78b2434ed68f7a95433711a04b3 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 5 Aug 2018 10:52:37 +0800
Subject: [PATCH 1122/1406] change images

---
 assets/images/global.png | Bin 0 -> 216249 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/global.png

diff --git a/assets/images/global.png b/assets/images/global.png
new file mode 100644
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From fbd5a5c39f561a3806626801c366855d73257ef6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 5 Aug 2018 11:52:03 +0800
Subject: [PATCH 1123/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index 6e6ee1d9..30b53725 100644
--- a/README.md
+++ b/README.md
@@ -11,7 +11,6 @@
 <p align="center">
 <img width="100%" align="center" src="assets/images/global.png" />
 </p>
-
 * 机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。
 * 机器学习：多领域交叉学科，涉及概率论统计学，逼近论，凸分析，算法复杂度理论等多门学科。
 * 机器学习的应用：语音识别，自动驾驶，语言翻译，计算机视觉，推荐系统，无人机，识别垃圾邮件，人脸识别，电商推荐系统。

From 4472bbecdbecd11ea94cd45869ddf265550f7c94 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 6 Aug 2018 08:54:53 +0800
Subject: [PATCH 1124/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 3cf6989c..70d70092 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -5,4 +5,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 堆叠自动编码器(Stacked AutoEncoder)
 自动编码器（AutoEncoder，AE）就是一种尽可能复现输入信号的神经网络，其输出向量与输入向量同维，常按照输入向量的某种形式，通过隐层学习一个数据的表示或对原始数据进行有效编码。值得注意的是，这种自编码器是一种不利用类标签的非线性特征提取方法， 就方法本身而言， 这种特征提取的目的在于保留和获得更好的信息表示， 而不是执行分类任务，尽管有时这两个目标是相关的。
 
+堆叠自编码器（Stacked Autoencoder，SAE）实际上就是做这样的事情，如自编码器，稀疏自编码器和降噪自编码器都是单个自编码器，它们通过虚构一个 x -> h -> x 的三层网络，能过学习出一种特征变化 h = f(wx+b) 。实际上，当训练结束后，输出层已经没有什么意义了，我们一般将其去掉，即将自编码器表示为：
+
 

From c2b5d3229466a191c6fcb98b70bea4745fe9e252 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 6 Aug 2018 09:05:12 +0800
Subject: [PATCH 1125/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 70d70092..aab98ccb 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -3,8 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 堆叠自动编码器(Stacked AutoEncoder)
-自动编码器（AutoEncoder，AE）就是一种尽可能复现输入信号的神经网络，其输出向量与输入向量同维，常按照输入向量的某种形式，通过隐层学习一个数据的表示或对原始数据进行有效编码。值得注意的是，这种自编码器是一种不利用类标签的非线性特征提取方法， 就方法本身而言， 这种特征提取的目的在于保留和获得更好的信息表示， 而不是执行分类任务，尽管有时这两个目标是相关的。
-
-堆叠自编码器（Stacked Autoencoder，SAE）实际上就是做这样的事情，如自编码器，稀疏自编码器和降噪自编码器都是单个自编码器，它们通过虚构一个 x -> h -> x 的三层网络，能过学习出一种特征变化 h = f(wx+b) 。实际上，当训练结束后，输出层已经没有什么意义了，我们一般将其去掉，即将自编码器表示为：
-
 
+堆叠自编码器(Stacked Autoencoder，SAE)

From c5c93fad6143733830c33bd012f19b70839beceb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 9 Aug 2018 08:50:01 +0800
Subject: [PATCH 1126/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index aab98ccb..00281e32 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -4,4 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 堆叠自动编码器(Stacked AutoEncoder)
 
+自从Hinton 2006年的工作之后，越来越多的研究者开始关注各种自编码器模型相应的堆叠模型。实际上，自编码器（Auto-Encoder）是一个较早的概念了，比如Hinton等人在1986, 1989年的工作。
+
 堆叠自编码器(Stacked Autoencoder，SAE)

From e55880c6dab925cb2ff1cde267fa8af903c06969 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 9 Aug 2018 08:51:37 +0800
Subject: [PATCH 1127/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 00281e32..c78a5ce2 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -6,4 +6,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 自从Hinton 2006年的工作之后，越来越多的研究者开始关注各种自编码器模型相应的堆叠模型。实际上，自编码器（Auto-Encoder）是一个较早的概念了，比如Hinton等人在1986, 1989年的工作。
 
+自编码器可以理解为一个试图去还原其原始输入的系统。
+
 堆叠自编码器(Stacked Autoencoder，SAE)

From f4642862b53de85ef125fb44ac9ee0a4799038d1 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 9 Aug 2018 08:54:09 +0800
Subject: [PATCH 1128/1406] add images

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/373.jpg

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From 115e1cf249bc46ce4d246f36e507cef7d1409c35 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 9 Aug 2018 08:56:02 +0800
Subject: [PATCH 1129/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index c78a5ce2..dd90796d 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -7,5 +7,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 自从Hinton 2006年的工作之后，越来越多的研究者开始关注各种自编码器模型相应的堆叠模型。实际上，自编码器（Auto-Encoder）是一个较早的概念了，比如Hinton等人在1986, 1989年的工作。
 
 自编码器可以理解为一个试图去还原其原始输入的系统。
-
-堆叠自编码器(Stacked Autoencoder，SAE)
+<p align="center">
+<img width="300" align="center" src="../../images/373.jpg" />
+</p>

From 1f2598537c886ea672f32bc0148a5c31222a72ae Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 11 Aug 2018 15:41:29 +0800
Subject: [PATCH 1130/1406] change page of DL0.6

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From 0005344f0257dc13b6c6ba6707b61996ffd5f084 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 11 Aug 2018 16:09:08 +0800
Subject: [PATCH 1131/1406] change page of DL

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 assets/images/374.jpg

diff --git a/assets/images/374.jpg b/assets/images/374.jpg
deleted file mode 100644
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GIT binary patch
literal 0
HcmV?d00001

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From 836d218ac513de3eee6ac4f8fd3c1601b334395f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 11 Aug 2018 16:13:20 +0800
Subject: [PATCH 1132/1406] change page of DL

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/374.jpg

diff --git a/assets/images/374.jpg b/assets/images/374.jpg
new file mode 100644
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GIT binary patch
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literal 0
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From f44a3f84eca887317a8df8175a0604e92d70de9d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:15:16 +0800
Subject: [PATCH 1133/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index dd90796d..4af33e49 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -10,3 +10,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/373.jpg" />
 </p>
+
+图中，虚线蓝色框内就是一个自编码器模型，它由编码器（Encoder）和解码器（Decoder）两部分组成，本质上都是对输入信号做某种变换。
+编码器将输入信号x变换成编码信号y，而解码器将编码y转换成输出信号<img width="300" align="center" src="../../images/374.jpg" />，即

From d028aa22d1f4509532c1b659008d13264d506a7a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:17:34 +0800
Subject: [PATCH 1134/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 4af33e49..4174abdf 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -12,4 +12,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 图中，虚线蓝色框内就是一个自编码器模型，它由编码器（Encoder）和解码器（Decoder）两部分组成，本质上都是对输入信号做某种变换。
-编码器将输入信号x变换成编码信号y，而解码器将编码y转换成输出信号<img width="300" align="center" src="../../images/374.jpg" />，即
+编码器将输入信号x变换成编码信号y，而解码器将编码y转换成输出信号<img width="10" align="center" src="../../images/374.jpg" />，即
+<p align="center">
+<img width="300" align="center" src="../../images/375.jpg" />
+</p>
+
+而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="300" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。

From 3e403608e0e0d0e273ef89311ba6e2014814170a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:17:58 +0800
Subject: [PATCH 1135/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 4174abdf..ac9c9a77 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -12,9 +12,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 图中，虚线蓝色框内就是一个自编码器模型，它由编码器（Encoder）和解码器（Decoder）两部分组成，本质上都是对输入信号做某种变换。
-编码器将输入信号x变换成编码信号y，而解码器将编码y转换成输出信号<img width="10" align="center" src="../../images/374.jpg" />，即
+编码器将输入信号x变换成编码信号y，而解码器将编码y转换成输出信号<img width="20" align="center" src="../../images/374.jpg" />，即
 <p align="center">
 <img width="300" align="center" src="../../images/375.jpg" />
 </p>
 
-而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="300" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
+而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="20" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。

From fe7a8393687a32b9522447cf5c538bc634d37216 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:18:19 +0800
Subject: [PATCH 1136/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ac9c9a77..e36fea28 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -17,4 +17,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/375.jpg" />
 </p>
 
-而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="20" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
+而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="100" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。

From 18d5550f75116b00242d4964944f75240284454c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:22:43 +0800
Subject: [PATCH 1137/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index e36fea28..638c39f1 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -17,4 +17,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/375.jpg" />
 </p>
 
-而自编码器的目的是，让输出尽可能复现输入x，即但是，这样问题就来了——如果f和g都是恒等映射，那不就恒有<img width="100" align="center" src="../../images/376.jpg" />了？不错，确实如此，但这样的变换——没有任何卵用啊！因此，我们经常对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
+而自编码器的目的是，让输出尽可能复现输入x.但是，这样问题就来了,如果f和g都是恒等映射，那就是<img width="100" align="center" src="../../images/376.jpg" />？事实确实如此，但这样的变换就没有什么用了，所以我们需要对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
+
+在这里需要强调一点，对于自编码器，往往并不关系输出是什么，因常我们只需要关心中间层的编码，或者是从输入到编码的映射。在我们强迫编码y和输入x不同的情况下，系统还能够去复原原始信号x，那么说明编码y已经承载了原始数据的所有信息，但以一种不同的形式！这就是特征提取。这个是通过自动学出来的，事实上，自动学习原始数据的特征表达也是神经网络和深度学习的核心目的之一。
+
+自编码器与神经网络，其中神经网络就是在对原始信号逐层地做非线性变换：
+
+<p align="center">
+<img width="300" align="center" src="../../images/377.jpg" />
+</p>

From 1b985d3e11839cf46557b46344fabb8bca3dfea0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:24:38 +0800
Subject: [PATCH 1138/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 638c39f1..bee364b7 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -26,3 +26,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/377.jpg" />
 </p>
+
+该网络把输入层数据<img width="30" align="center" src="../../images/378.jpg" />转换到中间层（隐层）<img width="30" align="center" src="../../images/379.jpg" />，再转换到输出层<img width="30" align="center" src="../../images/380.jpg" />。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示即为。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示为:
+<p align="center">
+<img width="300" align="center" src="../../images/381.jpg" />
+</p>

From 882f53ba4ae59612dd035dcc01559e3af72634b0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:25:07 +0800
Subject: [PATCH 1139/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index bee364b7..b886d377 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -27,7 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/377.jpg" />
 </p>
 
-该网络把输入层数据<img width="30" align="center" src="../../images/378.jpg" />转换到中间层（隐层）<img width="30" align="center" src="../../images/379.jpg" />，再转换到输出层<img width="30" align="center" src="../../images/380.jpg" />。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示即为。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示为:
+该网络把输入层数据<img width="70" align="center" src="../../images/378.jpg" />转换到中间层（隐层）<img width="70" align="center" src="../../images/379.jpg" />，再转换到输出层<img width="70" align="center" src="../../images/380.jpg" />。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示即为。图中的每个节点代表数据的一个维度（偏置项图中未标出）。每两层之间的变换都是“线性变化”+“非线性激活”，用公式表示为:
 <p align="center">
 <img width="300" align="center" src="../../images/381.jpg" />
 </p>

From 2ad495e5a9448e97927f8cdd279cde7fe9d0ba58 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:27:30 +0800
Subject: [PATCH 1140/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index b886d377..7dc47bff 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -31,3 +31,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/381.jpg" />
 </p>
+
+神经网络通常可以用于分类，这样可以得道从输入层到输出层的变换函数。因此，我们需要定义一个目标函数来衡量当前的输出和真实结果的差异，利用该函数去逐步调整（如梯度下降）系统的参数<img width="70" align="center" src="../../images/382.jpg" />，以使得整个网络尽可能去拟合训练数据。如果有正则约束的话，还同时要求模型尽量简单（以防止过拟合）。
+
+但是自编码器怎么表示呢？
+
+自编码器试图复现其原始输入，因此，在训练中，网络中的输出应与输入相同，即 y=x，因此，一个自编码器的输入、输出应有相同的结构，即：
+<p align="center">
+<img width="300" align="center" src="../../images/383.jpg" />
+</p>
+

From 1f6ef86145a6843da7bb37b003538a2e860799a3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:27:59 +0800
Subject: [PATCH 1141/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 7dc47bff..397c8003 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -32,7 +32,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/381.jpg" />
 </p>
 
-神经网络通常可以用于分类，这样可以得道从输入层到输出层的变换函数。因此，我们需要定义一个目标函数来衡量当前的输出和真实结果的差异，利用该函数去逐步调整（如梯度下降）系统的参数<img width="70" align="center" src="../../images/382.jpg" />，以使得整个网络尽可能去拟合训练数据。如果有正则约束的话，还同时要求模型尽量简单（以防止过拟合）。
+神经网络通常可以用于分类，这样可以得道从输入层到输出层的变换函数。因此，我们需要定义一个目标函数来衡量当前的输出和真实结果的差异，利用该函数去逐步调整（如梯度下降）系统的参数<img width=130" align="center" src="../../images/382.jpg" />，以使得整个网络尽可能去拟合训练数据。如果有正则约束的话，还同时要求模型尽量简单（以防止过拟合）。
 
 但是自编码器怎么表示呢？
 

From c262d428080c225856646d958ad9ae9ca015599f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:28:26 +0800
Subject: [PATCH 1142/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 397c8003..43dfad95 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -32,7 +32,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/381.jpg" />
 </p>
 
-神经网络通常可以用于分类，这样可以得道从输入层到输出层的变换函数。因此，我们需要定义一个目标函数来衡量当前的输出和真实结果的差异，利用该函数去逐步调整（如梯度下降）系统的参数<img width=130" align="center" src="../../images/382.jpg" />，以使得整个网络尽可能去拟合训练数据。如果有正则约束的话，还同时要求模型尽量简单（以防止过拟合）。
+神经网络通常可以用于分类，这样可以得道从输入层到输出层的变换函数。因此，我们需要定义一个目标函数来衡量当前的输出和真实结果的差异，利用该函数去逐步调整（如梯度下降）系统的参数<img width="130" align="center" src="../../images/382.jpg" />，以使得整个网络尽可能去拟合训练数据。如果有正则约束的话，还同时要求模型尽量简单（以防止过拟合）。
 
 但是自编码器怎么表示呢？
 

From 196bf106600ff6a96e252bfcef1aa007f52cb22c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:32:24 +0800
Subject: [PATCH 1143/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 43dfad95..00fd19a3 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -41,3 +41,8 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/383.jpg" />
 </p>
 
+这里我们可以利用训练数据训练这个网络，等训练结束后，这个网络即学习出了<img width="100" align="center" src="../../images/384.jpg" />的能力。对我们来说，此时的h是至关重要的，因为它是在尽量不损失信息量的情况下，对原始数据的另一种表达。结合神经网络的惯例，我们再将自编码器的公式表示如下：（假设激活函数是sigmoid，用s表示）
+
+<p align="center">
+<img width="300" align="center" src="../../images/385.jpg" />
+</p>

From 4ec682d33bc45b32d3aa197daa583af05b27421f Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 11 Aug 2018 16:34:27 +0800
Subject: [PATCH 1144/1406] change page of DL

---
 assets/images/386.jpg | Bin 0 -> 1368 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/386.jpg

diff --git a/assets/images/386.jpg b/assets/images/386.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..5564322219ae03eed9f8e5f834b83415e49d6b6c
GIT binary patch
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literal 0
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From 3d111bb0ed8a786105d834db49a2679440494fd3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:37:03 +0800
Subject: [PATCH 1145/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 00fd19a3..ec6418d6 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -46,3 +46,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="300" align="center" src="../../images/385.jpg" />
 </p>
+
+其中，<img width="30" align="center" src="../../images/386.jpg" />表示损失函数，结合数据的不同形式，可以是二次误差（squared error loss）或交叉熵误差（cross entropy loss）。如果<img width="30" align="center" src="../../images/387.jpg" />，一般称为tied weights。

From 4ffbb8ee9a70e1090fd22eea05a51eae8694e8ac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:44:44 +0800
Subject: [PATCH 1146/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ec6418d6..ab67e110 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -17,7 +17,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/375.jpg" />
 </p>
 
-而自编码器的目的是，让输出尽可能复现输入x.但是，这样问题就来了,如果f和g都是恒等映射，那就是<img width="100" align="center" src="../../images/376.jpg" />？事实确实如此，但这样的变换就没有什么用了，所以我们需要对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
+而自编码器的目的是，让输出尽可能复现输入x.但是，这样问题就来了,如果f和g都是恒等映射，那就是<img width="70" align="center" src="../../images/376.jpg" />,实际上事实确实如此，但这样的变换就没有什么用了，所以我们需要对中间信号y（也叫作“编码”）做一定的约束，这样，系统往往能学出很有趣的编码变换f和编码y。
 
 在这里需要强调一点，对于自编码器，往往并不关系输出是什么，因常我们只需要关心中间层的编码，或者是从输入到编码的映射。在我们强迫编码y和输入x不同的情况下，系统还能够去复原原始信号x，那么说明编码y已经承载了原始数据的所有信息，但以一种不同的形式！这就是特征提取。这个是通过自动学出来的，事实上，自动学习原始数据的特征表达也是神经网络和深度学习的核心目的之一。
 
@@ -48,3 +48,19 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 其中，<img width="30" align="center" src="../../images/386.jpg" />表示损失函数，结合数据的不同形式，可以是二次误差（squared error loss）或交叉熵误差（cross entropy loss）。如果<img width="30" align="center" src="../../images/387.jpg" />，一般称为tied weights。
+
+这里我们会给隐层加入一定的约束。从数据维度来看，常见以下两种情况：
+
+* n>p，即隐层维度小于输入数据维度。从x→h的变换是一种降维的操作，网络试图以更小的维度去描述原始数据而尽量不损失数据信息。实际上，当每两层之间的变换均为线性，且监督训练的误差是二次型误差时，该网络等价于PCA！
+
+* n<p ，即隐层维度大于输入数据维度。虽然我们同时约束h的表达尽量稀疏（有大量维度为0，未被激活），此时的编码器便是非常有名的“稀疏自编码器”。可为什么稀疏的表达就是好的？这是因为，有人尝试从人脑机理对比，人类神经系统在某一刺激下，大部分神经元是被抑制的。
+
+学习过深度学习的都明白，深度学习中深度网络的重要性在于其能够逐层地学习原始数据的多种表达。每一层的都以底一层的表达为基础，但往往更抽象，更加适合复杂的分类等任务。
+
+
+堆叠自编码器实际上就在做这样的事情，如前所述，单个自编码器通过虚构<img width="30" align="center" src="../../images/388.jpg" />的三层网络，能够学习出一种特征变化<img width="30" align="center" src="../../images/389.jpg" />(这里用θ表示变换的参数，包括W,b和激活函数)。实际上，当训练结束后，输出层就没什么意义了，我们一般会将其去掉的，即将自编码器表示为:
+<p align="center">
+<img width="200" align="center" src="../../images/390.jpg" />
+</p>
+
+

From e418189e9d4064a944d12e4d9ea2b4ea2f1283e3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:48:56 +0800
Subject: [PATCH 1147/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ab67e110..a5100166 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -63,4 +63,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/390.jpg" />
 </p>
 
+自编码器模型这里表示为3层的神经网络，这是因为训练的需要，我们将原始数据作为假想的目标输出，以此构建监督误差来训练整个网络。等训练结束后，输出层就可以去掉了，而我们关心的只是从x到h的变换过程。
+
+接下来的思路就很自然了——我们已经得到特征表达h，那么我们就可以将h再当做原始信息，训练一个新的自编码器，得到新的特征表达。
+
+堆叠自编码器（Stacked Auto-Encoder, SAE）,这里Stacked就是逐层垒叠的意思，跟“栈”有点像，当把多个自编码器Stack起来之后就是如下的过程：
+<p align="center">
+<img width="200" align="center" src="../../images/391.jpg" />
+</p>
 

From 6a2259b644365a9650037d3bffb6a71681dffa61 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 16:49:20 +0800
Subject: [PATCH 1148/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index a5100166..ccf1da06 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -60,7 +60,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 堆叠自编码器实际上就在做这样的事情，如前所述，单个自编码器通过虚构<img width="30" align="center" src="../../images/388.jpg" />的三层网络，能够学习出一种特征变化<img width="30" align="center" src="../../images/389.jpg" />(这里用θ表示变换的参数，包括W,b和激活函数)。实际上，当训练结束后，输出层就没什么意义了，我们一般会将其去掉的，即将自编码器表示为:
 <p align="center">
-<img width="200" align="center" src="../../images/390.jpg" />
+<img width="500" align="center" src="../../images/390.jpg" />
 </p>
 
 自编码器模型这里表示为3层的神经网络，这是因为训练的需要，我们将原始数据作为假想的目标输出，以此构建监督误差来训练整个网络。等训练结束后，输出层就可以去掉了，而我们关心的只是从x到h的变换过程。
@@ -69,6 +69,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 堆叠自编码器（Stacked Auto-Encoder, SAE）,这里Stacked就是逐层垒叠的意思，跟“栈”有点像，当把多个自编码器Stack起来之后就是如下的过程：
 <p align="center">
-<img width="200" align="center" src="../../images/391.jpg" />
+<img width="500" align="center" src="../../images/391.jpg" />
 </p>
 

From dd665e936391c8b296980d943d66000a1766a3e5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:00:52 +0800
Subject: [PATCH 1149/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ccf1da06..86b8a04c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -72,3 +72,21 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="500" align="center" src="../../images/391.jpg" />
 </p>
 
+这里需要注意的是，整个网络的训练不是一蹴而就的，而是需要逐层进行。根据n,m,k结构，实际上我们是先训练网络n→m→n，得到n→m的变换，然后再训练
+m→k→m，得到m→k的变换。最终堆叠成SAE，即为n→m→k的结果，整个过程就像一层层往上构建网络，这个就是非常有名的
+layer-wise unsuperwised pre-training（逐层非监督预训练）。
+
+稀疏自编码器如前所示，这种模型背后的思想是，高维而稀疏的表达是好的。一般而言h中哪些节点是被抑制的（对于sigmoid单元即输出为0），而是指定一个稀疏性参数ρ，，代表隐藏神经元的平均活跃程度（在训练集上取平均）。比如，当ρ=0.05时，可以认为隐层节点在95%的时间里都是被一直的，只有5%的机会被激活。实际上，为了满足这一条件，隐层神经元的活跃度需要接近于0。
+
+既然要求平均激活度为ρ，那么我们只要引入一个度量，来衡量神经元i的实际激活度<img width="70" align="center" src="../../images/394.jpg" />与期望激活度ρ之间的差异即可，然后将这个度量添加到目标函数作为正则，训练整个网络即可。那么，什么样的度量适合这个任务呢？了解过概率论、信息论基础的人应该清楚——相对熵，也就是KL散度（KL divergence）。因此，整个网络所添加的惩罚项：
+<p align="center">
+<img width="300" align="center" src="../../images/392.jpg" />
+</p>
+
+我们可以从下图（摘自UFLDL）中直观理解KL散度作为惩罚项的含义。图中假设平均激活度ρ=0.2。
+
+<p align="center">
+<img width="300" align="center" src="../../images/393.jpg" />
+</p>
+
+可以看出，当<img width="70" align="center" src="../../images/394.jpg" />一旦偏离期望激活度ρ，这种误差便急剧增大，从而作为惩罚项添加到目标函数，指导整个网络学习出稀疏的特征表达。

From 5d18c40cb1ba3126c6145f4222ee651e7ace1916 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:01:25 +0800
Subject: [PATCH 1150/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 86b8a04c..400cdea2 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -78,15 +78,15 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 稀疏自编码器如前所示，这种模型背后的思想是，高维而稀疏的表达是好的。一般而言h中哪些节点是被抑制的（对于sigmoid单元即输出为0），而是指定一个稀疏性参数ρ，，代表隐藏神经元的平均活跃程度（在训练集上取平均）。比如，当ρ=0.05时，可以认为隐层节点在95%的时间里都是被一直的，只有5%的机会被激活。实际上，为了满足这一条件，隐层神经元的活跃度需要接近于0。
 
-既然要求平均激活度为ρ，那么我们只要引入一个度量，来衡量神经元i的实际激活度<img width="70" align="center" src="../../images/394.jpg" />与期望激活度ρ之间的差异即可，然后将这个度量添加到目标函数作为正则，训练整个网络即可。那么，什么样的度量适合这个任务呢？了解过概率论、信息论基础的人应该清楚——相对熵，也就是KL散度（KL divergence）。因此，整个网络所添加的惩罚项：
+既然要求平均激活度为ρ，那么我们只要引入一个度量，来衡量神经元i的实际激活度<img width="10" align="center" src="../../images/394.jpg" />与期望激活度ρ之间的差异即可，然后将这个度量添加到目标函数作为正则，训练整个网络即可。那么，什么样的度量适合这个任务呢？了解过概率论、信息论基础的人应该清楚——相对熵，也就是KL散度（KL divergence）。因此，整个网络所添加的惩罚项：
 <p align="center">
-<img width="300" align="center" src="../../images/392.jpg" />
+<img width="500" align="center" src="../../images/392.jpg" />
 </p>
 
 我们可以从下图（摘自UFLDL）中直观理解KL散度作为惩罚项的含义。图中假设平均激活度ρ=0.2。
 
 <p align="center">
-<img width="300" align="center" src="../../images/393.jpg" />
+<img width="500" align="center" src="../../images/393.jpg" />
 </p>
 
-可以看出，当<img width="70" align="center" src="../../images/394.jpg" />一旦偏离期望激活度ρ，这种误差便急剧增大，从而作为惩罚项添加到目标函数，指导整个网络学习出稀疏的特征表达。
+可以看出，当<img width="10" align="center" src="../../images/394.jpg" />一旦偏离期望激活度ρ，这种误差便急剧增大，从而作为惩罚项添加到目标函数，指导整个网络学习出稀疏的特征表达。

From 3d999fb14f20f971995bbacce38a3f471b02ad21 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:05:47 +0800
Subject: [PATCH 1151/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 400cdea2..fa7b320f 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -80,7 +80,7 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 既然要求平均激活度为ρ，那么我们只要引入一个度量，来衡量神经元i的实际激活度<img width="10" align="center" src="../../images/394.jpg" />与期望激活度ρ之间的差异即可，然后将这个度量添加到目标函数作为正则，训练整个网络即可。那么，什么样的度量适合这个任务呢？了解过概率论、信息论基础的人应该清楚——相对熵，也就是KL散度（KL divergence）。因此，整个网络所添加的惩罚项：
 <p align="center">
-<img width="500" align="center" src="../../images/392.jpg" />
+<img width="300" align="center" src="../../images/392.jpg" />
 </p>
 
 我们可以从下图（摘自UFLDL）中直观理解KL散度作为惩罚项的含义。图中假设平均激活度ρ=0.2。
@@ -90,3 +90,8 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 </p>
 
 可以看出，当<img width="10" align="center" src="../../images/394.jpg" />一旦偏离期望激活度ρ，这种误差便急剧增大，从而作为惩罚项添加到目标函数，指导整个网络学习出稀疏的特征表达。
+
+
+降噪自编码器(Stacked Denoising Autoencoders)核心思想是，一个能够从中恢复出原始信号的表达未必是最好的，能够对“被污染/破坏”的原始数据编码、解码，然后还能恢复真正的原始数据，这样的特征才是好的。
+
+假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="50" align="center" src="../../images/374.jpg" />，然后再对<img width="50" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="50" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="50" align="center" src="../../images/396.jpg" />变成了<img width="50" align="center" src="../../images/397.jpg" />。

From 8d2cb6c6e205fc72cff92054917e09ba70435546 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:06:19 +0800
Subject: [PATCH 1152/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index fa7b320f..8a4e30ea 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -94,4 +94,4 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 降噪自编码器(Stacked Denoising Autoencoders)核心思想是，一个能够从中恢复出原始信号的表达未必是最好的，能够对“被污染/破坏”的原始数据编码、解码，然后还能恢复真正的原始数据，这样的特征才是好的。
 
-假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="50" align="center" src="../../images/374.jpg" />，然后再对<img width="50" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="50" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="50" align="center" src="../../images/396.jpg" />变成了<img width="50" align="center" src="../../images/397.jpg" />。
+假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="50" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="20" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。

From 89d25578e1ef89ea2361e46b959969d9d7117527 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:06:42 +0800
Subject: [PATCH 1153/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 8a4e30ea..11779c0c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -94,4 +94,4 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 降噪自编码器(Stacked Denoising Autoencoders)核心思想是，一个能够从中恢复出原始信号的表达未必是最好的，能够对“被污染/破坏”的原始数据编码、解码，然后还能恢复真正的原始数据，这样的特征才是好的。
 
-假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="50" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="20" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。
+假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="20" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="30" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。

From 52a1e5f01c378735fab1e0cb2849132de6fb9397 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:07:01 +0800
Subject: [PATCH 1154/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index 11779c0c..ad24802f 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -94,4 +94,4 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 降噪自编码器(Stacked Denoising Autoencoders)核心思想是，一个能够从中恢复出原始信号的表达未必是最好的，能够对“被污染/破坏”的原始数据编码、解码，然后还能恢复真正的原始数据，这样的特征才是好的。
 
-假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="20" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="30" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。
+假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="20" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="80" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。

From b035ba3776c26836d733eccac5b7892bf0c17e62 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:13:35 +0800
Subject: [PATCH 1155/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ad24802f..ccda441c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -94,4 +94,29 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 
 降噪自编码器(Stacked Denoising Autoencoders)核心思想是，一个能够从中恢复出原始信号的表达未必是最好的，能够对“被污染/破坏”的原始数据编码、解码，然后还能恢复真正的原始数据，这样的特征才是好的。
 
-假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="20" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="80" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="100" align="center" src="../../images/396.jpg" />变成了<img width="100" align="center" src="../../images/397.jpg" />。
+假设原始数据x被我们“故意破坏”，比如加入高斯白噪，或者把某些维度数据抹掉，变成了<img width="20" align="center" src="../../images/374.jpg" />，然后再对<img width="20" align="center" src="../../images/374.jpg" />编码、解码，得到恢复信号<img width="100" align="center" src="../../images/395.jpg" />，该恢复信号尽可能逼近未被污染的数据x。此时，监督训练的误差从<img width="120" align="center" src="../../images/396.jpg" />变成了<img width="120" align="center" src="../../images/397.jpg" />。
+
+降噪自编码器的系统结构如下图:
+
+<p align="center">
+<img width="300" align="center" src="../../images/398.jpg" />
+</p>
+
+深度学习兴起正式因为逐层预训练方法的提出，使得深度网络的训练成为可能。对于一个深度网络而言，这种逐层预训练的方法，正是前面介绍的这种堆叠自动编码器(Stacked AutoEncoder)。对于常见的分类任务，一般分为以下两个阶段：
+
+*  逐层预训练(layer-wise pre-training)
+*  微调(fune-tuning )
+
+上面讲述的的自动编码器，本质上都是非监督学习，自动编码器各层的输出都是原始数据的不同表达。对于分类任务，往往在自动编码器顶端再添加一分类层（如Softmax层），并结合有标注的训练数据，在误差函数的指导下，对系统的参数进行微调，以使得整个网络能够完成所需的分类任务。
+
+<p align="center">
+<img width="300" align="center" src="../../images/399.jpg" />
+</p>
+
+对于微调过程，即可以只调整分类层的参数（此时相当于把整个SAE当做一个feature extractor），也可以调整整个网络的参数（适合训练数据量比较大的情况）。
+
+但是为什么训练稀疏自编码器为什么一般都是三层的结构，实际上这里的三层是指训练单个自编码器所假想的3层神经网络，这对任何基于神经网络的编码器都是这样。多层的稀疏自编码器自然是有的，只不过是通过layer-wise pre-training这种方式逐层堆叠起来的，而不是直接去训练多层的网络。
+
+实际上，这正是在训练深层神经网络中遇到的问题。直接去训练一个深层的自编码器，其实本质上就是在做深度网络的训练，由于梯度扩散等问题，这样的网络往往根本无法训练。这倒不是因为会破坏稀疏性等原因，只要网络能够训练，对模型施加的约束总能得到相应的结果。
+
+但是为什么逐层预训练就可以使得深度网络的训练成为可能了呢？其实一个直观的解释是，预训练好的网络在一定程度上拟合了训练数据的结构，这使得整个网络的初始值是在一个合适的状态，便于有监督阶段加快迭代收敛。

From 163d9ed8ea4bd19dd7607fe374e81edb0c54b258 Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sat, 11 Aug 2018 17:14:22 +0800
Subject: [PATCH 1156/1406] delete images

---
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From 58c64f5a95e3c86112887f85d5ce125f6f5350f9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 11 Aug 2018 17:17:57 +0800
Subject: [PATCH 1157/1406] Update DL.0.6.md

---
 assets/src/DL/DL.0.6.md | 586 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 586 insertions(+)

diff --git a/assets/src/DL/DL.0.6.md b/assets/src/DL/DL.0.6.md
index ccda441c..a711993c 100644
--- a/assets/src/DL/DL.0.6.md
+++ b/assets/src/DL/DL.0.6.md
@@ -120,3 +120,589 @@ layer-wise unsuperwised pre-training（逐层非监督预训练）。
 实际上，这正是在训练深层神经网络中遇到的问题。直接去训练一个深层的自编码器，其实本质上就是在做深度网络的训练，由于梯度扩散等问题，这样的网络往往根本无法训练。这倒不是因为会破坏稀疏性等原因，只要网络能够训练，对模型施加的约束总能得到相应的结果。
 
 但是为什么逐层预训练就可以使得深度网络的训练成为可能了呢？其实一个直观的解释是，预训练好的网络在一定程度上拟合了训练数据的结构，这使得整个网络的初始值是在一个合适的状态，便于有监督阶段加快迭代收敛。
+
+#### 应用示例
+```python
+# This piece of software is bound by The MIT License (MIT)
+# Copyright (c) 2014 Siddharth Agrawal
+# Code written by : Siddharth Agrawal
+# Email ID : siddharth.950@gmail.com
+
+import struct
+import array
+import numpy
+import math
+import time
+import scipy.io
+import scipy.optimize
+
+""" Returns elementwise sigmoid output of input array """
+
+def sigmoid(x):
+
+    return (1 / (1 + numpy.exp(-x)))
+    
+""" Returns the groundtruth matrix for a set of labels """
+    
+def getGroundTruth(labels):
+
+    """ Prepare data needed to construct groundtruth matrix """
+
+    labels = numpy.array(labels).flatten()
+    data   = numpy.ones(len(labels))
+    indptr = numpy.arange(len(labels)+1)
+    
+    """ Compute the groundtruth matrix and return """
+    
+    ground_truth = scipy.sparse.csr_matrix((data, labels, indptr))
+    ground_truth = numpy.transpose(ground_truth.todense())
+    
+    return ground_truth
+
+""" The Sparse Autoencoder class """
+
+class SparseAutoencoder(object):
+
+    """ Initialization of Autoencoder object """
+
+    def __init__(self, visible_size, hidden_size, rho, lamda, beta):
+    
+        """ Initialize parameters of the Autoencoder object """
+    
+        self.visible_size = visible_size    # number of input units
+        self.hidden_size = hidden_size      # number of hidden units
+        self.rho = rho                      # desired average activation of hidden units
+        self.lamda = lamda                  # weight decay parameter
+        self.beta = beta                    # weight of sparsity penalty term
+        
+        """ Set limits for accessing 'theta' values """
+        
+        self.limit0 = 0
+        self.limit1 = hidden_size * visible_size
+        self.limit2 = 2 * hidden_size * visible_size
+        self.limit3 = 2 * hidden_size * visible_size + hidden_size
+        self.limit4 = 2 * hidden_size * visible_size + hidden_size + visible_size
+        
+        """ Initialize Neural Network weights randomly
+            W1, W2 values are chosen in the range [-r, r] """
+        
+        r = math.sqrt(6) / math.sqrt(visible_size + hidden_size + 1)
+        
+        rand = numpy.random.RandomState(int(time.time()))
+        
+        W1 = numpy.asarray(rand.uniform(low = -r, high = r, size = (hidden_size, visible_size)))
+        W2 = numpy.asarray(rand.uniform(low = -r, high = r, size = (visible_size, hidden_size)))
+        
+        """ Bias values are initialized to zero """
+        
+        b1 = numpy.zeros((hidden_size, 1))
+        b2 = numpy.zeros((visible_size, 1))
+
+        """ Create 'theta' by unrolling W1, W2, b1, b2 """
+
+        self.theta = numpy.concatenate((W1.flatten(), W2.flatten(),
+                                        b1.flatten(), b2.flatten()))
+
+    """ Returns gradient of 'theta' using Backpropagation algorithm """
+        
+    def sparseAutoencoderCost(self, theta, input):
+        
+        """ Extract weights and biases from 'theta' input """
+        
+        W1 = theta[self.limit0 : self.limit1].reshape(self.hidden_size, self.visible_size)
+        W2 = theta[self.limit1 : self.limit2].reshape(self.visible_size, self.hidden_size)
+        b1 = theta[self.limit2 : self.limit3].reshape(self.hidden_size, 1)
+        b2 = theta[self.limit3 : self.limit4].reshape(self.visible_size, 1)
+        
+        """ Compute output layers by performing a feedforward pass
+            Computation is done for all the training inputs simultaneously """
+        
+        hidden_layer = sigmoid(numpy.dot(W1, input) + b1)
+        output_layer = sigmoid(numpy.dot(W2, hidden_layer) + b2)
+        
+        """ Estimate the average activation value of the hidden layers """
+        
+        rho_cap = numpy.sum(hidden_layer, axis = 1) / input.shape[1]
+        
+        """ Compute intermediate difference values using Backpropagation algorithm """
+        
+        diff = output_layer - input
+        
+        sum_of_squares_error = 0.5 * numpy.sum(numpy.multiply(diff, diff)) / input.shape[1]
+        weight_decay         = 0.5 * self.lamda * (numpy.sum(numpy.multiply(W1, W1)) +
+                                                   numpy.sum(numpy.multiply(W2, W2)))
+        KL_divergence        = self.beta * numpy.sum(self.rho * numpy.log(self.rho / rho_cap) +
+                                                    (1 - self.rho) * numpy.log((1 - self.rho) / (1 - rho_cap)))
+        cost                 = sum_of_squares_error + weight_decay + KL_divergence
+        
+        KL_div_grad = self.beta * (-(self.rho / rho_cap) + ((1 - self.rho) / (1 - rho_cap)))
+        
+        del_out = numpy.multiply(diff, numpy.multiply(output_layer, 1 - output_layer))
+        del_hid = numpy.multiply(numpy.dot(numpy.transpose(W2), del_out) + numpy.transpose(numpy.matrix(KL_div_grad)), 
+                                 numpy.multiply(hidden_layer, 1 - hidden_layer))
+        
+        """ Compute the gradient values by averaging partial derivatives
+            Partial derivatives are averaged over all training examples """
+            
+        W1_grad = numpy.dot(del_hid, numpy.transpose(input))
+        W2_grad = numpy.dot(del_out, numpy.transpose(hidden_layer))
+        b1_grad = numpy.sum(del_hid, axis = 1)
+        b2_grad = numpy.sum(del_out, axis = 1)
+            
+        W1_grad = W1_grad / input.shape[1] + self.lamda * W1
+        W2_grad = W2_grad / input.shape[1] + self.lamda * W2
+        b1_grad = b1_grad / input.shape[1]
+        b2_grad = b2_grad / input.shape[1]
+        
+        """ Transform numpy matrices into arrays """
+        
+        W1_grad = numpy.array(W1_grad)
+        W2_grad = numpy.array(W2_grad)
+        b1_grad = numpy.array(b1_grad)
+        b2_grad = numpy.array(b2_grad)
+        
+        """ Unroll the gradient values and return as 'theta' gradient """
+        
+        theta_grad = numpy.concatenate((W1_grad.flatten(), W2_grad.flatten(),
+                                        b1_grad.flatten(), b2_grad.flatten()))
+                                        
+        return [cost, theta_grad]
+
+
+""" The Softmax Regression class """
+
+class SoftmaxRegression(object):
+
+    """ Initialization of Regressor object """
+
+    def __init__(self, input_size, num_classes, lamda):
+    
+        """ Initialize parameters of the Regressor object """
+    
+        self.input_size  = input_size  # input vector size
+        self.num_classes = num_classes # number of classes
+        self.lamda       = lamda       # weight decay parameter
+        
+        """ Randomly initialize the class weights """
+        
+        rand = numpy.random.RandomState(int(time.time()))
+        
+        self.theta = 0.005 * numpy.asarray(rand.normal(size = (num_classes*input_size, 1)))
+        
+    """ Returns the cost and gradient of 'theta' at a particular 'theta' """
+        
+    def softmaxCost(self, theta, input, labels):
+    
+        """ Compute the groundtruth matrix """
+    
+        ground_truth = getGroundTruth(labels)
+        
+        """ Reshape 'theta' for ease of computation """
+        
+        theta = theta.reshape(self.num_classes, self.input_size)
+        
+        """ Compute the class probabilities for each example """
+        
+        theta_x       = numpy.dot(theta, input)
+        hypothesis    = numpy.exp(theta_x)      
+        probabilities = hypothesis / numpy.sum(hypothesis, axis = 0)
+        
+        """ Compute the traditional cost term """
+        
+        cost_examples    = numpy.multiply(ground_truth, numpy.log(probabilities))
+        traditional_cost = -(numpy.sum(cost_examples) / input.shape[1])
+        
+        """ Compute the weight decay term """
+        
+        theta_squared = numpy.multiply(theta, theta)
+        weight_decay  = 0.5 * self.lamda * numpy.sum(theta_squared)
+        
+        """ Add both terms to get the cost """
+        
+        cost = traditional_cost + weight_decay
+        
+        """ Compute and unroll 'theta' gradient """
+        
+        theta_grad = -numpy.dot(ground_truth - probabilities, numpy.transpose(input))
+        theta_grad = theta_grad / input.shape[1] + self.lamda * theta
+        theta_grad = numpy.array(theta_grad)
+        theta_grad = theta_grad.flatten()
+        
+        return [cost, theta_grad]
+
+""" Loads the images from the provided file name """
+
+def loadMNISTImages(file_name):
+
+    """ Open the file """
+
+    image_file = open(file_name, 'rb')
+    
+    """ Read header information from the file """
+    
+    head1 = image_file.read(4)
+    head2 = image_file.read(4)
+    head3 = image_file.read(4)
+    head4 = image_file.read(4)
+    
+    """ Format the header information for useful data """
+    
+    num_examples = struct.unpack('>I', head2)[0]
+    num_rows     = struct.unpack('>I', head3)[0]
+    num_cols     = struct.unpack('>I', head4)[0]
+    
+    """ Initialize dataset as array of zeros """
+    
+    dataset = numpy.zeros((num_rows*num_cols, num_examples))
+    
+    """ Read the actual image data """
+    
+    images_raw  = array.array('B', image_file.read())
+    image_file.close()
+    
+    """ Arrange the data in columns """
+    
+    for i in range(num_examples):
+    
+        limit1 = num_rows * num_cols * i
+        limit2 = num_rows * num_cols * (i + 1)
+        
+        dataset[:, i] = images_raw[limit1 : limit2]
+    
+    """ Normalize and return the dataset """    
+            
+    return dataset / 255
+""" Loads the image labels from the provided file name """
+    
+def loadMNISTLabels(file_name):
+
+    """ Open the file """
+
+    label_file = open(file_name, 'rb')
+    
+    """ Read header information from the file """
+    
+    head1 = label_file.read(4)
+    head2 = label_file.read(4)
+    
+    """ Format the header information for useful data """
+    
+    num_examples = struct.unpack('>I', head2)[0]
+    
+    """ Initialize data labels as array of zeros """
+    
+    labels = numpy.zeros((num_examples, 1), dtype = numpy.int)
+    
+    """ Read the label data """
+    
+    labels_raw = array.array('b', label_file.read())
+    label_file.close()
+    
+    """ Copy and return the label data """
+    
+    labels[:, 0] = labels_raw[:]
+    
+    return labels
+    
+""" Returns the hidden layer activations of the Autoencoder """
+
+def feedForwardAutoencoder(theta, hidden_size, visible_size, input):
+
+    """ Define limits to access useful data """
+
+    limit0 = 0
+    limit1 = hidden_size * visible_size
+    limit2 = 2 * hidden_size * visible_size
+    limit3 = 2 * hidden_size * visible_size + hidden_size
+    
+    """ Access W1 and b1 from 'theta' """
+    
+    W1 = theta[limit0 : limit1].reshape(hidden_size, visible_size)
+    b1 = theta[limit2 : limit3].reshape(hidden_size, 1)
+    
+    """ Compute the hidden layer activations """
+    
+    hidden_layer = 1 / (1 + numpy.exp(-(numpy.dot(W1, input) + b1)))
+    
+    return hidden_layer
+
+""" Returns a row of Stacked Autoencoder parameters """
+
+def stack2Params(stack):
+
+    """ Initialize an empty list of parameters """
+
+    params = []
+    num_layers = len(stack) / 2
+	
+    """ For each layer in the neural network, append the corresponding parameters """
+	
+    for i in range(num_layers):
+    
+        params = numpy.concatenate((params, numpy.array(stack[i, "W"]).flatten()))
+        params = numpy.concatenate((params, numpy.array(stack[i, "b"]).flatten()))
+        
+    return params
+""" Returns a stack of Stacked Autoencoder parameters """
+
+def params2Stack(params, net_config):
+
+    """ Initialize an empty stack """
+
+    stack  = {}
+    limit0 = 0
+    
+    for i in range(len(net_config)-2):
+    
+        """ Calculate limits of layer parameters, using neural network config """
+    
+        limit1 = limit0 + net_config[i] * net_config[i+1]
+        limit2 = limit1 + net_config[i+1]
+        
+        """ Extract layer parameters, and store in the stack """
+        
+        stack[i, "W"] = params[limit0 : limit1].reshape(net_config[i+1], net_config[i])
+        stack[i, "b"] = params[limit1 : limit2].reshape(net_config[i+1], 1)
+        
+        limit0 = limit2
+        
+    return stack
+    
+""" Function for finetuning the Stacked Autoencoder """
+
+def stackedAutoencoderCost(theta, net_config, lamda, data, labels):
+
+    """ Calculate limits for Softmax parameters """
+
+    input_size   = net_config[-2]
+    num_classes  = net_config[-1]
+    
+    limit0 = 0
+    limit1 = num_classes * input_size
+    
+    """ Extract Softmax and layer parameters """
+    
+    softmax_theta = theta[limit0 : limit1].reshape(num_classes, input_size)
+    stack         = params2Stack(theta[limit1 :], net_config)
+    
+    num_layers = len(stack) / 2
+    
+    """ Calculate activations for every layer """
+    
+    activation    = {}
+    activation[0] = data
+    
+    for i in range(num_layers):
+    
+        activation[i+1] = sigmoid(numpy.dot(stack[i, "W"], activation[i]) + stack[i, "b"])
+        
+    """ Compute the groundtruth matrix """
+    
+    ground_truth = getGroundTruth(labels)
+    
+    """ Compute the class probabilities for each example """
+    
+    theta_x       = numpy.dot(softmax_theta, activation[num_layers])
+    hypothesis    = numpy.exp(theta_x)      
+    probabilities = hypothesis / numpy.sum(hypothesis, axis = 0)
+    
+    """ Compute the traditional cost term """
+    
+    cost_examples    = numpy.multiply(ground_truth, numpy.log(probabilities))
+    traditional_cost = -(numpy.sum(cost_examples) / data.shape[1])
+    
+    """ Compute the weight decay term """
+    
+    theta_squared = numpy.multiply(softmax_theta, softmax_theta)
+    weight_decay  = 0.5 * lamda * numpy.sum(theta_squared)
+    
+    """ Add both terms to get the cost """
+    
+    cost = traditional_cost + weight_decay
+    
+    """ Compute Softmax 'theta' gradient """
+    
+    softmax_theta_grad = -numpy.dot(ground_truth - probabilities, numpy.transpose(activation[num_layers]))
+    softmax_theta_grad = softmax_theta_grad / data.shape[1] + lamda * softmax_theta
+    
+    """ Compute intermediate difference values using Backpropagation algorithm """
+    
+    delta = {}    
+    delta[num_layers] = -numpy.multiply(numpy.dot(numpy.transpose(softmax_theta), ground_truth - probabilities),
+                                        numpy.multiply(activation[num_layers], 1 - activation[num_layers]))
+    for i in range(num_layers-1):
+    
+        index        = num_layers - i - 1
+        delta[index] = numpy.multiply(numpy.dot(numpy.transpose(stack[index, "W"]), delta[index+1]),
+                                       numpy.multiply(activation[index], 1 - activation[index]))
+                                       
+    """ Compute the partial derivatives, with respect to the layer parameters """
+                                       
+    stack_grad = {}
+    
+    for i in range(num_layers):
+    
+        index = num_layers - i - 1
+        stack_grad[index, "W"] = numpy.dot(delta[index+1], numpy.transpose(activation[index])) / data.shape[1]
+        stack_grad[index, "b"] = numpy.sum(delta[index+1], axis = 1) / data.shape[1]
+    
+    """ Concatenate the gradient values and return as 'theta' gradient """
+        
+    params_grad = stack2Params(stack_grad)
+    theta_grad  = numpy.concatenate((numpy.array(softmax_theta_grad).flatten(),
+                                     numpy.array(params_grad).flatten()))
+    
+    return [cost, theta_grad]
+    
+
+""" Returns predictions using the trained Stacked Autoencoder model """
+
+def stackedAutoencoderPredict(theta, net_config, data):
+
+    """ Calculate limits for Softmax parameters """
+
+    input_size   = net_config[-2]
+    num_classes  = net_config[-1]
+    
+    limit0 = 0
+    limit1 = num_classes * input_size
+    
+    """ Extract Softmax and layer parameters """
+    
+    softmax_theta = theta[limit0 : limit1].reshape(num_classes, input_size)
+    stack         = params2Stack(theta[limit1 :], net_config)
+    
+    num_layers = len(stack) / 2
+    
+    """ Calculate the activations of the final layer """
+    
+    activation = data
+    
+    for i in range(num_layers):
+    
+        activation = sigmoid(numpy.dot(stack[i, "W"], activation) + stack[i, "b"])
+        
+    """ Compute the class probabilities for each example """
+        
+    theta_x       = numpy.dot(softmax_theta, activation)
+    hypothesis    = numpy.exp(theta_x)      
+    probabilities = hypothesis / numpy.sum(hypothesis, axis = 0)
+    
+    """ Give the predictions based on probability values """
+    
+    predictions       = numpy.zeros((data.shape[1], 1))
+    predictions[:, 0] = numpy.argmax(probabilities, axis = 0)
+    
+    return predictions
+
+
+""" Loads data, trains the Stacked Autoencoder model and predicts classes for test data """
+
+def executeStackedAutoencoder():
+    
+    """ Define the parameters of the first Autoencoder """
+    
+    visible_size   = 784    # size of input vector
+    hidden_size1   = 200    # size of hidden layer vector of first autoencoder
+    hidden_size2   = 200    # size of hidden layer vector of second autoencoder
+    rho            = 0.1    # desired average activation of hidden units
+    lamda          = 0.003  # weight decay parameter
+    beta           = 3      # weight of sparsity penalty term
+    max_iterations = 200    # number of optimization iterations
+    num_classes    = 10     # number of classes
+    
+    """ Load MNIST images for training and testing """
+    
+    train_data    = loadMNISTImages('train-images.idx3-ubyte')
+    train_labels  = loadMNISTLabels('train-labels.idx1-ubyte')
+    
+    """ Initialize the first Autoencoder with the above parameters """
+    
+    encoder1 = SparseAutoencoder(visible_size, hidden_size1, rho, lamda, beta)
+    
+    """ Run the L-BFGS algorithm to get the optimal parameter values """
+    
+    opt_solution   = scipy.optimize.minimize(encoder1.sparseAutoencoderCost, encoder1.theta, 
+                                             args = (train_data,), method = 'L-BFGS-B', 
+                                             jac = True, options = {'maxiter': max_iterations})
+    sae1_opt_theta = opt_solution.x
+    
+    """ Get the features corresponding to first Autoencoder """
+    
+    sae1_features = feedForwardAutoencoder(sae1_opt_theta, hidden_size1, visible_size, train_data)
+    
+    """ Initialize the second Autoencoder with the above parameters """
+    
+    encoder2 = SparseAutoencoder(hidden_size1, hidden_size2, rho, lamda, beta)
+    
+    """ Run the L-BFGS algorithm to get the optimal parameter values """
+    
+    opt_solution   = scipy.optimize.minimize(encoder2.sparseAutoencoderCost, encoder2.theta, 
+                                             args = (sae1_features,), method = 'L-BFGS-B', 
+                                             jac = True, options = {'maxiter': max_iterations})
+    sae2_opt_theta = opt_solution.x
+    
+    """ Get the features corresponding to second Autoencoder """
+    
+    sae2_features = feedForwardAutoencoder(sae2_opt_theta, hidden_size2, hidden_size1, sae1_features)
+    
+    """ Initialize Softmax Regressor with the above parameters """
+    
+    regressor = SoftmaxRegression(hidden_size2, num_classes, lamda)
+    
+    """ Run the L-BFGS algorithm to get the optimal parameter values """
+    
+    opt_solution      = scipy.optimize.minimize(regressor.softmaxCost, regressor.theta, 
+                                                args = (sae2_features, train_labels,), method = 'L-BFGS-B', 
+                                                jac = True, options = {'maxiter': max_iterations})
+    softmax_opt_theta = opt_solution.x
+    
+    """ Create a stack of the Stacked Autoencoder parameters """
+    
+    stack = {}
+    stack[0, "W"] = sae1_opt_theta[encoder1.limit0 : encoder1.limit1].reshape(hidden_size1, visible_size)
+    stack[1, "W"] = sae2_opt_theta[encoder2.limit0 : encoder2.limit1].reshape(hidden_size2, hidden_size1)
+    stack[0, "b"] = sae1_opt_theta[encoder1.limit2 : encoder1.limit3].reshape(hidden_size1, 1)
+    stack[1, "b"] = sae2_opt_theta[encoder2.limit2 : encoder2.limit3].reshape(hidden_size2, 1)
+    
+    """ Create a vector of the Stacked Autoencoder parameters for optimization """
+    
+    stack_params     = stack2Params(stack)
+    stacked_ae_theta = numpy.concatenate((softmax_opt_theta.flatten(), stack_params.flatten()))
+    
+    """ Create a neural network configuration, with number of units in each layer """
+    
+    net_config = [visible_size, hidden_size1, hidden_size2, num_classes]
+    
+    """ Load MNIST test images and labels """
+    
+    test_data   = loadMNISTImages('t10k-images.idx3-ubyte') 
+    test_labels = loadMNISTLabels('t10k-labels.idx1-ubyte')
+    
+    """ Get predictions after greedy training """
+    
+    predictions = stackedAutoencoderPredict(stacked_ae_theta, net_config, test_data)
+    
+    """ Print accuracy of the trained model """
+    
+    correct = test_labels[:, 0] == predictions[:, 0]
+    print """Accuracy after greedy training :""", numpy.mean(correct)
+    
+    """ Finetune the greedily trained model """
+    
+    opt_solution = scipy.optimize.minimize(stackedAutoencoderCost, stacked_ae_theta, 
+                                           args = (net_config, lamda, train_data, train_labels,),
+                                           method = 'L-BFGS-B', jac = True, options = {'maxiter': max_iterations})
+    stacked_ae_opt_theta = opt_solution.x
+    
+    """ Get predictions after finetuning """
+    
+    predictions = stackedAutoencoderPredict(stacked_ae_opt_theta, net_config, test_data)
+    
+    """ Print accuracy of the trained model """
+    
+    correct = test_labels[:, 0] == predictions[:, 0]
+    print """Accuracy after finetuning :""", numpy.mean(correct)
+    
+executeStackedAutoencoder()
+```

From b156b6373605c754b4419ee77d9da5714e31794c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 08:53:12 +0800
Subject: [PATCH 1158/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index a8f3f1c3..be03243d 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -3,3 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 生成式对抗网络(Generative Adversarial Networks)
+生成对抗网络（英语：Generative Adversarial Network，简称GAN）是非监督式学习的一种方法，通过让两个神经网络相互博弈的方式进行学习。该方法由伊恩·古德费洛等人于2014年提出。
+
+

From a2abf715ab52be92cc9284bcb2990f3edd8b51cd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 08:53:55 +0800
Subject: [PATCH 1159/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index be03243d..f19f4e56 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -5,4 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 生成式对抗网络(Generative Adversarial Networks)
 生成对抗网络（英语：Generative Adversarial Network，简称GAN）是非监督式学习的一种方法，通过让两个神经网络相互博弈的方式进行学习。该方法由伊恩·古德费洛等人于2014年提出。
 
+生成对抗网络由一个生成网络与一个判别网络组成。生成网络从潜在空间（latent space）中随机采样作为输入，其输出结果需要尽量模仿训练集中的真实样本。判别网络的输入则为真实样本或生成网络的输出，其目的是将生成网络的输出从真实样本中尽可能分辨出来。而生成网络则要尽可能地欺骗判别网络。两个网络相互对抗、不断调整参数，最终目的是使判别网络无法判断生成网络的输出结果是否真实。
+
+生成对抗网络常用于生成以假乱真的图片。此外，该方法还被用于生成视频、三维物体模型等。
 

From 84ecf28b1dc5544cb3d8514afc3287e8123cd55d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:23:08 +0800
Subject: [PATCH 1160/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index f19f4e56..75bd3df2 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -9,3 +9,23 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 生成对抗网络常用于生成以假乱真的图片。此外，该方法还被用于生成视频、三维物体模型等。
 
+机器学习的模型可大体分为两类，生成模型（Generative Model）和判别模型（Discriminative Model）。判别模型需要输入变量 ，通过某种模型来预测 。生成模型是给定某种隐含信息，来随机产生观测数据。
+
+举个例子:
+* 判别模型：给定一张图，判断这张图里的动物是猫还是狗
+* 生成模型：给一系列猫的图片，生成一张新的猫咪（不在数据集里）
+
+对于判别模型，损失函数是容易定义的，因为输出的目标相对简单。但对于生成模型，损失函数的定义就不是那么容易。我们对于生成结果的期望，往往是一个暧昧不清，难以数学公理化定义的范式。所以不妨把生成模型的回馈部分，交给判别模型处理。这就是Goodfellow他将机器学习中的两大类模型，Generative和Discrimitive给紧密地联合在了一起 。
+
+GAN的基本原理其实非常简单，这里以生成图片为例进行说明。假设我们有两个网络，G（Generator）和D（Discriminator）。正如它的名字所暗示的那样，它们的功能分别是：
+
+G是一个生成图片的网络，它接收一个随机的噪声z，通过这个噪声生成图片，记做G(z)。
+
+D是一个判别网络，判别一张图片是不是“真实的”。它的输入参数是x，x代表一张图片，输出D（x）代表x为真实图片的概率，如果为1，就代表100%是真实的图片，而输出为0，就代表不可能是真实的图片。
+
+在训练过程中，生成网络G的目标就是尽量生成真实的图片去欺骗判别网络D。而D的目标就是尽量把G生成的图片和真实的图片分别开来。这样，G和D构成了一个动态的“博弈过程”。
+
+最后博弈的结果是什么？在最理想的状态下，G可以生成足以“以假乱真”的图片G(z)。对于D来说，它难以判定G生成的图片究竟是不是真实的，因此D(G(z)) = 0.5。
+这样我们的目的就达成了：我们得到了一个生成式的模型G，它可以用来生成图片。 
+Goodfellow从理论上证明了该算法的收敛性 ，以及在模型收敛时，生成数据具有和真实数据相同的分布（保证了模型效果）。
+

From 03c3580a98cb2acd4e694eaa17a3beb9511eff44 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:24:20 +0800
Subject: [PATCH 1161/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index 75bd3df2..953e0dd2 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -3,7 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 生成式对抗网络(Generative Adversarial Networks)
-生成对抗网络（英语：Generative Adversarial Network，简称GAN）是非监督式学习的一种方法，通过让两个神经网络相互博弈的方式进行学习。该方法由伊恩·古德费洛等人于2014年提出。
+生成对抗网络（Generative Adversarial Network，简称GAN）是非监督式学习的一种方法，通过让两个神经网络相互博弈的方式进行学习。该方法由伊恩·古德费洛等人于2014年提出。
 
 生成对抗网络由一个生成网络与一个判别网络组成。生成网络从潜在空间（latent space）中随机采样作为输入，其输出结果需要尽量模仿训练集中的真实样本。判别网络的输入则为真实样本或生成网络的输出，其目的是将生成网络的输出从真实样本中尽可能分辨出来。而生成网络则要尽可能地欺骗判别网络。两个网络相互对抗、不断调整参数，最终目的是使判别网络无法判断生成网络的输出结果是否真实。
 
@@ -29,3 +29,4 @@ D是一个判别网络，判别一张图片是不是“真实的”。它的输
 这样我们的目的就达成了：我们得到了一个生成式的模型G，它可以用来生成图片。 
 Goodfellow从理论上证明了该算法的收敛性 ，以及在模型收敛时，生成数据具有和真实数据相同的分布（保证了模型效果）。
 
+应用领域:目前生成对抗网络最常使用的地方就是图像生成，如超分辨率任务，语义分割等等

From 1d19614ac40994130adfd8b9b1a2d2429e144bee Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Mon, 13 Aug 2018 17:28:32 +0800
Subject: [PATCH 1162/1406] change images

---
 assets/images/400.jpg | Bin 0 -> 224410 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/400.jpg

diff --git a/assets/images/400.jpg b/assets/images/400.jpg
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HcmV?d00001


From 3e689aed69fb83dddf241fe02af12c4496c7f1ac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:30:11 +0800
Subject: [PATCH 1163/1406] Update DL.0.4.md

---
 assets/src/DL/DL.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.4.md b/assets/src/DL/DL.0.4.md
index eab8e525..23c62f29 100644
--- a/assets/src/DL/DL.0.4.md
+++ b/assets/src/DL/DL.0.4.md
@@ -74,7 +74,7 @@ Deep(Bidirectional)RNNs与Bidirectional RNNs相似，只是对于每一步的输
 回声状态网络是一种特殊类型的循环神经网络，其基本思想是：使用大规模随机连接的循环网络取代经典神经网络中的中间层，从而简化网络的训练过程。因此ESNs的关键是中间的储备池。网络中的参数包括：为储备池中节点的连接权值矩阵，为输入层到储备池之间的连接权值矩阵，表明储备池中的神经元之间是连接的，为输出层到储备池之间的反馈连接权值矩阵，表明储备池会有输出层来的反馈，为输入层、储备池、输出层到输出层的连接权值矩阵，表明输出层不仅与储备池连接，还与输入层和自己连接。表示输出层的偏置项。
 
  对于ESNs，关键是储备池的四个参数，如储备池内部连接权谱半径SR(，只有SR <1时，ESNs才能具有回声状态属性)、储备池规模N(即储备池中神经元的个数)、储备池输入单元尺度IS(IS为储备池的输入信号连接到储备池内部神经元之前需要相乘的一个尺度因子)、储备池稀疏程度SD(即为储备池中互相连接的神经元个数占储备池神经元总个数的比例)。对于IS，如果需要处理的任务的非线性越强，那么输入单元尺度越大。该原则的本质就是通过输入单元尺度IS，将输入变换到神经元激活函数相应的范围(神经元激活函数的不同输入范围，其非线性程度不同)。
- <p align="center">
+<p align="center">
 <img width="300" align="center" src="../../images/368.jpg" />
 </p>
 

From c5b788710117d6b0e7e327e8d709e54c1775574a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:30:37 +0800
Subject: [PATCH 1164/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index 953e0dd2..cc61d49c 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -14,6 +14,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 举个例子:
 * 判别模型：给定一张图，判断这张图里的动物是猫还是狗
 * 生成模型：给一系列猫的图片，生成一张新的猫咪（不在数据集里）
+<p align="center">
+<img width="300" align="center" src="../../images/400.jpg" />
+</p>
+
 
 对于判别模型，损失函数是容易定义的，因为输出的目标相对简单。但对于生成模型，损失函数的定义就不是那么容易。我们对于生成结果的期望，往往是一个暧昧不清，难以数学公理化定义的范式。所以不妨把生成模型的回馈部分，交给判别模型处理。这就是Goodfellow他将机器学习中的两大类模型，Generative和Discrimitive给紧密地联合在了一起 。
 

From fac1a7a94331ee987142bca3c46cff225676b7c4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:30:59 +0800
Subject: [PATCH 1165/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index cc61d49c..a861b553 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -15,7 +15,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 判别模型：给定一张图，判断这张图里的动物是猫还是狗
 * 生成模型：给一系列猫的图片，生成一张新的猫咪（不在数据集里）
 <p align="center">
-<img width="300" align="center" src="../../images/400.jpg" />
+<img width="500" align="center" src="../../images/400.jpg" />
 </p>
 
 

From a2a93d270cf5a76bb848cea7d8119cac8fbdb3c6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:35:29 +0800
Subject: [PATCH 1166/1406] Update DL.0.7.md

---
 assets/src/DL/DL.0.7.md | 113 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 113 insertions(+)

diff --git a/assets/src/DL/DL.0.7.md b/assets/src/DL/DL.0.7.md
index a861b553..bcbaf62f 100644
--- a/assets/src/DL/DL.0.7.md
+++ b/assets/src/DL/DL.0.7.md
@@ -34,3 +34,116 @@ D是一个判别网络，判别一张图片是不是“真实的”。它的输
 Goodfellow从理论上证明了该算法的收敛性 ，以及在模型收敛时，生成数据具有和真实数据相同的分布（保证了模型效果）。
 
 应用领域:目前生成对抗网络最常使用的地方就是图像生成，如超分辨率任务，语义分割等等
+
+#### 应用实例:
+```python
+import tensorflow as tf
+from tensorflow.examples.tutorials.mnist import input_data
+import numpy as np
+import matplotlib as mpl
+mpl.use('Agg')
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+import os,sys
+
+sys.path.append('utils')
+from nets import *
+from datas import *
+
+def sample_z(m, n):
+	return np.random.uniform(-1., 1., size=[m, n])
+
+class DCGAN():
+	def __init__(self, generator, discriminator, data):
+		self.generator = generator
+		self.discriminator = discriminator
+		self.data = data
+
+		# data
+		self.z_dim = self.data.z_dim
+		self.size = self.data.size
+		self.channel = self.data.channel
+
+		self.X = tf.placeholder(tf.float32, shape=[None, self.size, self.size, self.channel])
+		self.z = tf.placeholder(tf.float32, shape=[None, self.z_dim])
+
+		# nets
+		self.G_sample = self.generator(self.z)
+
+		self.D_real, _ = self.discriminator(self.X)
+		self.D_fake, _ = self.discriminator(self.G_sample, reuse = True)
+		
+		# loss
+		self.D_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=self.D_real, labels=tf.ones_like(self.D_real))) + tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=self.D_fake, labels=tf.zeros_like(self.D_fake)))
+		self.G_loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=self.D_fake, labels=tf.ones_like(self.D_fake)))
+
+		# solver
+		self.D_solver = tf.train.AdamOptimizer(learning_rate=2e-4).minimize(self.D_loss, var_list=self.discriminator.vars)
+		self.G_solver = tf.train.AdamOptimizer(learning_rate=2e-4).minimize(self.G_loss, var_list=self.generator.vars)
+		
+		self.saver = tf.train.Saver()
+		gpu_options = tf.GPUOptions(allow_growth=True)
+		self.sess = tf.Session(config=tf.ConfigProto(gpu_options=gpu_options))
+
+	def train(self, sample_dir, ckpt_dir='ckpt', training_epoches = 1000000, batch_size = 32):
+		fig_count = 0
+		self.sess.run(tf.global_variables_initializer())
+		
+		for epoch in range(training_epoches):
+			# update D
+			X_b = self.data(batch_size)
+			self.sess.run(
+				self.D_solver,
+				feed_dict={self.X: X_b, self.z: sample_z(batch_size, self.z_dim)}
+				)
+			# update G
+			k = 1
+			for _ in range(k):
+				self.sess.run(
+					self.G_solver,
+					feed_dict={self.z: sample_z(batch_size, self.z_dim)}
+				)
+
+			# save img, model. print loss
+			if epoch % 100 == 0 or epoch < 100:
+				D_loss_curr = self.sess.run(
+						self.D_loss,
+            			feed_dict={self.X: X_b, self.z: sample_z(batch_size, self.z_dim)})
+				G_loss_curr = self.sess.run(
+						self.G_loss,
+						feed_dict={self.z: sample_z(batch_size, self.z_dim)})
+				print('Iter: {}; D loss: {:.4}; G_loss: {:.4}'.format(epoch, D_loss_curr, G_loss_curr))
+
+				if epoch % 1000 == 0:
+					samples = self.sess.run(self.G_sample, feed_dict={self.z: sample_z(16, self.z_dim)})
+
+					fig = self.data.data2fig(samples)
+					plt.savefig('{}/{}.png'.format(sample_dir, str(fig_count).zfill(3)), bbox_inches='tight')
+					fig_count += 1
+					plt.close(fig)
+
+				#if epoch % 2000 == 0:
+					#self.saver.save(self.sess, os.path.join(ckpt_dir, "dcgan.ckpt"))
+
+
+if __name__ == '__main__':
+
+	# constraint GPU
+	os.environ['CUDA_VISIBLE_DEVICES'] = '3'
+
+	# save generated images
+	sample_dir = 'Samples/celebA_dcgan'
+	if not os.path.exists(sample_dir):
+		os.makedirs(sample_dir)
+
+	# param
+	generator = G_conv()
+	discriminator = D_conv()
+
+	data = celebA()
+
+	# run
+	dcgan = DCGAN(generator, discriminator, data)
+	dcgan.train(sample_dir)
+
+```

From f1b27a9111214b320e95541d2af3dea485f97154 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Mon, 13 Aug 2018 17:46:05 +0800
Subject: [PATCH 1167/1406] change page of DRA

---
 README.md                 | 2 +-
 assets/src/DRA/DRA.0.1.md | 5 +++++
 assets/src/DRA/DRA.0.2.md | 5 +++++
 3 files changed, 11 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/DRA/DRA.0.1.md
 create mode 100644 assets/src/DRA/DRA.0.2.md

diff --git a/README.md b/README.md
index 30b53725..9fc31158 100644
--- a/README.md
+++ b/README.md
@@ -140,7 +140,7 @@
      * [分层时间记忆(Hierarchical Temporal Memory)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.5.md) 
      * [堆叠自动编码器(Stacked AutoEncoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
- * [降维算法]()
+ * [降维算法(Dimensionality Reduction Algorithm)]()
      * [主成分分析法（PCA）]()
      * [主成分回归（PCR）]()
      * [偏最小二乘回归（PLSR）]()
diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
new file mode 100644
index 00000000..d7d106d8
--- /dev/null
+++ b/assets/src/DRA/DRA.0.1.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 降维算法(Dimensionality Reduction Algorithm)
diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
new file mode 100644
index 00000000..b8289c25
--- /dev/null
+++ b/assets/src/DRA/DRA.0.2.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 降维算法(Dimensionality Reduction Algorithm

From 5815e4ad83391de18890bf7dc636ab881a87e0cd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:48:59 +0800
Subject: [PATCH 1168/1406] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 9fc31158..bccacaaa 100644
--- a/README.md
+++ b/README.md
@@ -140,8 +140,8 @@
      * [分层时间记忆(Hierarchical Temporal Memory)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.5.md) 
      * [堆叠自动编码器(Stacked AutoEncoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
- * [降维算法(Dimensionality Reduction Algorithm)]()
-     * [主成分分析法（PCA）]()
+ * [降维算法(Dimensionality Reduction Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.1.md)
+     * [主成分分析法（PCA）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
      * [主成分回归（PCR）]()
      * [偏最小二乘回归（PLSR）]()
      * [萨蒙映射]()

From 468e1b39708efdeb69d51f1dbc00930a2af4b800 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 17:59:48 +0800
Subject: [PATCH 1169/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index d7d106d8..8fd64c14 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -3,3 +3,25 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 降维算法(Dimensionality Reduction Algorithm)
+
+机器学习领域中所谓的降维就是指采用某种映射方法，将原高维空间中的数据点映射到低维度的空间中。降维的本质是学习一个映射函数 f : x->y，其中 x 是原始数据点的表达，目前最多使用向量表达形式。 y 是数据点映射后的低维向量表达，通常 y 的维度小于 x 的维度（当然提高维度也是可以的）。f 可能是显式的或隐式的、线性的或非线性的。
+
+目前大部分降维算法处理向量表达的数据，也有一些降维算法处理高阶张量表达的数据。之所以使用降维后的数据表示是因为在原始的高维空间中，包含有冗余信息以及噪音信息，在实际应用例如图像识别中造成了误差，降低了准确率；而通过降维, 我们希望减少冗余信息所造成的误差, 提高识别（或其他应用）的精度。又或者希望通过降维算法来寻找数据内部的本质结构特征。降维算法可以细分为特征选择和特征提取两大方法。
+
+降维目前主要有四种常用的降维算法:主成分分析(PCA),线性判别分析(LDA),局部线性嵌入(LLE),拉普拉斯特征映射(LE)。
+
+* 主成分分析(PCA)
+
+主成分分析(Principal Component Analysis,简称PCA)是最常用的线性降维方法，它的目标是通过某种线性投影，将高维的数据映射到低维的空间中表示，并期望在所投影的维度上数据的方差最大，以此使用较少的数据维度，同时保留住较多的原数据点的特性。
+
+通俗的理解，如果把所有的点都映射到一起，那么几乎所有的信息（如点和点之间的距离关系）都丢失了，而如果映射后方差尽可能的大，那么数据点则会分散开来，以此来保留更多的信息。可以证明，PCA 是丢失原始数据信息最少的一种线性降维方式。（实际上就是最接近原始数据，但是 PCA 并不试图去探索数据内在结构）。
+
+* 线性判别分析(LDA)
+线性判别分析(Linear Discriminant Analysis,简称LDA)是一种有监督的（supervised）线性降维算法。与 PCA 保持数据信息不同，LDA 是为了使得降维后的数据点尽可能地容易被区分！
+
+* 局部线性嵌入(LLE)
+局部线性嵌入(Locally linear embedding,简称LLE）是一种非线性降维算法，它能够使降维后的数据较好地保持原有流形结构。LLE 可以说是流形学习方法最经典的工作之一。很多后续的流形学习、降维方法都与 LLE 有密切联系。
+
+* 拉普拉斯特征映射(LE)
+拉普拉斯特征映射（Laplacian Eigenmaps,简称LE）看问题的角度和 LLE 有些相似，也是用局部的角度去构建数据之间的关系。它的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。Laplacian Eigenmaps 可以反映出数据内在的流形结构。
+

From 758ab0451a17965238da6a77378bda321317e498 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 18:04:56 +0800
Subject: [PATCH 1170/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 8fd64c14..b9a18de3 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 目前大部分降维算法处理向量表达的数据，也有一些降维算法处理高阶张量表达的数据。之所以使用降维后的数据表示是因为在原始的高维空间中，包含有冗余信息以及噪音信息，在实际应用例如图像识别中造成了误差，降低了准确率；而通过降维, 我们希望减少冗余信息所造成的误差, 提高识别（或其他应用）的精度。又或者希望通过降维算法来寻找数据内部的本质结构特征。降维算法可以细分为特征选择和特征提取两大方法。
 
-降维目前主要有四种常用的降维算法:主成分分析(PCA),线性判别分析(LDA),局部线性嵌入(LLE),拉普拉斯特征映射(LE)。
+降维目前主要常用的降维算法是:主成分分析(PCA),线性判别分析(LDA),局部线性嵌入(LLE),拉普拉斯特征映射(LE)。
 
 * 主成分分析(PCA)
 
@@ -25,3 +25,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 拉普拉斯特征映射(LE)
 拉普拉斯特征映射（Laplacian Eigenmaps,简称LE）看问题的角度和 LLE 有些相似，也是用局部的角度去构建数据之间的关系。它的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。Laplacian Eigenmaps 可以反映出数据内在的流形结构。
 
+降维算法(Dimensionality Reduction Algorithm)的应用算法有：
+* 主成分分析法（PCA）
+* 主成分回归（PCR）
+* 偏最小二乘回归（PLSR）
+* 萨蒙映射]()
+* 多维尺度分析法（MDS)
+* 投影寻踪法(PP)
+* 线性判别分析法（LDA）
+* 混合判别分析法（MDA）
+* 二次判别分析法（QDA）
+* 灵活判别分析法（Flexible Discriminant Analysis，简称FDA)

From 81325c213314618ec08b5f9680cd14e9a9d4cefb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 13 Aug 2018 18:11:25 +0800
Subject: [PATCH 1171/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 23 +++++++++++++----------
 1 file changed, 13 insertions(+), 10 deletions(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index b9a18de3..64e9339a 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -17,22 +17,25 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 通俗的理解，如果把所有的点都映射到一起，那么几乎所有的信息（如点和点之间的距离关系）都丢失了，而如果映射后方差尽可能的大，那么数据点则会分散开来，以此来保留更多的信息。可以证明，PCA 是丢失原始数据信息最少的一种线性降维方式。（实际上就是最接近原始数据，但是 PCA 并不试图去探索数据内在结构）。
 
 * 线性判别分析(LDA)
+
 线性判别分析(Linear Discriminant Analysis,简称LDA)是一种有监督的（supervised）线性降维算法。与 PCA 保持数据信息不同，LDA 是为了使得降维后的数据点尽可能地容易被区分！
 
 * 局部线性嵌入(LLE)
+
 局部线性嵌入(Locally linear embedding,简称LLE）是一种非线性降维算法，它能够使降维后的数据较好地保持原有流形结构。LLE 可以说是流形学习方法最经典的工作之一。很多后续的流形学习、降维方法都与 LLE 有密切联系。
 
 * 拉普拉斯特征映射(LE)
+
 拉普拉斯特征映射（Laplacian Eigenmaps,简称LE）看问题的角度和 LLE 有些相似，也是用局部的角度去构建数据之间的关系。它的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。Laplacian Eigenmaps 可以反映出数据内在的流形结构。
 
 降维算法(Dimensionality Reduction Algorithm)的应用算法有：
-* 主成分分析法（PCA）
-* 主成分回归（PCR）
-* 偏最小二乘回归（PLSR）
-* 萨蒙映射]()
-* 多维尺度分析法（MDS)
-* 投影寻踪法(PP)
-* 线性判别分析法（LDA）
-* 混合判别分析法（MDA）
-* 二次判别分析法（QDA）
-* 灵活判别分析法（Flexible Discriminant Analysis，简称FDA)
+* 主成分分析法（Principal Component Analysis）
+* 主成分回归（Principle Component Regression）
+* 偏最小二乘回归（Partial Least Squares Regression）
+* 萨蒙映射(Sammon Mapping)
+* 多维尺度分析法（Multidimensional Scaling)
+* 投影寻踪法(Projection Pursuit)
+* 线性判别分析法（Linear Discriminant Analysis）
+* 二次判别分析法（discriminant_analysis.QuadraticDiscriminantAnalysis）
+* 局部线性嵌入(LLE)
+* 拉普拉斯特征映射(LE)

From 501ca90111bd9131126ced991372f59f8747b68a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 19 Aug 2018 21:20:50 +0800
Subject: [PATCH 1172/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index b8289c25..9e4bc1b3 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 降维算法(Dimensionality Reduction Algorithm
+#### 降维算法(Dimensionality Reduction Algorithm）

From 2e29e781121a8a79260c16d16a70bee7cdda5b2d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 19 Aug 2018 21:21:06 +0800
Subject: [PATCH 1173/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 9e4bc1b3..a363c0b3 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 降维算法(Dimensionality Reduction Algorithm）
+#### 主成分分析(Principal Component Analysis)

From b42d2ce11ac05603e2ab50af0782620cfa18ed37 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 21 Aug 2018 09:03:31 +0800
Subject: [PATCH 1174/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 64e9339a..036d8cbb 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -10,13 +10,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 降维目前主要常用的降维算法是:主成分分析(PCA),线性判别分析(LDA),局部线性嵌入(LLE),拉普拉斯特征映射(LE)。
 
-* 主成分分析(PCA)
+* 主成分分析(Principal Component Analysis)
 
 主成分分析(Principal Component Analysis,简称PCA)是最常用的线性降维方法，它的目标是通过某种线性投影，将高维的数据映射到低维的空间中表示，并期望在所投影的维度上数据的方差最大，以此使用较少的数据维度，同时保留住较多的原数据点的特性。
 
 通俗的理解，如果把所有的点都映射到一起，那么几乎所有的信息（如点和点之间的距离关系）都丢失了，而如果映射后方差尽可能的大，那么数据点则会分散开来，以此来保留更多的信息。可以证明，PCA 是丢失原始数据信息最少的一种线性降维方式。（实际上就是最接近原始数据，但是 PCA 并不试图去探索数据内在结构）。
 
-* 线性判别分析(LDA)
+* 线性判别分析(Linear Discriminant Analysis)
 
 线性判别分析(Linear Discriminant Analysis,简称LDA)是一种有监督的（supervised）线性降维算法。与 PCA 保持数据信息不同，LDA 是为了使得降维后的数据点尽可能地容易被区分！
 

From 82a335bd53fd3e5486522f3e1cb5eb2744897240 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 21 Aug 2018 09:04:26 +0800
Subject: [PATCH 1175/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 036d8cbb..194ecc78 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -20,11 +20,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性判别分析(Linear Discriminant Analysis,简称LDA)是一种有监督的（supervised）线性降维算法。与 PCA 保持数据信息不同，LDA 是为了使得降维后的数据点尽可能地容易被区分！
 
-* 局部线性嵌入(LLE)
+* 局部线性嵌入(Locally linear embedding)
 
 局部线性嵌入(Locally linear embedding,简称LLE）是一种非线性降维算法，它能够使降维后的数据较好地保持原有流形结构。LLE 可以说是流形学习方法最经典的工作之一。很多后续的流形学习、降维方法都与 LLE 有密切联系。
 
-* 拉普拉斯特征映射(LE)
+* 拉普拉斯特征映射(Laplacian Eigenmaps)
 
 拉普拉斯特征映射（Laplacian Eigenmaps,简称LE）看问题的角度和 LLE 有些相似，也是用局部的角度去构建数据之间的关系。它的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。Laplacian Eigenmaps 可以反映出数据内在的流形结构。
 

From 902c3098ad121793f60359558e1aa05a39f8b280 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 24 Aug 2018 08:53:55 +0800
Subject: [PATCH 1176/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index a363c0b3..1fb4b09c 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -3,3 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分分析(Principal Component Analysis)
+
+在多元统计分析中，主成分分析（Principal components analysis，PCA）是一种分析、简化数据集的技术。主成分分析经常用于减少数据集的维数，同时保持数据集中的对方差贡献最大的特征。这是通过保留低阶主成分，忽略高阶主成分做到的。这样低阶成分往往能够保留住数据的最重要方面。但是，这也不是一定的，要视具体应用而定。由于主成分分析依赖所给数据，所以数据的准确性对分析结果影响很大。
+
+主成分分析由卡尔·皮尔逊于1901年发明，用于分析数据及建立数理模型。其方法主要是通过对协方差矩阵进行特征分解，以得出数据的主成分（即特征向量）与它们的权值（即特征值）。PCA是最简单的以特征量分析多元统计分布的方法。其结果可以理解为对原数据中的方差做出解释：哪一个方向上的数据值对方差的影响最大？换而言之，PCA提供了一种降低数据维度的有效办法；如果分析者在原数据中除掉最小的特征值所对应的成分，那么所得的低维度数据必定是最优化的（也即，这样降低维度必定是失去讯息最少的方法）。主成分分析在分析复杂数据时尤为有用，比如人脸识别。

From 064e197ab6bffa4637c9472e11fb5f5178d40b6c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 26 Aug 2018 16:53:22 +0800
Subject: [PATCH 1177/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 1fb4b09c..3ad17069 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分分析(Principal Component Analysis)
-
 在多元统计分析中，主成分分析（Principal components analysis，PCA）是一种分析、简化数据集的技术。主成分分析经常用于减少数据集的维数，同时保持数据集中的对方差贡献最大的特征。这是通过保留低阶主成分，忽略高阶主成分做到的。这样低阶成分往往能够保留住数据的最重要方面。但是，这也不是一定的，要视具体应用而定。由于主成分分析依赖所给数据，所以数据的准确性对分析结果影响很大。
 
 主成分分析由卡尔·皮尔逊于1901年发明，用于分析数据及建立数理模型。其方法主要是通过对协方差矩阵进行特征分解，以得出数据的主成分（即特征向量）与它们的权值（即特征值）。PCA是最简单的以特征量分析多元统计分布的方法。其结果可以理解为对原数据中的方差做出解释：哪一个方向上的数据值对方差的影响最大？换而言之，PCA提供了一种降低数据维度的有效办法；如果分析者在原数据中除掉最小的特征值所对应的成分，那么所得的低维度数据必定是最优化的（也即，这样降低维度必定是失去讯息最少的方法）。主成分分析在分析复杂数据时尤为有用，比如人脸识别。

From b812afa9d959c8269942ee7f3a0d227f1d834229 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 29 Aug 2018 08:50:41 +0800
Subject: [PATCH 1178/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 3ad17069..2bf8bd21 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -6,3 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 在多元统计分析中，主成分分析（Principal components analysis，PCA）是一种分析、简化数据集的技术。主成分分析经常用于减少数据集的维数，同时保持数据集中的对方差贡献最大的特征。这是通过保留低阶主成分，忽略高阶主成分做到的。这样低阶成分往往能够保留住数据的最重要方面。但是，这也不是一定的，要视具体应用而定。由于主成分分析依赖所给数据，所以数据的准确性对分析结果影响很大。
 
 主成分分析由卡尔·皮尔逊于1901年发明，用于分析数据及建立数理模型。其方法主要是通过对协方差矩阵进行特征分解，以得出数据的主成分（即特征向量）与它们的权值（即特征值）。PCA是最简单的以特征量分析多元统计分布的方法。其结果可以理解为对原数据中的方差做出解释：哪一个方向上的数据值对方差的影响最大？换而言之，PCA提供了一种降低数据维度的有效办法；如果分析者在原数据中除掉最小的特征值所对应的成分，那么所得的低维度数据必定是最优化的（也即，这样降低维度必定是失去讯息最少的方法）。主成分分析在分析复杂数据时尤为有用，比如人脸识别。
+
+PCA是最简单的以特征量分析多元统计分布的方法。通常情况下，这种运算可以被看作是揭露数据的内部结构，从而更好的解释数据的变量的方法。如果一个多元数据集能够在一个高维数据空间坐标系中被显现出来，那么PCA就能够提供一幅比较低维度的图像，这幅图像即为在讯息最多的点上原对象的一个‘投影’。这样就可以利用少量的主成分使得数据的维度降低了。
+
+PCA跟因子分析密切相关，并且已经有很多混合这两种分析的统计包。而真实要素分析则是假定底层结构，求得微小差异矩阵的特征向量。

From e75b05feb988d2224d42a080f91f5ac0039e289d Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Wed, 29 Aug 2018 08:53:36 +0800
Subject: [PATCH 1179/1406] change page of Dl

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/401.jpg

diff --git a/assets/images/401.jpg b/assets/images/401.jpg
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From 2f25c1d58abc14c488fc0953b37b301fecc5445c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 29 Aug 2018 08:54:31 +0800
Subject: [PATCH 1180/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 2bf8bd21..2cd0e3bb 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -10,3 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 PCA是最简单的以特征量分析多元统计分布的方法。通常情况下，这种运算可以被看作是揭露数据的内部结构，从而更好的解释数据的变量的方法。如果一个多元数据集能够在一个高维数据空间坐标系中被显现出来，那么PCA就能够提供一幅比较低维度的图像，这幅图像即为在讯息最多的点上原对象的一个‘投影’。这样就可以利用少量的主成分使得数据的维度降低了。
 
 PCA跟因子分析密切相关，并且已经有很多混合这两种分析的统计包。而真实要素分析则是假定底层结构，求得微小差异矩阵的特征向量。
+
+<p align="center">
+<img width="600" align="center" src="../../images/401.jpg" />
+</p>

From d35ca2bf84460d15bcf936fc759ee6a85c620c99 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 29 Aug 2018 08:54:44 +0800
Subject: [PATCH 1181/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 2cd0e3bb..bb87cd59 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -12,5 +12,5 @@ PCA是最简单的以特征量分析多元统计分布的方法。通常情况
 PCA跟因子分析密切相关，并且已经有很多混合这两种分析的统计包。而真实要素分析则是假定底层结构，求得微小差异矩阵的特征向量。
 
 <p align="center">
-<img width="600" align="center" src="../../images/401.jpg" />
+<img width="300" align="center" src="../../images/401.jpg" />
 </p>

From 6edbfea1070ed2ccd20f2368c08fb8f0983877f1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 29 Aug 2018 08:55:02 +0800
Subject: [PATCH 1182/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index bb87cd59..3aa78a3c 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -14,3 +14,4 @@ PCA跟因子分析密切相关，并且已经有很多混合这两种分析的
 <p align="center">
 <img width="300" align="center" src="../../images/401.jpg" />
 </p>
+主成分分析实例：一个平均值为(1, 3)、标准差在(0.878, 0.478)方向上为3、在其正交方向为1的高斯分布。这里以黑色显示的两个向量是这个分布的协方差矩阵的特征向量，其长度按对应的特征值之平方根为比例，并且移动到以原分布的平均值为原点。

From 8a9bbbc02ea50a360b60bc5cf7777cf33f519463 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 1 Sep 2018 10:04:23 +0800
Subject: [PATCH 1183/1406] Update README.md

---
 README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/README.md b/README.md
index bccacaaa..9aa3e6bf 100644
--- a/README.md
+++ b/README.md
@@ -11,23 +11,28 @@
 <p align="center">
 <img width="100%" align="center" src="assets/images/global.png" />
 </p>
+
 * 机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。
 * 机器学习：多领域交叉学科，涉及概率论统计学，逼近论，凸分析，算法复杂度理论等多门学科。
 * 机器学习的应用：语音识别，自动驾驶，语言翻译，计算机视觉，推荐系统，无人机，识别垃圾邮件，人脸识别，电商推荐系统。
 * 机器学习的基本概念：训练集，测试集，特征值，监督学习，非监督学习，分类，回归 
 
 目前国内在AI感知层面应用已经百花齐放，主要是无人驾驶、智能音箱、嵌入式。但在认知层面还是比较缺乏，所以新入行的AI应用团队可以放在认知层。如开头所述，认知层最重要的是算法，因此需要阅读Nature上最领先的算法公司DeepMind的几篇大作，如下：
+
 * 2016.01.Mastering the game of Go with deep neural networks and tree search
 * 2016.10.Hybrid computing using a neural network with dynamic external memory
 * 2017.10.Mastering the game of Go without human knowledge
 
 #### 机器学习步骤框架
+
 * 把数据拆分为训练集合测试集
 * 用训练集合训练集的特征向量来训练算法
 * 用学习来的算法运用在测试集上累评估算法(可能要设计到调整参数(parameter tuning) 用来验证集(validation set))
 
 #### 机器学习
+
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
+
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)

From fb84b86da5588542960c474777317115145a6629 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 1 Sep 2018 10:04:53 +0800
Subject: [PATCH 1184/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index 9aa3e6bf..a1e5795d 100644
--- a/README.md
+++ b/README.md
@@ -32,7 +32,6 @@
 #### 机器学习
 
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
-
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
  * [机器学习环境的搭建](https://github.com/AI-algorithms/Algorithms-Tutorial/blob/master/src/Machine%20Learning/ML.01.md)

From 9d92679b9415b8f9ca9eb6ceafb00569b5e0de2a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Sep 2018 08:44:07 +0800
Subject: [PATCH 1185/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 3aa78a3c..ab1960a0 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分分析(Principal Component Analysis)
+
 在多元统计分析中，主成分分析（Principal components analysis，PCA）是一种分析、简化数据集的技术。主成分分析经常用于减少数据集的维数，同时保持数据集中的对方差贡献最大的特征。这是通过保留低阶主成分，忽略高阶主成分做到的。这样低阶成分往往能够保留住数据的最重要方面。但是，这也不是一定的，要视具体应用而定。由于主成分分析依赖所给数据，所以数据的准确性对分析结果影响很大。
 
 主成分分析由卡尔·皮尔逊于1901年发明，用于分析数据及建立数理模型。其方法主要是通过对协方差矩阵进行特征分解，以得出数据的主成分（即特征向量）与它们的权值（即特征值）。PCA是最简单的以特征量分析多元统计分布的方法。其结果可以理解为对原数据中的方差做出解释：哪一个方向上的数据值对方差的影响最大？换而言之，PCA提供了一种降低数据维度的有效办法；如果分析者在原数据中除掉最小的特征值所对应的成分，那么所得的低维度数据必定是最优化的（也即，这样降低维度必定是失去讯息最少的方法）。主成分分析在分析复杂数据时尤为有用，比如人脸识别。

From 89a79ebf13fe497ce1eb9489c6a13408225c8f88 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Sep 2018 08:45:44 +0800
Subject: [PATCH 1186/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 87 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 87 insertions(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index ab1960a0..fc919b0e 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -16,3 +16,90 @@ PCA跟因子分析密切相关，并且已经有很多混合这两种分析的
 <img width="300" align="center" src="../../images/401.jpg" />
 </p>
 主成分分析实例：一个平均值为(1, 3)、标准差在(0.878, 0.478)方向上为3、在其正交方向为1的高斯分布。这里以黑色显示的两个向量是这个分布的协方差矩阵的特征向量，其长度按对应的特征值之平方根为比例，并且移动到以原分布的平均值为原点。
+
+#### 应用示例
+```python
+
+# coding:utf-8
+"""
+from __future__ import division
+import numpy as np
+import pandas as pd
+
+# 根据保留多少维特征进行降维
+class PCAcomponent(object):
+    def __init__(self, X, N=3):
+        self.X = X
+        self.N = N
+        self.variance_ratio = []
+        self.low_dataMat = []
+
+    def _fit(self):
+        X_mean = np.mean(self.X, axis=0)
+        dataMat = self.X - X_mean
+        # 另一种计算协方差矩阵的方法：dataMat.T * dataMat / dataMat.shape[0]
+        # 若rowvar非0，一列代表一个样本；为0，一行代表一个样本
+        covMat = np.cov(dataMat, rowvar=False)
+        # 求特征值和特征向量，特征向量是按列放的，即一列代表一个特征向量
+        eigVal, eigVect = np.linalg.eig(np.mat(covMat))
+        eigValInd = np.argsort(eigVal)
+        eigValInd = eigValInd[-1:-(self.N + 1):-1]  # 取前N个较大的特征值
+        small_eigVect = eigVect[:, eigValInd]  # *N维投影矩阵
+        self.low_dataMat = dataMat * small_eigVect  # 投影变换后的新矩阵
+        # reconMat = (low_dataMat * small_eigVect.I) + X_mean  # 重构数据
+        # 输出每个维度所占的方差百分比
+        [self.variance_ratio.append(eigVal[i] / sum(eigVal)) for i in eigValInd]
+        return self.low_dataMat
+
+    def fit(self):
+        self._fit()
+        return self
+
+
+# 根据保留多大方差百分比进行降维
+class PCApercent(object):
+    def __init__(self, X, percentage=0.95):
+        self.X = X
+        self.percentage = percentage
+        self.variance_ratio = []
+        self.low_dataMat = []
+
+    # 通过方差百分比选取前n个主成份
+    def percent2n(self, eigVal):
+        sortVal = np.sort(eigVal)[-1::-1]
+        percentSum, componentNum = 0, 0
+        for i in sortVal:
+            percentSum += i
+            componentNum += 1
+            if percentSum >= sum(sortVal) * self.percentage:
+                break
+        return componentNum
+
+    def _fit(self):
+        X_mean = np.mean(self.X, axis=0)
+        dataMat = self.X - X_mean
+        covMat = np.cov(dataMat, rowvar=False)
+        eigVal, eigVect = np.linalg.eig(np.mat(covMat))
+        n = self.percent2n(eigVal)
+        eigValInd = np.argsort(eigVal)
+        eigValInd = eigValInd[-1:-(n + 1):-1]
+        n_eigVect = eigVect[:, eigValInd]
+        self.low_dataMat = dataMat * n_eigVect
+        [self.variance_ratio.append(eigVal[i] / sum(eigVal)) for i in eigValInd]
+        return self.low_dataMat
+
+    def fit(self):
+        self._fit()
+        return self
+
+df = pd.read_csv(r'iris.txt', header=None)
+data, label = df[range(len(df.columns) - 1)], df[[len(df.columns) - 1]]
+data = np.mat(data)
+print("Original dataset = {}*{}".format(data.shape[0], data.shape[1]))
+pca = PCAcomponent(data, 3)
+# pca = PCApercent(data, 0.98)
+pca.fit()
+print(pca.low_dataMat)
+print(pca.variance_ratio)
+
+```

From 8ea4e74d1aabef2c0e633ec33a6f3e2f04ae3d58 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Sep 2018 08:46:06 +0800
Subject: [PATCH 1187/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index fc919b0e..343f99be 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -19,7 +19,6 @@ PCA跟因子分析密切相关，并且已经有很多混合这两种分析的
 
 #### 应用示例
 ```python
-
 # coding:utf-8
 """
 from __future__ import division

From cb506f4506114edba3bd11cee4018c78085b60e0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 6 Sep 2018 08:54:46 +0800
Subject: [PATCH 1188/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index a1e5795d..6f0dc8aa 100644
--- a/README.md
+++ b/README.md
@@ -146,7 +146,7 @@
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
  * [降维算法(Dimensionality Reduction Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.1.md)
      * [主成分分析法（PCA）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
-     * [主成分回归（PCR）]()
+     * [主成分回归（PCR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.３.md)
      * [偏最小二乘回归（PLSR）]()
      * [萨蒙映射]()
      * [多维尺度分析法（MDS]()

From 1873793c12367cbf71343ddb8464f78136bf128b Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 6 Sep 2018 08:57:34 +0800
Subject: [PATCH 1189/1406] change page of DRA

---
 assets/src/DRA/DRA.0.3.md | 5 +++++
 assets/src/DRA/DRA.0.4.md | 5 +++++
 2 files changed, 10 insertions(+)
 create mode 100644 assets/src/DRA/DRA.0.3.md
 create mode 100644 assets/src/DRA/DRA.0.4.md

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
new file mode 100644
index 00000000..a363c0b3
--- /dev/null
+++ b/assets/src/DRA/DRA.0.3.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 主成分分析(Principal Component Analysis)
diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
new file mode 100644
index 00000000..a363c0b3
--- /dev/null
+++ b/assets/src/DRA/DRA.0.4.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 主成分分析(Principal Component Analysis)

From 5f6953d9be2387f0c783fad1bcc7193a2e951258 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 6 Sep 2018 08:58:36 +0800
Subject: [PATCH 1190/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 6f0dc8aa..48a463f7 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@
  * [降维算法(Dimensionality Reduction Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.1.md)
      * [主成分分析法（PCA）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
      * [主成分回归（PCR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.３.md)
-     * [偏最小二乘回归（PLSR）]()
+     * [偏最小二乘回归（PLSR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.４.md)
      * [萨蒙映射]()
      * [多维尺度分析法（MDS]()
      * [投影寻踪法（PP）]()

From 4b51422f2d09004c1584eb76a1c5e871dea80b9a Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Thu, 6 Sep 2018 09:00:14 +0800
Subject: [PATCH 1191/1406] change page of readme

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 48a463f7..de71e772 100644
--- a/README.md
+++ b/README.md
@@ -146,8 +146,8 @@
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
  * [降维算法(Dimensionality Reduction Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.1.md)
      * [主成分分析法（PCA）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
-     * [主成分回归（PCR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.３.md)
-     * [偏最小二乘回归（PLSR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.４.md)
+     * [主成分回归（PCR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.3.md)
+     * [偏最小二乘回归（PLSR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.4.md)
      * [萨蒙映射]()
      * [多维尺度分析法（MDS]()
      * [投影寻踪法（PP）]()

From 1693c07f380ae92e8eb9e1d7df497e28fcc75894 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 6 Sep 2018 09:01:24 +0800
Subject: [PATCH 1192/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index a363c0b3..170df0fa 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 主成分分析(Principal Component Analysis)
+#### 主成分回归（PCR）

From c514f25cc92baa9b761f815c24bee19e5d878ff3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 6 Sep 2018 09:01:33 +0800
Subject: [PATCH 1193/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index a363c0b3..27c46939 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 主成分分析(Principal Component Analysis)
+#### 偏最小二乘回归（PLSR）

From 40f444210998af69f2d09c7a7517cf69b53237fa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 7 Sep 2018 08:49:50 +0800
Subject: [PATCH 1194/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 170df0fa..dca9a2b8 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分回归（PCR）
+主成分回归分析 Principal Component Regression（PCR）是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。

From 93ca99323c64dbf410615b9247525bc06ba754f5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 7 Sep 2018 08:58:10 +0800
Subject: [PATCH 1195/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index dca9a2b8..80461da7 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分回归（PCR）
-主成分回归分析 Principal Component Regression（PCR）是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。
+在建立多元线性回归方程时,由于自变量间存在多重共线性,常常会发现某些自变量的系数极不稳定,当增减变量时,其值会出现很大变化,甚至出现与实际情况相悖的符号,以致难以对所建回归方程给予符合实际的解释。主成分回归分析 Principal Component Regression（PCR）是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。

From 15ae7009e64a0c1f918cf727e082f9c46973b3ec Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 10 Sep 2018 09:04:48 +0800
Subject: [PATCH 1196/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 80461da7..7a49937f 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 主成分回归（PCR）
-在建立多元线性回归方程时,由于自变量间存在多重共线性,常常会发现某些自变量的系数极不稳定,当增减变量时,其值会出现很大变化,甚至出现与实际情况相悖的符号,以致难以对所建回归方程给予符合实际的解释。主成分回归分析 Principal Component Regression（PCR）是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。
+在建立多元线性回归方程时,由于自变量间存在多重共线性,常常会发现某些自变量的系数极不稳定,当增减变量时,其值会出现很大变化,甚至出现与实际情况相悖的符号,以致难以对所建回归方程给予符合实际的解释。主成分回归分析(Principal Component Regression)是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。

From cdbf89e7faa48dc196578a99e69b65bbd3975320 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 10 Sep 2018 09:10:18 +0800
Subject: [PATCH 1197/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 7a49937f..0a3f6bab 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -2,5 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 主成分回归（PCR）
+#### 主成分回归分析(PCR)
 在建立多元线性回归方程时,由于自变量间存在多重共线性,常常会发现某些自变量的系数极不稳定,当增减变量时,其值会出现很大变化,甚至出现与实际情况相悖的符号,以致难以对所建回归方程给予符合实际的解释。主成分回归分析(Principal Component Regression)是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。

From 96b0d4cfa6bc94c0f80abaaf76bf54a1648885d7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 08:49:51 +0800
Subject: [PATCH 1198/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 9 +--------
 1 file changed, 1 insertion(+), 8 deletions(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 194ecc78..a1f39fce 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -31,11 +31,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 降维算法(Dimensionality Reduction Algorithm)的应用算法有：
 * 主成分分析法（Principal Component Analysis）
 * 主成分回归（Principle Component Regression）
-* 偏最小二乘回归（Partial Least Squares Regression）
-* 萨蒙映射(Sammon Mapping)
-* 多维尺度分析法（Multidimensional Scaling)
-* 投影寻踪法(Projection Pursuit)
-* 线性判别分析法（Linear Discriminant Analysis）
-* 二次判别分析法（discriminant_analysis.QuadraticDiscriminantAnalysis）
-* 局部线性嵌入(LLE)
-* 拉普拉斯特征映射(LE)
+

From 7b224905e7337c4967cfa312ee5f6ef465355cf8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 08:51:29 +0800
Subject: [PATCH 1199/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index a1f39fce..0e4a7130 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -30,5 +30,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 降维算法(Dimensionality Reduction Algorithm)的应用算法有：
 * 主成分分析法（Principal Component Analysis）
-* 主成分回归（Principle Component Regression）
+* 多维缩放(multidimensional scaling)
 

From 5bd20f762886c88b67e20d740c43b392fa03c9c4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:03:21 +0800
Subject: [PATCH 1200/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 0e4a7130..67690315 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -20,9 +20,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性判别分析(Linear Discriminant Analysis,简称LDA)是一种有监督的（supervised）线性降维算法。与 PCA 保持数据信息不同，LDA 是为了使得降维后的数据点尽可能地容易被区分！
 
-* 局部线性嵌入(Locally linear embedding)
+* 局部线性嵌入(Locally Linear embedding)
 
-局部线性嵌入(Locally linear embedding,简称LLE）是一种非线性降维算法，它能够使降维后的数据较好地保持原有流形结构。LLE 可以说是流形学习方法最经典的工作之一。很多后续的流形学习、降维方法都与 LLE 有密切联系。
+局部线性嵌入(Locally Linear embedding,简称LLE）是一种非线性降维算法，它能够使降维后的数据较好地保持原有流形结构。LLE 可以说是流形学习方法最经典的工作之一。很多后续的流形学习、降维方法都与 LLE 有密切联系。
 
 * 拉普拉斯特征映射(Laplacian Eigenmaps)
 
@@ -31,4 +31,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 降维算法(Dimensionality Reduction Algorithm)的应用算法有：
 * 主成分分析法（Principal Component Analysis）
 * 多维缩放(multidimensional scaling)
+* 线性判别分析(Linear Discriminant Analysis)
+* 等度量映射(Isomap)
+* 局部线性嵌入(LLE)
+* t-SNE
+* Deep Autoencoder Networks
 

From 38c4416728b10c943b8b3bca1f78051206c22abd Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Tue, 11 Sep 2018 09:18:16 +0800
Subject: [PATCH 1201/1406] change page of DRA

---
 assets/images/402.jpg     | Bin 0 -> 226077 bytes
 assets/src/DRA/DRA.0.1.md |  19 +++++++++----------
 2 files changed, 9 insertions(+), 10 deletions(-)
 create mode 100644 assets/images/402.jpg

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literal 0
HcmV?d00001

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 194ecc78..27faf3ad 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -29,13 +29,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 拉普拉斯特征映射（Laplacian Eigenmaps,简称LE）看问题的角度和 LLE 有些相似，也是用局部的角度去构建数据之间的关系。它的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。Laplacian Eigenmaps 可以反映出数据内在的流形结构。
 
 降维算法(Dimensionality Reduction Algorithm)的应用算法有：
-* 主成分分析法（Principal Component Analysis）
-* 主成分回归（Principle Component Regression）
-* 偏最小二乘回归（Partial Least Squares Regression）
-* 萨蒙映射(Sammon Mapping)
-* 多维尺度分析法（Multidimensional Scaling)
-* 投影寻踪法(Projection Pursuit)
-* 线性判别分析法（Linear Discriminant Analysis）
-* 二次判别分析法（discriminant_analysis.QuadraticDiscriminantAnalysis）
-* 局部线性嵌入(LLE)
-* 拉普拉斯特征映射(LE)
+
+* 主成分分析法(Principal Component Analysis)
+* 多维缩放(Mutiple Dimensional Scaling)
+* 线性判别分析(Linear Discriminant Analysis)
+* 等度量映射(IsometricMapping,Isomap)
+* 局部线性嵌入(Locally linear embedding)
+* 拉普拉斯特征映射(Laplacian Eigenmaps)
+* t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE)
+* 深度自动编码器(Deep Autoencoder Networks)
\ No newline at end of file

From 0f6c05b6453cdf9788b7554428046ff042d5fee6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:22:26 +0800
Subject: [PATCH 1202/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index fabad441..4e70ceda 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -38,3 +38,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 拉普拉斯特征映射(Laplacian Eigenmaps)
 * t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE)
 * 深度自动编码器(Deep Autoencoder Networks)
+
+不同降维算法的区别和特征对比:
+
+<p align="center">
+<img width="300" align="center" src="../../images/402.jpg" />
+</p>

From f354481d75687fe39587e2c657403c1950bb8b8d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:22:48 +0800
Subject: [PATCH 1203/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 4e70ceda..6646a84d 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -42,5 +42,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 不同降维算法的区别和特征对比:
 
 <p align="center">
-<img width="300" align="center" src="../../images/402.jpg" />
+<img width="600" align="center" src="../../images/402.jpg" />
 </p>

From 6516a860e17ca86b3c05228731c17218492854e8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:23:10 +0800
Subject: [PATCH 1204/1406] Update DRA.0.1.md

---
 assets/src/DRA/DRA.0.1.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.1.md b/assets/src/DRA/DRA.0.1.md
index 6646a84d..4a82ff22 100644
--- a/assets/src/DRA/DRA.0.1.md
+++ b/assets/src/DRA/DRA.0.1.md
@@ -42,5 +42,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 不同降维算法的区别和特征对比:
 
 <p align="center">
-<img width="600" align="center" src="../../images/402.jpg" />
+<img width="800" align="center" src="../../images/402.jpg" />
 </p>

From f452cfc8b6f67a448292b38cb24a2672fa786ff8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:25:34 +0800
Subject: [PATCH 1205/1406] Update README.md

---
 README.md | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/README.md b/README.md
index de71e772..6b50ac59 100644
--- a/README.md
+++ b/README.md
@@ -145,16 +145,14 @@
      * [堆叠自动编码器(Stacked AutoEncoder)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.6.md) 
      * [生成式对抗网络(Generative Adversarial Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DL/DL.0.7.md)
  * [降维算法(Dimensionality Reduction Algorithm)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.1.md)
-     * [主成分分析法（PCA）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
-     * [主成分回归（PCR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.3.md)
-     * [偏最小二乘回归（PLSR）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.4.md)
-     * [萨蒙映射]()
-     * [多维尺度分析法（MDS]()
-     * [投影寻踪法（PP）]()
-     * [线性判别分析法（LDA）]()
-     * [混合判别分析法（MDA）]()
-     * [二次判别分析法（QDA）]()
-     * [灵活判别分析法（Flexible Discriminant Analysis，FDA]()
+     * [主成分分析法(Principal Component Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.2.md)
+     * [多维缩放(Mutiple Dimensional Scaling)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.3.md)
+     * [线性判别分析(Linear Discriminant Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.4.md)
+     * [等度量映射(IsometricMapping,Isomap)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.5.md)
+     * [局部线性嵌入(Locally linear embedding)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.6.md)
+     * [拉普拉斯特征映射(Laplacian Eigenmaps)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.7.md)
+     * [t－分布随机近邻嵌入(t-SNE)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.8.md)
+     * [深度自动编码器(Deep Autoencoder Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.9.md)
  * [集成算法]()
       * [Boosting]()
       * [Bagging]()

From 04edff583bb5f46e00dd26f9f949317702bb9037 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Tue, 11 Sep 2018 09:46:05 +0800
Subject: [PATCH 1206/1406] change page of DRA

---
 assets/src/DRA/DRA.0.5.md | 5 +++++
 assets/src/DRA/DRA.0.6.md | 5 +++++
 assets/src/DRA/DRA.0.7.md | 5 +++++
 assets/src/DRA/DRA.0.8.md | 5 +++++
 assets/src/DRA/DRA.0.9.md | 5 +++++
 5 files changed, 25 insertions(+)
 create mode 100644 assets/src/DRA/DRA.0.5.md
 create mode 100644 assets/src/DRA/DRA.0.6.md
 create mode 100644 assets/src/DRA/DRA.0.7.md
 create mode 100644 assets/src/DRA/DRA.0.8.md
 create mode 100644 assets/src/DRA/DRA.0.9.md

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
new file mode 100644
index 00000000..27c46939
--- /dev/null
+++ b/assets/src/DRA/DRA.0.5.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 偏最小二乘回归（PLSR）
diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
new file mode 100644
index 00000000..27c46939
--- /dev/null
+++ b/assets/src/DRA/DRA.0.6.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 偏最小二乘回归（PLSR）
diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
new file mode 100644
index 00000000..27c46939
--- /dev/null
+++ b/assets/src/DRA/DRA.0.7.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 偏最小二乘回归（PLSR）
diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
new file mode 100644
index 00000000..27c46939
--- /dev/null
+++ b/assets/src/DRA/DRA.0.8.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 偏最小二乘回归（PLSR）
diff --git a/assets/src/DRA/DRA.0.9.md b/assets/src/DRA/DRA.0.9.md
new file mode 100644
index 00000000..27c46939
--- /dev/null
+++ b/assets/src/DRA/DRA.0.9.md
@@ -0,0 +1,5 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### 偏最小二乘回归（PLSR）

From 028f5c78dc92198e5d4e8ec0c55b2cf0feead15e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:48:07 +0800
Subject: [PATCH 1207/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 0a3f6bab..26c9b7ac 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -2,5 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 主成分回归分析(PCR)
-在建立多元线性回归方程时,由于自变量间存在多重共线性,常常会发现某些自变量的系数极不稳定,当增减变量时,其值会出现很大变化,甚至出现与实际情况相悖的符号,以致难以对所建回归方程给予符合实际的解释。主成分回归分析(Principal Component Regression)是一种多元回归分析方法，旨在解决自变量间存在多重共线性问题。
+#### 多维缩放(Mutiple Dimensional Scaling)

From 63a3399502531c65803a1ed8903f239fc4d3af40 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:48:30 +0800
Subject: [PATCH 1208/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 27c46939..48ff374b 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### 线性判别分析(Linear Discriminant Analysis)

From e0669763917a11e2924b76e75dfcd02bda430e4d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:48:50 +0800
Subject: [PATCH 1209/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 27c46939..788023fc 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### 等度量映射(IsometricMapping,Isomap)

From fc86cd88d2beb582346b20d18ca5e318e665a4a9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:49:15 +0800
Subject: [PATCH 1210/1406] Update DRA.0.6.md

---
 assets/src/DRA/DRA.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
index 27c46939..2d986c3c 100644
--- a/assets/src/DRA/DRA.0.6.md
+++ b/assets/src/DRA/DRA.0.6.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### 局部线性嵌入(Locally linear embedding)

From c8bb7a147167f6eb63b9b85c590411bbba7ea3ca Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:49:31 +0800
Subject: [PATCH 1211/1406] Update DRA.0.6.md

---
 assets/src/DRA/DRA.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
index 2d986c3c..1867dc6c 100644
--- a/assets/src/DRA/DRA.0.6.md
+++ b/assets/src/DRA/DRA.0.6.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 局部线性嵌入(Locally linear embedding)
+#### 局部线性嵌入(Locally Linear Embedding)

From d08aa99d87bcc2d32fb71815301bafe35f1e1f5a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:50:04 +0800
Subject: [PATCH 1212/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 6b50ac59..bcbbe450 100644
--- a/README.md
+++ b/README.md
@@ -149,7 +149,7 @@
      * [多维缩放(Mutiple Dimensional Scaling)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.3.md)
      * [线性判别分析(Linear Discriminant Analysis)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.4.md)
      * [等度量映射(IsometricMapping,Isomap)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.5.md)
-     * [局部线性嵌入(Locally linear embedding)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.6.md)
+     * [局部线性嵌入(Locally Linear Embedding)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.6.md)
      * [拉普拉斯特征映射(Laplacian Eigenmaps)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.7.md)
      * [t－分布随机近邻嵌入(t-SNE)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.8.md)
      * [深度自动编码器(Deep Autoencoder Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.9.md)

From 9294b00b8f95a93eef79c3dfeeb066e7a84e7b76 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:50:40 +0800
Subject: [PATCH 1213/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 27c46939..0a29994c 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### 拉普拉斯特征映射(Laplacian Eigenmaps)

From 5b7bb3e5c03a4a7a90a0c2c33aba92dfa6760cb6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:51:21 +0800
Subject: [PATCH 1214/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 27c46939..3e7af32b 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -2,4 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### t－分布随机近邻嵌入(t-SNE)
+t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE)

From 39e10abde672a7ebf0a9dff7827fcb3ce5317cbb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Sep 2018 09:51:34 +0800
Subject: [PATCH 1215/1406] Update DRA.0.9.md

---
 assets/src/DRA/DRA.0.9.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.9.md b/assets/src/DRA/DRA.0.9.md
index 27c46939..1780af93 100644
--- a/assets/src/DRA/DRA.0.9.md
+++ b/assets/src/DRA/DRA.0.9.md
@@ -2,4 +2,4 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### 偏最小二乘回归（PLSR）
+#### 深度自动编码器(Deep Autoencoder Networks)

From 9392d563837e51358e7c2cd97700e3f37bc2efe4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 12 Sep 2018 08:37:31 +0800
Subject: [PATCH 1216/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 26c9b7ac..161db9b4 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多维缩放(Mutiple Dimensional Scaling)
+
+降维就是能够用一组个数为d的向量zi来代表个数为D的向量xi所包含的有用信息，其中d<D。假设对一张512*512大小的图片，用svm来做分类，最直接的做法是将图按照行或者列展开变成长度为512*512的输入向量xi，跟svm的参数相乘。假如能够将512*512的向量在保留有用信息的情况下降维到100，那么存储输入和参数的空间会减少很多，计算向量乘法的时间也会减少很多。所以降维能够有效的减少计算时间。而高维空间的数据很有可能出现分布稀疏的情况，即100个样本在100维空间分布肯定是非常稀疏的，每增加一维所需的样本个数呈指数级增长，这种在高维空间中样本稀疏的问题被称为维数灾难。降维可以缓解这种问题。

From def2bfe509bd59d5c5b5d469030cef86fa404361 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 12 Sep 2018 08:37:50 +0800
Subject: [PATCH 1217/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 161db9b4..52c368e3 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### 多维缩放(Mutiple Dimensional Scaling)
 
 降维就是能够用一组个数为d的向量zi来代表个数为D的向量xi所包含的有用信息，其中d<D。假设对一张512*512大小的图片，用svm来做分类，最直接的做法是将图按照行或者列展开变成长度为512*512的输入向量xi，跟svm的参数相乘。假如能够将512*512的向量在保留有用信息的情况下降维到100，那么存储输入和参数的空间会减少很多，计算向量乘法的时间也会减少很多。所以降维能够有效的减少计算时间。而高维空间的数据很有可能出现分布稀疏的情况，即100个样本在100维空间分布肯定是非常稀疏的，每增加一维所需的样本个数呈指数级增长，这种在高维空间中样本稀疏的问题被称为维数灾难。降维可以缓解这种问题。
+
+而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。

From 2b2907b6097ed7bdb72866fe713257e071d3a0de Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 12 Sep 2018 09:26:40 +0800
Subject: [PATCH 1218/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 52c368e3..e23cd790 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -7,3 +7,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 降维就是能够用一组个数为d的向量zi来代表个数为D的向量xi所包含的有用信息，其中d<D。假设对一张512*512大小的图片，用svm来做分类，最直接的做法是将图按照行或者列展开变成长度为512*512的输入向量xi，跟svm的参数相乘。假如能够将512*512的向量在保留有用信息的情况下降维到100，那么存储输入和参数的空间会减少很多，计算向量乘法的时间也会减少很多。所以降维能够有效的减少计算时间。而高维空间的数据很有可能出现分布稀疏的情况，即100个样本在100维空间分布肯定是非常稀疏的，每增加一维所需的样本个数呈指数级增长，这种在高维空间中样本稀疏的问题被称为维数灾难。降维可以缓解这种问题。
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
+
+一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性/非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论后面一种。后面一种的角度一般有两种思路来实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
+
+

From 5400d91d43e74585f4d01011fc310f94bbc9f84e Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@sunmi.com>
Date: Wed, 12 Sep 2018 09:37:37 +0800
Subject: [PATCH 1219/1406] change images

---
 assets/images/403.jpg | Bin 0 -> 110999 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/403.jpg

diff --git a/assets/images/403.jpg b/assets/images/403.jpg
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From 267dd56a8a4159f2324f8334afb7af2f4ac49c23 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 12 Sep 2018 09:39:15 +0800
Subject: [PATCH 1220/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index e23cd790..4adc3edd 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -10,4 +10,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性/非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论后面一种。后面一种的角度一般有两种思路来实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
-
+<p align="center">
+<img width="500" align="center" src="../../images/403.jpg" />
+</p>

From 6b614f3c97e7adb51292d7c67f85ad13ad632392 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 13 Sep 2018 08:52:25 +0800
Subject: [PATCH 1221/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 4adc3edd..dc94dcb0 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
 
-一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性/非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论后面一种。后面一种的角度一般有两种思路来实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
+一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性，另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。后面一种的角度一般有两种思路来实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
 <p align="center">
 <img width="500" align="center" src="../../images/403.jpg" />

From 2dddb891ca8bc45b54c704e8a06e695e505b5642 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 13 Sep 2018 08:53:27 +0800
Subject: [PATCH 1222/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index dc94dcb0..c1e1bf21 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -8,7 +8,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
 
-一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性，另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。后面一种的角度一般有两种思路来实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
+一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性，另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
+
+另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
 <p align="center">
 <img width="500" align="center" src="../../images/403.jpg" />

From c8df7087f7a225e173790eeac1d1d1b7cc37bedd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 13 Sep 2018 08:55:24 +0800
Subject: [PATCH 1223/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index c1e1bf21..bf960627 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -10,7 +10,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性，另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
 
-另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下左图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
+另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
 <p align="center">
 <img width="500" align="center" src="../../images/403.jpg" />

From f40056b3e8c27e3195d3bd25d81a1cb764b9c42e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 14 Sep 2018 08:38:30 +0800
Subject: [PATCH 1224/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index bf960627..977d9daa 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -15,3 +15,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/403.jpg" />
 </p>
+
+
+MDS的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变

From 582132b828822d4b85a5fce5b28ac5000e501767 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 14 Sep 2018 08:38:52 +0800
Subject: [PATCH 1225/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 977d9daa..3195d1db 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -17,4 +17,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
-MDS的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变
+多维缩放(Mutiple Dimensional Scaling)的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变.

From 8c8224ebed15537f627e353d053cdafc0abc7154 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 15 Sep 2018 09:09:08 +0800
Subject: [PATCH 1226/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 3195d1db..09706b20 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -16,5 +16,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="500" align="center" src="../../images/403.jpg" />
 </p>
 
-
 多维缩放(Mutiple Dimensional Scaling)的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变.

From 7027a0cefa325d1912efa291ece1efe616478a90 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 19 Sep 2018 08:49:52 +0800
Subject: [PATCH 1227/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 09706b20..18352601 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -1,5 +1,6 @@
 ### Deeplearning Algorithms tutorial
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多维缩放(Mutiple Dimensional Scaling)

From 7281a586911ea783dc890aea0fd2220c9e29a83f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 24 Sep 2018 18:22:59 +0800
Subject: [PATCH 1228/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 48ff374b..016cdea7 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -2,4 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+
 #### 线性判别分析(Linear Discriminant Analysis)

From d3ca2a39c9033fec8714dc759f8419fec5bd115e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Oct 2018 20:23:47 +0800
Subject: [PATCH 1229/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 343f99be..96da9d5a 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -20,7 +20,7 @@ PCA跟因子分析密切相关，并且已经有很多混合这两种分析的
 #### 应用示例
 ```python
 # coding:utf-8
-"""
+
 from __future__ import division
 import numpy as np
 import pandas as pd

From fbd25f6f80dd2b1fd0648f7c52728309ae29a43d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Oct 2018 20:24:01 +0800
Subject: [PATCH 1230/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 96da9d5a..38dc3675 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -19,8 +19,6 @@ PCA跟因子分析密切相关，并且已经有很多混合这两种分析的
 
 #### 应用示例
 ```python
-# coding:utf-8
-
 from __future__ import division
 import numpy as np
 import pandas as pd

From a50a763ff031829a25f23c60282c03e5716faf76 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Oct 2018 20:24:19 +0800
Subject: [PATCH 1231/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 38dc3675..a2b2dcbe 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -13,7 +13,7 @@ PCA是最简单的以特征量分析多元统计分布的方法。通常情况
 PCA跟因子分析密切相关，并且已经有很多混合这两种分析的统计包。而真实要素分析则是假定底层结构，求得微小差异矩阵的特征向量。
 
 <p align="center">
-<img width="300" align="center" src="../../images/401.jpg" />
+<img width="500" align="center" src="../../images/401.jpg" />
 </p>
 主成分分析实例：一个平均值为(1, 3)、标准差在(0.878, 0.478)方向上为3、在其正交方向为1的高斯分布。这里以黑色显示的两个向量是这个分布的协方差矩阵的特征向量，其长度按对应的特征值之平方根为比例，并且移动到以原分布的平均值为原点。
 

From d8fbeba554c81b7ae7bdf0eeebf7c08a8c876545 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 6 Oct 2018 20:24:39 +0800
Subject: [PATCH 1232/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index a2b2dcbe..38dc3675 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -13,7 +13,7 @@ PCA是最简单的以特征量分析多元统计分布的方法。通常情况
 PCA跟因子分析密切相关，并且已经有很多混合这两种分析的统计包。而真实要素分析则是假定底层结构，求得微小差异矩阵的特征向量。
 
 <p align="center">
-<img width="500" align="center" src="../../images/401.jpg" />
+<img width="300" align="center" src="../../images/401.jpg" />
 </p>
 主成分分析实例：一个平均值为(1, 3)、标准差在(0.878, 0.478)方向上为3、在其正交方向为1的高斯分布。这里以黑色显示的两个向量是这个分布的协方差矩阵的特征向量，其长度按对应的特征值之平方根为比例，并且移动到以原分布的平均值为原点。
 

From df817499763c9febf42a325f7e1b16e79f2cf87f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 19:54:30 +0800
Subject: [PATCH 1233/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 86 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 86 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 18352601..c9989bcc 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -18,3 +18,89 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 多维缩放(Mutiple Dimensional Scaling)的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变.
+
+
+应用示例:
+```python
+
+
+import os, sys, getopt, pdb
+from numpy import *
+from numpy.linalg import *
+from numpy.random import *
+import pylab
+
+def mds(d, dimensions = 2):
+    """
+    Multidimensional Scaling - Given a matrix of interpoint distances,
+    find a set of low dimensional points that have similar interpoint
+    distances.
+    """
+
+    (n,n) = d.shape
+    E = (-0.5 * d**2)
+
+    # Use mat to get column and row means to act as column and row means.
+    Er = mat(mean(E,1))
+    Es = mat(mean(E,0))
+
+    # From Principles of Multivariate Analysis: A User's Perspective (page 107).
+    F = array(E - transpose(Er) - Es + mean(E))
+
+    [U, S, V] = svd(F)
+
+    Y = U * sqrt(S)
+
+    return (Y[:,0:dimensions], S)
+
+def norm(vec):
+    return sqrt(sum(vec**2))
+
+def square_points(size):
+    nsensors = size ** 2
+    return array([(i / size, i % size) for i in range(nsensors)])
+
+def test():
+
+    points = square_points(10)
+
+    distance = zeros((100,100))
+    for (i, pointi) in enumerate(points):
+        for (j, pointj) in enumerate(points):
+            distance[i,j] = norm(pointi - pointj)
+
+    Y, eigs = mds(distance)
+
+    pylab.figure(1)
+    pylab.plot(Y[:,0],Y[:,1],'.')
+
+    pylab.figure(2)
+    pylab.plot(points[:,0], points[:,1], '.')
+
+    pylab.show()
+
+def main():
+
+    def usage():
+	print sys.argv[0] + "[-h] [-d]"
+
+    try:
+        (options, args) = getopt.getopt(sys.argv[1:], 'dh', ['help','debug'])
+    except getopt.GetoptError:
+        # print help information and exit:
+        usage()
+        sys.exit(2)
+
+    for o, a in options:
+        if o in ('-h', '--help'):
+            usage()
+            sys.exit()
+	elif o in ('-d', '--debug'):
+	    pdb.set_trace()
+
+    test()
+
+if __name__ == "__main__":
+    main()
+
+```

From aa17082e81ab49ce5a911f57dc78ec1bccb79602 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 19:55:12 +0800
Subject: [PATCH 1234/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index c9989bcc..345322b9 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -22,8 +22,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 应用示例:
 ```python
-
-
 import os, sys, getopt, pdb
 from numpy import *
 from numpy.linalg import *

From aa5da4ac0e7f2a8104225360ac31922fff6dc1dd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 19:59:23 +0800
Subject: [PATCH 1235/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 345322b9..1a73a970 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -19,6 +19,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 多维缩放(Mutiple Dimensional Scaling)的目标是在降维的过程中将数据的dissimilarity(差异性)保持下来，也可以理解降维让高维空间中的距离关系与低维空间中距离关系保持不变.
 
+算法原理:
+
+假定m个样本在原始空间的距离矩阵为
+
 
 应用示例:
 ```python

From e0d48b8079567d36232312de4dd7ae8f4296762c Mon Sep 17 00:00:00 2001
From: keke <2536485681@qq.com>
Date: Sun, 7 Oct 2018 20:33:30 +0800
Subject: [PATCH 1236/1406] add picture

---
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z839B1=10$hApX8&2b<|?f$<qcPzirwD834$0ejixco~q?Hgk|KC2=y;e@RciM?naz
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HcmV?d00001


From bfd58f3e65e000ab41718086f94f1d51d7931f8c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 20:38:34 +0800
Subject: [PATCH 1237/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 1a73a970..468cdaa6 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为
+假定m个样本在原始空间的距离矩阵为<img width="300" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素
+
+
 
 
 应用示例:

From fec0e74f4633803c2e1f27e55d782f15f5012653 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 20:40:44 +0800
Subject: [PATCH 1238/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 468cdaa6..bb03087e 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="300" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="100" align="center" src="../../images/436.jpg" />
 
 
 

From 924851ade1c5236740b87db56b44f3742317d932 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 20:43:16 +0800
Subject: [PATCH 1239/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index bb03087e..7fe2fa1b 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="100" align="center" src="../../images/436.jpg" />
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="70" align="center" src="../../images/404.jpg" />和<img width="70" align="center" src="../../images/437.jpg" /> 的距离。
 
 
 

From b0f87ec6178bac456cc2ef1b6c79b485097a8c95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 20:46:06 +0800
Subject: [PATCH 1240/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 7fe2fa1b..af8f38fd 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -9,7 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
 
-一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性，另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
+一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性,另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
 
 另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="70" align="center" src="../../images/404.jpg" />和<img width="70" align="center" src="../../images/437.jpg" /> 的距离。
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="70" align="center" src="../../images/404.jpg" />和<img width="70" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
 
 
 

From 7d8e85244c792858cd1171e463a8f4dc782b2dac Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 20:59:01 +0800
Subject: [PATCH 1241/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 93 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 91 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index af8f38fd..71c50229 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -9,7 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
 
-一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性,另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的projection方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
+一般来从两个角度来考虑做数据降维，一种是直接提取特征子集做特征抽取，例如从512*512图中只取中心部分，一种是通过线性, 另外是一种非线性的方式将原来高维空间变换到一个新的空间，这里主要讨论非线性。非线性一般是有两种方式去实现，一种是基于从高维空间映射到低维空间的 projection 方法，其中代表算法就是PCA，而其他的LDA、Autoencoder也算是这种，主要目的就是学习或者算出一个矩阵变换W，用这个矩阵与高维数据相乘得到低维数据。
 
 另一种是基于流形学习的方法，流形学习的目的是找到高维空间样本的低维描述，它假设在高维空间中数据会呈现一种有规律的低维流形排列，但是这种规律排列不能直接通过高维空间的欧式距离来衡量，如下图所示，某两点实际上的距离应该是下右图展开后的距离。如果能够有方法将高维空间中流形描述出来，那么在降维的过程中就能够保留这种空间关系，为了解决这个问题，流形学习假设高维空间的局部区域仍然具有欧式空间的性质，即它们的距离可以通过欧式距离算出(Isomap)，或者某点坐标能够由临近的节点线性组合算出(LLE)，从而可以获得高维空间的一种关系，而这种关系能够在低维空间中保留下来，从而基于这种关系表示来进行降维，因此流形学习可以用来压缩数据、可视化、获取有效的距离矩阵等。
 
@@ -21,10 +21,99 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="70" align="center" src="../../images/404.jpg" />和<img width="70" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="20" align="center" src="../../images/404.jpg" />和<img width="20" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
 
+令<img width="70" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="70" align="center" src="../../images/409.jpg" />，因而会有:
 
+<p align="center">
+<img width="300" align="center" src="../../images/410.jpg" />
+</p>
+
+则有：
+
+<p align="center">
+<img width="300" align="center" src="../../images/411.jpg" />
+</p>
+
+接下来我们用要用<img width="300" align="center" src="../../images/436.jpg" />来表示<img width="300" align="center" src="../../images/412.jpg" />. 
+
+通常我们为方便计算，首先需要对数据进行中心化，即<img width="300" align="center" src="../../images/413.jpg" />，则有:
+
+<p align="center">
+<img width="300" align="center" src="../../images/414.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/415.jpg" />
+</p>
+
+同理也有<img width="300" align="center" src="../../images/416.jpg" />.则我们可以得到 
+<p align="center">
+<img width="300" align="center" src="../../images/417.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/418.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/419.jpg" />
+</p>
+
+
+其中<img width="100" align="center" src="../../images/420.jpg" />为矩阵B的迹，定义为<img width="100" align="center" src="../../images/421.jpg" />则可得到： 
+
+<p align="center">
+<img width="300" align="center" src="../../images/422.jpg" />
+</p>
+
+因而:
+
+<p align="center">
+<img width="300" align="center" src="../../images/423.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/424.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/425.jpg" />
+</p>
+
+因此就会有:
+
+<p align="center">
+<img width="300" align="center" src="../../images/426.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/427.jpg" />
+</p>
+
+<p align="center">
+<img width="300" align="center" src="../../images/428.jpg" />
+</p>
+
+对于bij ，代入上式后得到:
+
+<p align="center">
+<img width="300" align="center" src="../../images/429.jpg" />
+</p>
+
+这样就可以求得降维后矩阵B的各个元素，接着对矩阵B 做特征值分解，即 
+
+<p align="center">
+<img width="300" align="center" src="../../images/430.jpg" />
+</p>
+
+通常，D 是一个对称实矩阵，此时得到的B刚好会有d个非0的特征值.其中 <img width="300" align="center" src="../../images/431.jpg" />为特征值构成的对角矩阵.假定其中有d∗ 个非零特征值，它们构成对角矩阵 <img width="300" align="center" src="../../images/432.jpg" />，令V∗表示相应的特征向量矩阵，则Z可表达为:
+
+<p align="center">
+<img width="300" align="center" src="../../images/433.jpg" />
+</p>
 
+此外如果想还原原始样本矩阵，就选择d 个特征值和对应的特征向量，如果想要达到降维目的，就取<img width="300" align="center" src="../../images/434.jpg" />个最大特征值和相应的特征向量.
 
 应用示例:
 ```python

From 086e5599c9b5410f6199668006e7e56fa1144cb4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:01:16 +0800
Subject: [PATCH 1242/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 71c50229..c496fc05 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -35,7 +35,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/411.jpg" />
 </p>
 
-接下来我们用要用<img width="300" align="center" src="../../images/436.jpg" />来表示<img width="300" align="center" src="../../images/412.jpg" />. 
+接下来我们用要用<img width="70" align="center" src="../../images/436.jpg" />来表示<img width="70" align="center" src="../../images/412.jpg" />. 
 
 通常我们为方便计算，首先需要对数据进行中心化，即<img width="300" align="center" src="../../images/413.jpg" />，则有:
 

From 7a73e6049db270116626a547795980048b399273 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:02:23 +0800
Subject: [PATCH 1243/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index c496fc05..018352ca 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="20" align="center" src="../../images/404.jpg" />和<img width="20" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="20" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
 
 令<img width="70" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="70" align="center" src="../../images/409.jpg" />，因而会有:
 

From f8a3d3a795813d319d359dfa0ec2fbf17affa5d5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:08:29 +0800
Subject: [PATCH 1244/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 018352ca..ec274593 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,12 +21,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="20" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="50" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="200" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
 
-令<img width="70" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="70" align="center" src="../../images/409.jpg" />，因而会有:
+因此令<img width="200" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="100" align="center" src="../../images/409.jpg" />，因而会有:
 
 <p align="center">
-<img width="300" align="center" src="../../images/410.jpg" />
+<img width="500" align="center" src="../../images/410.jpg" />
 </p>
 
 则有：
@@ -35,33 +35,33 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/411.jpg" />
 </p>
 
-接下来我们用要用<img width="70" align="center" src="../../images/436.jpg" />来表示<img width="70" align="center" src="../../images/412.jpg" />. 
+接下来我们用要用<img width="70" align="center" src="../../images/436.jpg" />来表示<img width="50" align="center" src="../../images/412.jpg" />. 
 
-通常我们为方便计算，首先需要对数据进行中心化，即<img width="300" align="center" src="../../images/413.jpg" />，则有:
+通常我们为方便计算，首先需要对数据进行中心化，即<img width="80" align="center" src="../../images/413.jpg" />，则有:
 
 <p align="center">
 <img width="300" align="center" src="../../images/414.jpg" />
 </p>
 
 <p align="center">
-<img width="300" align="center" src="../../images/415.jpg" />
+<img width="500" align="center" src="../../images/415.jpg" />
 </p>
 
-同理也有<img width="300" align="center" src="../../images/416.jpg" />.则我们可以得到 
+同理也有<img width="100" align="center" src="../../images/416.jpg" />.则我们可以得到 
 <p align="center">
-<img width="300" align="center" src="../../images/417.jpg" />
+<img width="500" align="center" src="../../images/417.jpg" />
 </p>
 
 <p align="center">
-<img width="300" align="center" src="../../images/418.jpg" />
+<img width="500" align="center" src="../../images/418.jpg" />
 </p>
 
 <p align="center">
-<img width="300" align="center" src="../../images/419.jpg" />
+<img width="500" align="center" src="../../images/419.jpg" />
 </p>
 
 
-其中<img width="100" align="center" src="../../images/420.jpg" />为矩阵B的迹，定义为<img width="100" align="center" src="../../images/421.jpg" />则可得到： 
+其中<img width="70" align="center" src="../../images/420.jpg" />为矩阵B的迹，定义为<img width="150" align="center" src="../../images/421.jpg" />则可得到： 
 
 <p align="center">
 <img width="300" align="center" src="../../images/422.jpg" />
@@ -104,7 +104,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 这样就可以求得降维后矩阵B的各个元素，接着对矩阵B 做特征值分解，即 
 
 <p align="center">
-<img width="300" align="center" src="../../images/430.jpg" />
+<img width="200" align="center" src="../../images/430.jpg" />
 </p>
 
 通常，D 是一个对称实矩阵，此时得到的B刚好会有d个非0的特征值.其中 <img width="300" align="center" src="../../images/431.jpg" />为特征值构成的对角矩阵.假定其中有d∗ 个非零特征值，它们构成对角矩阵 <img width="300" align="center" src="../../images/432.jpg" />，令V∗表示相应的特征向量矩阵，则Z可表达为:
@@ -113,7 +113,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/433.jpg" />
 </p>
 
-此外如果想还原原始样本矩阵，就选择d 个特征值和对应的特征向量，如果想要达到降维目的，就取<img width="300" align="center" src="../../images/434.jpg" />个最大特征值和相应的特征向量.
+此外如果想还原原始样本矩阵，就选择d 个特征值和对应的特征向量，如果想要达到降维目的，就取<img width="100" align="center" src="../../images/434.jpg" />个最大特征值和相应的特征向量.
 
 应用示例:
 ```python

From 267a86fb1a9870f42eb6658206852b08003b6207 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:10:36 +0800
Subject: [PATCH 1245/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index ec274593..091284ba 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="50" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="200" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="70" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="50" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="100" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="100" align="center" src="../../images/407.jpg" />.
 
 因此令<img width="200" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="100" align="center" src="../../images/409.jpg" />，因而会有:
 

From 95920e0fe14f6fa802103c4f90de671800e50c69 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:13:02 +0800
Subject: [PATCH 1246/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 091284ba..b704cab7 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -84,7 +84,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 因此就会有:
 
 <p align="center">
-<img width="300" align="center" src="../../images/426.jpg" />
+<img width="200" align="center" src="../../images/426.jpg" />
 </p>
 
 <p align="center">

From aa8b7365cffc5bd0766cdf26d4dcd63aadb460e3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:13:14 +0800
Subject: [PATCH 1247/1406] Update DRA.0.3.md


From 885c1520907014823a220366c8b03bbf7b9cff9d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 7 Oct 2018 21:15:44 +0800
Subject: [PATCH 1248/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index b704cab7..42c11ec8 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -35,7 +35,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/411.jpg" />
 </p>
 
-接下来我们用要用<img width="70" align="center" src="../../images/436.jpg" />来表示<img width="50" align="center" src="../../images/412.jpg" />. 
+接下来我们用要用<img width="70" align="center" src="../../images/436.jpg" />来表示<img width="30" align="center" src="../../images/412.jpg" />. 
 
 通常我们为方便计算，首先需要对数据进行中心化，即<img width="80" align="center" src="../../images/413.jpg" />，则有:
 

From 2736fb5b9abe50fbf7a4c593ee1fb6fbd0b3f9f2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Oct 2018 09:27:18 +0800
Subject: [PATCH 1249/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 42c11ec8..25786b43 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -117,6 +117,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 应用示例:
 ```python
+
 import os, sys, getopt, pdb
 from numpy import *
 from numpy.linalg import *

From afa082dc01d96fd586d63c8723e50f066b13df6e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Oct 2018 09:28:18 +0800
Subject: [PATCH 1250/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 25786b43..d5de0bd4 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="50" align="center" src="../../images/404.jpg" />和<img width="50" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="100" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="100" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="30" align="center" src="../../images/404.jpg" />和<img width="30" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="100" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="100" align="center" src="../../images/407.jpg" />.
 
 因此令<img width="200" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="100" align="center" src="../../images/409.jpg" />，因而会有:
 

From 508fecf0feebf113d3fb15bd20b09ed22a5f98df Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Oct 2018 09:29:23 +0800
Subject: [PATCH 1251/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index d5de0bd4..f2b4e3d4 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -113,7 +113,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="300" align="center" src="../../images/433.jpg" />
 </p>
 
-此外如果想还原原始样本矩阵，就选择d 个特征值和对应的特征向量，如果想要达到降维目的，就取<img width="100" align="center" src="../../images/434.jpg" />个最大特征值和相应的特征向量.
+此外如果想还原原始样本矩阵，就选择d 个特征值和对应的特征向量，如果想要达到降维目的，就取<img width="100" align="center" src="../../images/434.jpg" />个最大特征值和相应的特征向量。
 
 应用示例:
 ```python

From 83b76263559b5d0bfc5455497640d53d8c8e6a21 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 8 Oct 2018 09:32:33 +0800
Subject: [PATCH 1252/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 016cdea7..dd0ee2b1 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 
 #### 线性判别分析(Linear Discriminant Analysis)
+
+线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。

From e85f0b083c901f52a6f22b935340f59b1497526e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Oct 2018 09:11:51 +0800
Subject: [PATCH 1253/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index f2b4e3d4..4e5bff9d 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -5,7 +5,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 多维缩放(Mutiple Dimensional Scaling)
 
-降维就是能够用一组个数为d的向量zi来代表个数为D的向量xi所包含的有用信息，其中d<D。假设对一张512*512大小的图片，用svm来做分类，最直接的做法是将图按照行或者列展开变成长度为512*512的输入向量xi，跟svm的参数相乘。假如能够将512*512的向量在保留有用信息的情况下降维到100，那么存储输入和参数的空间会减少很多，计算向量乘法的时间也会减少很多。所以降维能够有效的减少计算时间。而高维空间的数据很有可能出现分布稀疏的情况，即100个样本在100维空间分布肯定是非常稀疏的，每增加一维所需的样本个数呈指数级增长，这种在高维空间中样本稀疏的问题被称为维数灾难。降维可以缓解这种问题。
+降维就是能够用一组个数为d的向量zi来代表个数为D的向量xi所包含的有用信息，其中d<D。例如有一张512*512大小的图片，我们用svm来做分类，最直接的做法是将图按照行或者列展开变成长度为512*512的输入向量xi，然后跟svm的参数相乘。假如能够将512*512的向量在保留有用信息的情况下降维到100，那么存储输入和参数的空间会减少很多，计算向量乘法的时间也会减少很多。所以降维能够有效的减少计算时间。而高维空间的数据很有可能出现分布稀疏的情况，即100个样本在100维空间分布肯定是非常稀疏的，每增加一维所需的样本个数呈指数级增长，这种在高维空间中样本稀疏的问题被称为维数灾难。降维可以缓解这种问题。
 
 而为什么可以降维，这是因为数据有冗余，要么是一些没有用的信息，要么是一些重复表达的信息，例如一张512*512的图只有中心100*100的区域内有非0值，剩下的区域就是没有用的信息，又或者一张图是成中心对称的，那么对称的部分信息就重复了。正确降维后的数据一般保留了原始数据的大部分的重要信息，它完全可以替代输入去做一些其他的工作，从而很大程度上可以减少计算量。例如降到二维或者三维来可视化。
 

From 13c0eb8a27eb57dd71f58d8c2a9bb17dd7bf8bd2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 10 Oct 2018 09:13:02 +0800
Subject: [PATCH 1254/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 4e5bff9d..81725651 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -107,7 +107,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="200" align="center" src="../../images/430.jpg" />
 </p>
 
-通常，D 是一个对称实矩阵，此时得到的B刚好会有d个非0的特征值.其中 <img width="300" align="center" src="../../images/431.jpg" />为特征值构成的对角矩阵.假定其中有d∗ 个非零特征值，它们构成对角矩阵 <img width="300" align="center" src="../../images/432.jpg" />，令V∗表示相应的特征向量矩阵，则Z可表达为:
+通常，D 是一个对称实矩阵，此时得到的B刚好会有d个非0的特征值.其中 <img width="200" align="center" src="../../images/431.jpg" />为特征值构成的对角矩阵.假定其中有d∗ 个非零特征值，它们构成对角矩阵 <img width="200" align="center" src="../../images/432.jpg" />，令V∗表示相应的特征向量矩阵，则Z可表达为:
 
 <p align="center">
 <img width="300" align="center" src="../../images/433.jpg" />

From c17bd67df3a36f1a64b8b36e25592ffffdc4cac6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 13 Oct 2018 08:51:36 +0800
Subject: [PATCH 1255/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index dd0ee2b1..561e7ea3 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -2,7 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-
 #### 线性判别分析(Linear Discriminant Analysis)
 
 线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。

From c7ad69662fae3a88e67c6edb58e20a577927eeaa Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Oct 2018 09:12:01 +0800
Subject: [PATCH 1256/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 561e7ea3..e40d704c 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -4,4 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 线性判别分析(Linear Discriminant Analysis)
 
-线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
+线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。
+
+通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。

From 838498549598b0647466c6eabd0c9951cb03e7ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Oct 2018 09:13:30 +0800
Subject: [PATCH 1257/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index e40d704c..3cb1315a 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -6,4 +6,12 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。
 
+线性判别分析 (Linear Discriminant Analysis)是对费舍尔的线性鉴别方法的归纳，这种方法使用统计学，模式识别和机器学习方法，试图找到两类物体或事件的特征的一个线性组合，以能够特征化或区分它们。所得的组合可用来作为一个线性分类器，或者，更常见的是，为后续的分类做降维处理。
+
+线性判别分析与方差分析（ANOVA）和回归分析紧密相关，这两种分析方法也试图通过一些特征或测量值的线性组合来表示一个因变量。然而，方差分析使用类别自变量和连续数因变量，而判别分析连续自变量和类别因变量（即类标签）。[3] 逻辑回归和概率回归比方差分析更类似于LDA，因为他们也是用连续自变量来解释类别因变量的。LDA的基本假设是自变量是正态分布的，当这一假设无法满足时，在实际应用中更倾向于用上述的其他方法。
+
+
+
 通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
+
+

From 52bfb94dcf9ee2a778e22525bf4b789d2732508b Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 16 Oct 2018 09:14:08 +0800
Subject: [PATCH 1258/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 3cb1315a..cbd4c7fa 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -6,11 +6,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 线性判别分析(Linear Discriminant Analysis)，是一种监督学习(supervised learning)算法。线性判别式分析也叫做Fisher线性判别(Fisher Linear Discriminant ,FLD)，是模式识别的经典算法，它是在1996年由Belhumeur引入模式识别和人工智能领域的。其鉴别分析的基本思想是将高维的模式样本投影到最佳鉴别矢量空间，以达到抽取分类信息和压缩特征空间维数的效果，投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离，即模式在该空间中有最佳的可分离性。因此，它是一种有效的特征抽取方法。使用这种方法能够使投影后模式样本的类间散布矩阵最大，并且同时类内散布矩阵最小。
 
-线性判别分析 (Linear Discriminant Analysis)是对费舍尔的线性鉴别方法的归纳，这种方法使用统计学，模式识别和机器学习方法，试图找到两类物体或事件的特征的一个线性组合，以能够特征化或区分它们。所得的组合可用来作为一个线性分类器，或者，更常见的是，为后续的分类做降维处理。
+线性判别分析(Linear Discriminant Analysis)是对费舍尔的线性鉴别方法的归纳，这种方法使用统计学，模式识别和机器学习方法，试图找到两类物体或事件的特征的一个线性组合，以能够特征化或区分它们。所得的组合可用来作为一个线性分类器，或者，更常见的是，为后续的分类做降维处理。
 
-线性判别分析与方差分析（ANOVA）和回归分析紧密相关，这两种分析方法也试图通过一些特征或测量值的线性组合来表示一个因变量。然而，方差分析使用类别自变量和连续数因变量，而判别分析连续自变量和类别因变量（即类标签）。[3] 逻辑回归和概率回归比方差分析更类似于LDA，因为他们也是用连续自变量来解释类别因变量的。LDA的基本假设是自变量是正态分布的，当这一假设无法满足时，在实际应用中更倾向于用上述的其他方法。
+线性判别分析(Linear Discriminant Analysis)与方差分析（ANOVA）和回归分析紧密相关，这两种分析方法也试图通过一些特征或测量值的线性组合来表示一个因变量。然而，方差分析使用类别自变量和连续数因变量，而判别分析连续自变量和类别因变量（即类标签）。[3] 逻辑回归和概率回归比方差分析更类似于LDA，因为他们也是用连续自变量来解释类别因变量的。LDA的基本假设是自变量是正态分布的，当这一假设无法满足时，在实际应用中更倾向于用上述的其他方法。
 
+线性判别分析(Linear Discriminant Analysis)也与主成分分析（PCA）和因子分析紧密相关，它们都在寻找最佳解释数据的变量线性组合。[4] LDA明确的尝试为数据类之间不同建立模型。 另一方面，PCA不考虑类的任何不同，因子分析是根据不同点而不是相同点来建立特征组合。判别的分析不同因子分析还在于，它不是一个相互依存技术：即必须区分出自变量和因变量（也称为准则变量）的不同。
 
+在对自变量每一次观察测量值都是连续量的时候，LDA能有效的起作用。当处理类别自变量时，与LDA相对应的技术称为判别反应分析。
 
 通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
 

From 0d9b7e90190b7feb334baae25dc2f2c33ba1537e Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Oct 2018 10:08:01 +0800
Subject: [PATCH 1259/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 788023fc..62a12e70 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -3,3 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 等度量映射(IsometricMapping,Isomap)
+等度量映射(Isomap)是最经典的非线性映射降维方法之一，它在MDS的基础上引入了“测地距离”的概念，直接解决了MDS使用欧氏距离无法应对非线性流形的问题。

From 135c9256c7e8093ebafcd9ef8020b9501d5a2a09 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 23 Oct 2018 10:10:55 +0800
Subject: [PATCH 1260/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 62a12e70..9e59e0ce 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 等度量映射(IsometricMapping,Isomap)
 等度量映射(Isomap)是最经典的非线性映射降维方法之一，它在MDS的基础上引入了“测地距离”的概念，直接解决了MDS使用欧氏距离无法应对非线性流形的问题。
+
+测地距离(Geometric Distance)是高维流形中两点之间的最短距离，高维流形中，空间是不规则的，所以最短距离不一定是直线距离(欧氏距离)。就像蚂蚁从立方体的一面爬到另一面，不能直接横穿立方体一样。

From 4331e7a53483c05f7164fd0c318201afcd2b160f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Oct 2018 09:38:50 +0800
Subject: [PATCH 1261/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 81725651..343ea82b 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -21,7 +21,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 算法原理:
 
-假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="30" align="center" src="../../images/404.jpg" />和<img width="30" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="100" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="100" align="center" src="../../images/407.jpg" />.
+假定m个样本在原始空间的距离矩阵为<img width="100" align="center" src="../../images/435.jpg" />，其第i 行和第j 列的元素<img width="70" align="center" src="../../images/436.jpg" />为样本<img width="30" align="center" src="../../images/404.jpg" />和<img width="30" align="center" src="../../images/437.jpg" /> 的距离。这样就可以获得样本在d′ 维空间的表示<img width="70" align="center" src="../../images/405.jpg" />,<img width="70" align="center" src="../../images/406.jpg" />，而且任意两个样本在d′ 维空间中的欧式距离等于原始空间中的距离，即<img width="100" align="center" src="../../images/407.jpg" />.
 
 因此令<img width="200" align="center" src="../../images/408.jpg" />，其中B 为降维后样本的内积矩阵，<img width="100" align="center" src="../../images/409.jpg" />，因而会有:
 

From 78f232882e459782180666571557f190f260f8d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 25 Oct 2018 09:40:10 +0800
Subject: [PATCH 1262/1406] Update DRA.0.3.md

---
 assets/src/DRA/DRA.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.3.md b/assets/src/DRA/DRA.0.3.md
index 343ea82b..92552131 100644
--- a/assets/src/DRA/DRA.0.3.md
+++ b/assets/src/DRA/DRA.0.3.md
@@ -61,7 +61,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 
-其中<img width="70" align="center" src="../../images/420.jpg" />为矩阵B的迹，定义为<img width="150" align="center" src="../../images/421.jpg" />则可得到： 
+其中<img width="60" align="center" src="../../images/420.jpg" />为矩阵B的迹，定义为<img width="150" align="center" src="../../images/421.jpg" />则可得到： 
 
 <p align="center">
 <img width="300" align="center" src="../../images/422.jpg" />

From 808e3a714b46345e2dd15c95df6a381ca0227d42 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Oct 2018 09:48:21 +0800
Subject: [PATCH 1263/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 8418b6b2..6a725c69 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -12,7 +12,6 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 卷积神经网络(Convolutional Neural Network)
-
 卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。

From 0919db48f767cada100fe4fd25698d492f5a5bbc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Oct 2018 09:48:37 +0800
Subject: [PATCH 1264/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 6a725c69..4f07eddd 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -21,7 +21,7 @@ CNN的基本结构包括两层，其一为特征提取层，每个神经元的
 CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 
 <p align="center">
-<img width="300" align="center" src="../../images/1.jpg" />
+<img width="320" align="center" src="../../images/1.jpg" />
 </p>
 
 

From dc6bcd8174e3a9fda99c25042d532b6e4917cadd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 29 Oct 2018 09:48:53 +0800
Subject: [PATCH 1265/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index 4f07eddd..e5d388b8 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -21,7 +21,7 @@ CNN的基本结构包括两层，其一为特征提取层，每个神经元的
 CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图形。由于CNN的特征检测层通过训练数据进行学习，所以在使用CNN时，避免了显式的特征抽取，而隐式地从训练数据中进行学习；再者由于同一特征映射面上的神经元权值相同，所以网络可以并行学习，这也是卷积网络相对于神经元彼此相连网络的一大优势。卷积神经网络以其局部权值共享的特殊结构在语音识别和图像处理方面有着独特的优越性，其布局更接近于实际的生物神经网络，权值共享降低了网络的复杂性，特别是多维输入向量的图像可以直接输入网络这一特点避免了特征提取和分类过程中数据重建的复杂度。
 
 <p align="center">
-<img width="320" align="center" src="../../images/1.jpg" />
+<img width="330" align="center" src="../../images/1.jpg" />
 </p>
 
 

From 60b2de23fcde5659e164e5aa48fab546d9d77198 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Nov 2018 09:33:22 +0800
Subject: [PATCH 1266/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index cbd4c7fa..57a0933c 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -14,6 +14,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在对自变量每一次观察测量值都是连续量的时候，LDA能有效的起作用。当处理类别自变量时，与LDA相对应的技术称为判别反应分析。
 
-通常，它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
+通常它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
 
 

From 4d7bb4cd022b52be62c23d4ad9437f67a0f0097a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 1 Nov 2018 09:38:20 +0800
Subject: [PATCH 1267/1406] Update DRA.0.4.md

---
 assets/src/DRA/DRA.0.4.md | 502 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 502 insertions(+)

diff --git a/assets/src/DRA/DRA.0.4.md b/assets/src/DRA/DRA.0.4.md
index 57a0933c..d9a3b485 100644
--- a/assets/src/DRA/DRA.0.4.md
+++ b/assets/src/DRA/DRA.0.4.md
@@ -17,3 +17,505 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 通常它能够保证投影后模式样本在新的空间中有最小的类内距离和最大的类间距离，即模式在该空间中有最佳的可分离性。
 
 
+应用示例:
+```python
+from __future__ import print_function
+
+import os
+import time
+import pickle
+import itertools
+import numpy as np
+import matplotlib.pyplot as plt
+
+import theano
+import lasagne
+
+# init color printer
+class BColors:
+    """
+    Colored command line output formatting
+    """
+    HEADER = '\033[95m'
+    OKBLUE = '\033[94m'
+    OKGREEN = '\033[92m'
+    WARNING = '\033[93m'
+    FAIL = '\033[91m'
+    ENDC = '\033[0m'
+    BOLD = '\033[1m'
+    UNDERLINE = '\033[4m'
+
+    def __init__(self):
+        """ Constructor """
+        pass
+
+    def print_colored(self, string, color):
+        """ Change color of string """
+        return color + string + BColors.ENDC
+
+col = BColors()
+
+
+def threaded_generator(generator, num_cached=10):
+    """
+    Threaded generator
+    """
+    import Queue
+    queue = Queue.Queue(maxsize=num_cached)
+    queue = Queue.Queue(maxsize=num_cached)
+    end_marker = object()
+
+    # define producer
+    def producer():
+        for item in generator:
+            #item = np.array(item)  # if needed, create a copy here
+            queue.put(item)
+        queue.put(end_marker)
+
+    # start producer
+    import threading
+    thread = threading.Thread(target=producer)
+    thread.daemon = True
+    thread.start()
+
+    # run as consumer
+    item = queue.get()
+    while item is not end_marker:
+        yield item
+        queue.task_done()
+        item = queue.get()
+
+
+def generator_from_iterator(iterator):
+    """
+    Compile generator from iterator
+    """
+    for x in iterator:
+        yield x
+
+
+def threaded_generator_from_iterator(iterator, num_cached=10):
+    """
+    Compile threaded generator from iterator
+    """
+    generator = generator_from_iterator(iterator)
+    return threaded_generator(generator, num_cached)
+
+
+def accuracy_score(t, p):
+    """
+    Compute accuracy
+    """
+    return float(np.sum(p == t)) / len(p)
+
+
+class LDA(object):
+    """ LDA Class """
+
+    def __init__(self, r=1e-3, n_components=None, verbose=False, show=False):
+        """ Constructor """
+        self.r = r
+        self.n_components = n_components
+
+        self.scalings_ = None
+        self.coef_ = None
+        self.intercept_ = None
+        self.means = None
+
+        self.verbose = verbose
+        self.show = show
+
+    def fit(self, X, y, X_te=None):
+        """ Compute lda on hidden layer """
+
+        # split into semi- and supervised- data
+        X_all = X.copy()
+        X = X[y >= 0]
+        y = y[y >= 0]
+
+        # get class labels
+        classes = np.unique(y)
+
+        # set number of components
+        if self.n_components is None:
+            self.n_components = len(classes) - 1
+
+        # compute means
+        means = []
+        for group in classes:
+            Xg = X[y == group, :]
+            means.append(Xg.mean(0))
+        self.means = np.asarray(means)
+
+        # compute covs
+        covs = []
+        for group in classes:
+            Xg = X[y == group, :]
+            Xg = Xg - np.mean(Xg, axis=0)
+            covs.append(np.cov(Xg.T))
+
+        # within scatter
+        Sw = np.average(covs, axis=0)
+
+        # total scatter
+        X_all = X_all - np.mean(X_all, axis=0)
+        if X_te is not None:
+            St = np.cov(np.concatenate((X_all, X_te)).T)
+        else:
+            St = np.cov(X_all.T)
+
+        # between scatter
+        Sb = St - Sw
+
+        # cope for numerical instability
+        Sw += np.identity(Sw.shape[0]) * self.r
+
+        # compute eigen decomposition
+        from scipy.linalg.decomp import eigh
+        evals, evecs = eigh(Sb, Sw)
+
+        # sort eigen vectors according to eigen values
+        evecs = evecs[:, np.argsort(evals)[::-1]]
+
+        # normalize eigen vectors
+        evecs /= np.apply_along_axis(np.linalg.norm, 0, evecs)
+
+        # compute lda data
+        self.scalings_ = evecs
+        self.coef_ = np.dot(self.means, evecs).dot(evecs.T)
+        self.intercept_ = (-0.5 * np.diag(np.dot(self.means, self.coef_.T)))
+
+        if self.verbose:
+            top_k_evals = evals[-self.n_components:]
+            print("LDA-Eigenvalues (Train):", np.array_str(top_k_evals, precision=2, suppress_small=True))
+            print("Ratio min(eigval)/max(eigval): %.3f, Mean(eigvals): %.3f" % (top_k_evals.min() / top_k_evals.max(), top_k_evals.mean()))
+
+        if self.show:
+            plt.figure("Eigenvalues")
+            ax = plt.subplot(111)
+            top_k_evals /= np.sum(top_k_evals)
+            plt.plot(range(self.n_components), top_k_evals, 'bo-')
+            plt.grid('on')
+            plt.xlabel('Eigenvalue', fontsize=20)
+            plt.ylabel('Explained Discriminative Variance', fontsize=20)
+            plt.ylim([0.0, 1.05 * np.max(top_k_evals)])
+
+            ax.tick_params(axis='x', labelsize=18)
+            ax.tick_params(axis='y', labelsize=18)
+
+        return evals
+
+    def transform(self, X):
+        """ transform data """
+        X_new = np.dot(X, self.scalings_)
+        return X_new[:, :self.n_components]
+
+    def predict_proba(self, X):
+        """ estimate probability """
+        prob = -(np.dot(X, self.coef_.T) + self.intercept_)
+        np.exp(prob, prob)
+        prob += 1
+        np.reciprocal(prob, prob)
+        prob /= prob.sum(axis=1).reshape((prob.shape[0], -1))
+        return prob
+
+    def predict_log_proba(self, X):
+        """ estimate log probability """
+        return np.log(self.predict_proba(X))
+
+
+def create_iter_functions(l_out, l_in, y_tensor_type, objective, learning_rate, l_2, compute_updates):
+    """ Create functions for training, validation and testing to iterate one epoch. """
+
+    # init target tensor
+    targets = y_tensor_type('y')
+
+    # compute train costs
+    tr_output = lasagne.layers.get_output(l_out, deterministic=False)
+    tr_cost = objective(tr_output, targets)
+
+    # compute validation costs
+    va_output = lasagne.layers.get_output(l_out, deterministic=True)
+    va_cost = objective(va_output, targets)
+
+    # collect all parameters of net and compute updates
+    all_params = lasagne.layers.get_all_params(l_out, trainable=True)
+
+    # add weight decay
+    if l_2 is not None:
+        tr_cost += l_2 * lasagne.regularization.apply_penalty(all_params, lasagne.regularization.l2)
+
+    # compute updates from gradients
+    all_grads = lasagne.updates.get_or_compute_grads(tr_cost, all_params)
+    updates = compute_updates(all_grads, all_params, learning_rate)
+
+    # compile iter functions
+    tr_outputs = [tr_cost]
+    iter_train = theano.function([l_in.input_var, targets], tr_outputs, updates=updates)
+
+    va_outputs = [va_cost, va_output]
+    iter_valid = theano.function([l_in.input_var, targets], va_outputs)
+
+    # compile output function
+    compute_output = theano.function([l_in.input_var], va_output)
+
+    return dict(train=iter_train, valid=iter_valid, test=iter_valid, compute_output=compute_output)
+
+
+def train(iter_funcs, dataset, train_batch_iter, valid_batch_iter, r):
+    """
+    Train the model with `dataset` with mini-batch training.
+    Each mini-batch has `batch_size` recordings.
+    """
+    import sys
+    import time
+
+    for epoch in itertools.count(1):
+
+        # iterate train batches
+        batch_train_losses = []
+        iterator = train_batch_iter(dataset['X_train'], dataset['y_train'])
+        generator = threaded_generator_from_iterator(iterator)
+
+        start, after = time.time(), time.time()
+        for i_batch, (X_b, y_b) in enumerate(generator):
+            batch_res = iter_funcs['train'](X_b, y_b)
+            batch_train_losses.append(batch_res[0])
+            after = time.time()
+            train_time = (after-start)
+
+            # report loss during training
+            perc = 100 * (float(i_batch) / train_batch_iter.n_batches)
+            dec = int(perc // 4)
+            progbar = "|" + dec * "#" + (25-dec) * "-" + "|"
+            vals = (perc, progbar, train_time, np.mean(batch_train_losses))
+            loss_str = " (%d%%) %s time: %.2fs, loss: %.5f" % vals
+            print(col.print_colored(loss_str, col.WARNING), end="\r")
+            sys.stdout.flush()
+
+        print("\x1b[K", end="\r")
+        avg_train_loss = np.mean(batch_train_losses)
+
+        # lda evaluation (accuracy based)
+
+        # iterate validation batches
+        batch_valid_losses = []
+        iterator = valid_batch_iter(dataset['X_valid'], dataset['y_valid'])
+        generator = threaded_generator_from_iterator(iterator)
+        net_output_va, y_va = None, np.zeros(0, dtype=np.int32)
+        for X_b, y_b in generator:
+            batch_res = iter_funcs['valid'](X_b, y_b)
+            batch_valid_losses.append(batch_res[0])
+
+            y_va = np.concatenate((y_va, y_b))
+            net_output = iter_funcs['compute_output'](X_b)
+            if net_output_va is None:
+                net_output_va = net_output
+            else:
+                net_output_va = np.vstack((net_output_va, net_output))
+
+        avg_valid_loss = np.mean(batch_valid_losses)
+
+        # compute train set net output
+        iterator = train_batch_iter(dataset['X_train'], dataset['y_train'])
+        generator = threaded_generator_from_iterator(iterator)
+        net_output_tr, y_tr = None, np.zeros(0, dtype=np.int32)
+        for i_batch, (X_b, y_b) in enumerate(generator):
+            y_tr = np.concatenate((y_tr, y_b))
+            net_output = iter_funcs['compute_output'](X_b)
+            if net_output_tr is None:
+                net_output_tr = net_output
+            else:
+                net_output_tr = np.vstack((net_output_tr, net_output))
+
+        # fit lda on net output
+        print("")
+        dlda = LDA(r=r, n_components=None, verbose=True)
+        evals = dlda.fit(net_output_tr, y_tr)
+
+        # predict on train set
+        proba = dlda.predict_proba(net_output_tr[y_tr >= 0])
+        y_tr_pr = np.argmax(proba, axis=1)
+        tr_acc = 100 * accuracy_score(y_tr[y_tr >= 0], y_tr_pr)
+
+        # predict on validation set
+        proba = dlda.predict_proba(net_output_va)
+        y_va_pr = np.argmax(proba, axis=1)
+        va_acc = 100 * accuracy_score(y_va, y_va_pr)
+
+        # estimate overfitting
+        overfit = va_acc / tr_acc
+
+        # collect results
+        yield {
+            'number': epoch,
+            'train_loss': avg_train_loss,
+            'train_acc': tr_acc,
+            'valid_loss': avg_valid_loss,
+            'valid_acc': va_acc,
+            'overfitting': overfit,
+            'eigenvalues': evals
+        }
+
+
+def fit(l_out, l_in, data, objective, y_tensor_type,
+        train_batch_iter, valid_batch_iter,
+        r=1e-3, num_epochs=100, patience=20,
+        learn_rate=0.01, update_learning_rate=None,
+        l_2=None, compute_updates=None,
+        exp_name='ff', out_path=None, dump_file=None):
+    """ Train model """
+
+    # log model evolution
+    log_file = os.path.join(out_path, 'results.pkl')
+
+    print("\n")
+    print(col.print_colored("Running Test Case: " + exp_name, BColors.UNDERLINE))
+
+    # adaptive learning rate
+    learning_rate = theano.shared(np.float32(learn_rate))
+    if update_learning_rate is None:
+        def update_learning_rate(lr, e):
+            return lr
+    learning_rate.set_value(update_learning_rate(learn_rate, 0))
+
+    # initialize evaluation output
+    pred_tr_err, pred_val_err, overfitting = [], [], []
+    tr_accs, va_accs = [], []
+    eigenvalues = []
+
+    print("Building model and compiling functions...")
+    iter_funcs = create_iter_functions(l_out, l_in, y_tensor_type, objective, learning_rate=learning_rate,
+                                       l_2=l_2, compute_updates=compute_updates)
+
+    print("Starting training...")
+    now = time.time()
+    try:
+
+        # initialize early stopping
+        last_improvement = 0
+        best_model = lasagne.layers.get_all_param_values(l_out)
+
+        # iterate training epochs
+        prev_acc_tr, prev_acc_va = 0.0, 0.0
+        for epoch in train(iter_funcs, data, train_batch_iter, valid_batch_iter, r):
+
+            print("Epoch {} of {} took {:.3f}s".format(
+                epoch['number'], num_epochs, time.time() - now))
+            now = time.time()
+
+            # update learning rate
+            learn_rate = update_learning_rate(learn_rate, epoch['number'])
+            learning_rate.set_value(learn_rate)
+
+            # --- collect train output ---
+
+            tr_loss, va_loss = epoch['train_loss'], epoch['valid_loss']
+            train_acc, valid_acc = epoch['train_acc'], epoch['valid_acc']
+            overfit = epoch['overfitting']
+
+            # prepare early stopping
+            if valid_acc >= prev_acc_va:
+                last_improvement = 0
+                best_model = lasagne.layers.get_all_param_values(l_out)
+
+                # dump net parameters during training
+                if dump_file is not None:
+                    with open(dump_file, 'w') as fp:
+                        params = lasagne.layers.get_all_param_values(l_out)
+                        pickle.dump(params, fp)
+
+            # increase improvement counter
+            last_improvement += 1
+
+            # plot train output
+            if train_acc is None:
+                txt_tr = 'costs_tr %.5f' % tr_loss
+            else:
+                txt_tr = 'costs_tr %.5f (%.3f), ' % (tr_loss, train_acc)
+            if train_acc >= prev_acc_tr:
+                txt_tr = col.print_colored(txt_tr, BColors.OKGREEN)
+                prev_acc_tr = train_acc
+
+            if valid_acc is None:
+                txt_val = ''
+            else:
+                txt_val = 'costs_val %.5f (%.3f), tr/val %.3f' % (va_loss, valid_acc, overfit)
+            if valid_acc >= prev_acc_va:
+                txt_val = col.print_colored(txt_val, BColors.OKGREEN)
+                prev_acc_va = valid_acc
+
+            print('  lr: %.5f' % learn_rate)
+            print('  ' + txt_tr + txt_val)
+
+            # collect model evolution data
+            tr_accs.append(train_acc)
+            va_accs.append(valid_acc)
+            pred_tr_err.append(tr_loss)
+            pred_val_err.append(va_loss)
+            overfitting.append(overfit)
+            eigenvalues.append(epoch['eigenvalues'])
+
+            # --- early stopping: preserve best model ---
+            if last_improvement > patience:
+                print(col.print_colored("Early Stopping!", BColors.WARNING))
+                status = "Epoch: %d, Best Validation Accuracy: %.3f" % (epoch['number'], prev_acc_va)
+                print(col.print_colored(status, BColors.WARNING))
+                break
+
+            # maximum number of epochs reached
+            if epoch['number'] >= num_epochs:
+                break
+
+            # shuffle train data
+            if not hasattr(data['X_train'], 'reset_batch_generator'):
+                rand_idx = np.random.permutation(data['X_train'].shape[0])
+                data['X_train'] = data['X_train'][rand_idx]
+                data['y_train'] = data['y_train'][rand_idx]
+
+            # save results
+            exp_res = dict()
+            exp_res['pred_tr_err'] = pred_tr_err
+            exp_res['tr_accs'] = tr_accs
+            exp_res['pred_val_err'] = pred_val_err
+            exp_res['va_accs'] = va_accs
+            exp_res['overfitting'] = overfitting
+            exp_res['eigenvalues'] = eigenvalues
+
+            with open(log_file, 'w') as fp:
+                pickle.dump(exp_res, fp)
+
+    except KeyboardInterrupt:
+        pass
+
+    # set net to best weights
+    lasagne.layers.set_all_param_values(l_out, best_model)
+
+    # evaluate on test set
+    test_losses, test_acc = [], []
+    iterator = valid_batch_iter(data['X_test'], data['y_test'])
+    for X_b, y_b in iterator:
+        loss_te = iter_funcs['test'](X_b, y_b)
+        test_losses.append(loss_te[0])
+        if len(loss_te) > 1:
+            test_acc.append(loss_te[1])
+
+    # compute evaluation measures
+    avg_loss_te = np.mean(test_losses)
+    avg_acc_te = np.mean(test_acc)
+
+    print("--------------------------------------------")
+    print('Loss on Test-Set: %.5f' % avg_loss_te)
+    print("--------------------------------------------\n")
+
+    if out_path is not None:
+
+        # add test results and save results
+        exp_res['avg_loss_te'] = avg_loss_te
+        exp_res['avg_acc_te'] = avg_acc_te
+
+        with open(log_file, 'w') as fp:
+            pickle.dump(exp_res, fp)
+
+    return l_out, prev_acc_va
+```

From b7a0263b511b5eafc2a99255774d48f0a9c1432a Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@qutoutiao.net>
Date: Fri, 2 Nov 2018 20:22:18 +0800
Subject: [PATCH 1268/1406] change page of images

---
 assets/images/438.jpg | Bin 0 -> 88292 bytes
 assets/images/439.jpg | Bin 0 -> 174078 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assets/images/438.jpg
 create mode 100644 assets/images/439.jpg

diff --git a/assets/images/438.jpg b/assets/images/438.jpg
new file mode 100644
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From fd0528af15874ff74cd529bc73742b21ce30d605 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Nov 2018 20:23:45 +0800
Subject: [PATCH 1269/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 9e59e0ce..aab61a9e 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -6,3 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 等度量映射(Isomap)是最经典的非线性映射降维方法之一，它在MDS的基础上引入了“测地距离”的概念，直接解决了MDS使用欧氏距离无法应对非线性流形的问题。
 
 测地距离(Geometric Distance)是高维流形中两点之间的最短距离，高维流形中，空间是不规则的，所以最短距离不一定是直线距离(欧氏距离)。就像蚂蚁从立方体的一面爬到另一面，不能直接横穿立方体一样。
+
+<p align="center">
+<img width="500" align="center" src="../../images/438.jpg" />
+</p>

From 96fa99f0906ce7c2d7855eff5caee288ef64d6ab Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Nov 2018 20:26:30 +0800
Subject: [PATCH 1270/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index aab61a9e..8bc8d7dd 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -10,3 +10,22 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="500" align="center" src="../../images/438.jpg" />
 </p>
+
+图中左边的两个点的最近距离是蓝色实线的距离，而不应该是虚线的距离。
+
+通常情况下真实的测地距离是非常难以求出的，但是等度量映射基于流形局部近似于欧式空间的定义提出了一种近似的求解方式。
+
+我们通常的做法是:
+
+1. 求得原样本的KNN图，并依据定义保留其欧式距离。
+2. 所有非KNN的点间的距离规定为无穷大。
+3. 用dijkstra或floyd求出任意两点的最短路便可近似表示两点间的测地距离。
+4. 然后等度量映射(Isomap)将得到的测地距离矩阵输入MDS完成降维。
+
+最后等度量映射(Isomap)将得到的测地距离矩阵输入MDS完成降维。
+
+最后的结果是这样的。
+
+<p align="center">
+<img width="500" align="center" src="../../images/439.jpg" />
+</p>

From 3914d86c7e9faab7952d51df1628329119aa4c08 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 2 Nov 2018 20:27:05 +0800
Subject: [PATCH 1271/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 8bc8d7dd..9603073c 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -8,7 +8,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 测地距离(Geometric Distance)是高维流形中两点之间的最短距离，高维流形中，空间是不规则的，所以最短距离不一定是直线距离(欧氏距离)。就像蚂蚁从立方体的一面爬到另一面，不能直接横穿立方体一样。
 
 <p align="center">
-<img width="500" align="center" src="../../images/438.jpg" />
+<img width="600" align="center" src="../../images/438.jpg" />
 </p>
 
 图中左边的两个点的最近距离是蓝色实线的距离，而不应该是虚线的距离。
@@ -27,5 +27,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 最后的结果是这样的。
 
 <p align="center">
-<img width="500" align="center" src="../../images/439.jpg" />
+<img width="600" align="center" src="../../images/439.jpg" />
 </p>

From 76f138c4043504e0432fb6e0fccd8c47c6de014a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 5 Nov 2018 17:49:11 +0800
Subject: [PATCH 1272/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 118 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 118 insertions(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 9603073c..0cc59df1 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -29,3 +29,121 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <p align="center">
 <img width="600" align="center" src="../../images/439.jpg" />
 </p>
+
+应用示例:
+```python
+from IsomapCuda import *
+from DataUtils import *
+import getopt,sys
+
+GPU_MEM_SIZE = 512
+
+def Isomap(dataSet,outfile,srcDims,trgDims,k,eps=1000000000., CIsomap=False):
+    """
+    Classical isomap
+    """
+    
+    #first do KNN
+    knnRefs,knnDists,knnm = KNN(dataSet,k,eps,srcDims)
+    mdists = []
+    if CIsomap:
+        mdists = C_Isomap(knnDists,knnm,k)
+    
+    #then do APSP
+    pathMatrix = APSP(knnRefs,knnDists,knnm,eps)
+    del knnRefs
+    del knnDists
+    del knnm
+    
+    #then normalize the matrix
+    normMatrix = NormMatrix(pathMatrix,mdists)
+    del pathMatrix
+    del mdists
+    
+    #then get eigenvalues
+    #embedding = EigenEmbedding(normMatrix,trgDims)
+    embedding = QEig(normMatrix,trgDims)
+    del normMatrix
+    
+    return embedding
+
+
+def NMIsomap(dataSet,outfile,srcDims,trgDims,k,eps=1000000000., saveSteps = False):
+    """
+    Non-Metric Isomap
+    """
+    
+    #first do KNN
+    knnRefs,knnDists = loadSplitTable(KNN(dataSet,k,eps,srcDims))
+    
+    #then do APSP
+    pathMatrix = APSP(knnRefs,knnDists,eps)
+    del knnRefs
+    del knnDists
+    
+    #XXX:hacky way of saving this info
+    if saveSteps:
+        saveTable(pathMatrix,outfile[:-4]+'_distances.csv')
+    
+    #then get the rank matrix
+    origDims = len(pathMatrix)
+    rankMatrix = RankMatrix(pathMatrix)
+    del pathMatrix
+    
+    #then get the NMDS embedding
+    embedding = NMDS(rankMatrix, loadMatrix(dataSet)[:,:trgDims], origDims, trgDims)
+    
+    return embedding
+
+
+
+if __name__ == '__main__':
+    arg_values = ['nonmetric=','outdims=','indims=','if=','of=','k=','eps=','help','h']
+    optlist, args = getopt.getopt(sys.argv[1:], 'x', arg_values)
+    
+    trgDims = 3
+    srcDims = 10000000000
+    k =6
+    eps = 1000000000.
+    infile='swissroll.csv'
+    outfile='embedding.csv'
+    nonmetric=False
+    
+    
+    for o in optlist:
+        if o[0].strip('-') == 'outdims':
+            trgDims = int(o[1])
+    for o in optlist:
+        if o[0].strip('-') == 'indims':
+            srcDims = int(o[1])
+    for o in optlist:
+        if o[0].strip('-') == 'if':
+            infile = o[1]
+    for o in optlist:
+        if o[0].strip('-') == 'of':
+            outfile = o[1]
+    for o in optlist:
+        if o[0].strip('-') == 'k':
+            k = int(o[1])
+    for o in optlist:
+        if o[0].strip('-') == 'nonmetric':
+            if o[1].strip(' \r\n\t') == 'True' or o[1].strip(' \r\n\t') == 'true':
+                nonmetric = True
+        
+    for o in optlist:
+        if o[0].strip('-') == 'help' or o[1].strip('-') == 'h':
+            print "The following commands are available:"
+            print "\t--if=inputfile\tDefaults to swissroll.csv"
+            print "\t--of=outputfile\tDefaults to embedding.csv"
+            print "\t--k=k_nearest_neighbours\tDefaults to 12"
+            print "\t--outdims=embedding_dimensions\tDefaults to 3"
+            print "\t--indims=input_dimensions\tDefaults to all in the input file"
+            print "\t--nonmetric\tEnables non-metric MDS embeddings"
+    result = None
+    if not nonmetric:
+        result = Isomap(infile,outfile,srcDims,trgDims,k,eps,False)
+    else:
+        result = NMIsomap(infile,outfile,srcDims,trgDims,k,eps,False)
+    
+    saveTable(result,outfile)
+```

From d27a6b4bf46fc00dc2c7c00052610727184327c1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Nov 2018 09:42:23 +0800
Subject: [PATCH 1273/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index 0cc59df1..add13cb9 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -4,7 +4,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 等度量映射(IsometricMapping,Isomap)
 等度量映射(Isomap)是最经典的非线性映射降维方法之一，它在MDS的基础上引入了“测地距离”的概念，直接解决了MDS使用欧氏距离无法应对非线性流形的问题。
-
 测地距离(Geometric Distance)是高维流形中两点之间的最短距离，高维流形中，空间是不规则的，所以最短距离不一定是直线距离(欧氏距离)。就像蚂蚁从立方体的一面爬到另一面，不能直接横穿立方体一样。
 
 <p align="center">

From 0a3b0adeb4708e9bec3a69c08dd7cbf774386a37 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Nov 2018 09:42:34 +0800
Subject: [PATCH 1274/1406] Update DRA.0.5.md

---
 assets/src/DRA/DRA.0.5.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.5.md b/assets/src/DRA/DRA.0.5.md
index add13cb9..5cc0bdbd 100644
--- a/assets/src/DRA/DRA.0.5.md
+++ b/assets/src/DRA/DRA.0.5.md
@@ -3,6 +3,7 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 等度量映射(IsometricMapping,Isomap)
+
 等度量映射(Isomap)是最经典的非线性映射降维方法之一，它在MDS的基础上引入了“测地距离”的概念，直接解决了MDS使用欧氏距离无法应对非线性流形的问题。
 测地距离(Geometric Distance)是高维流形中两点之间的最短距离，高维流形中，空间是不规则的，所以最短距离不一定是直线距离(欧氏距离)。就像蚂蚁从立方体的一面爬到另一面，不能直接横穿立方体一样。
 

From a9f352182bcb2ee75e0d56dab0e0ecfdb226473d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 8 Nov 2018 09:43:47 +0800
Subject: [PATCH 1275/1406] Update DRA.0.6.md

---
 assets/src/DRA/DRA.0.6.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
index 1867dc6c..9c0cea4e 100644
--- a/assets/src/DRA/DRA.0.6.md
+++ b/assets/src/DRA/DRA.0.6.md
@@ -3,3 +3,8 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 局部线性嵌入(Locally Linear Embedding)
+数据降维是指通过线性的或非线性的映射关系将高维数据转换成低维数据的过程。一般情况下，该低维数据代表了原始高维数据的主要成分（图1），并描述了原始高维数据的空间分布结构。由于经过降维后的数据更易于被分类、识别、可视化以及存储等，故数据降维技术在诸多科研领域受到了越来越多地关注。
+
+从数据本身的的性质特征来看，数据降维可以大致分为线性降维和非线性降维两种技术方法。其中，线性降维技术仅对于数据维数相对较低、且具有全局线性结构的数据有着很好的降维效果。然而，在实际的科学研究中，科研工作者却需要面对海量的非线性高维数据。因此，能够有效处理高维非线性数据的方法亟待被提出，本文将介绍一种用于处理高维非线性数据的降维方法。
+
+局部线性嵌入（Locally linear embedding, LLE）是一种非线性的降维方法，该算法由 Sam T.Roweis等人于2000年提出并发表在《Science》杂志上。LLE试图保留原始高维数据的局部性质，通过假设局部原始数据近似位于一张超平面上，从而使得该局部的某一个数据可以由其邻域数据线性表示。

From 4e06e3fee81598c3468c2872a6b386b2f22ef873 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 11 Nov 2018 21:18:11 +0800
Subject: [PATCH 1276/1406] Update CA.0.2.md

---
 assets/src/CA/CA.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CA/CA.0.2.md b/assets/src/CA/CA.0.2.md
index 45f66244..074cbff2 100644
--- a/assets/src/CA/CA.0.2.md
+++ b/assets/src/CA/CA.0.2.md
@@ -4,7 +4,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### K-均值(K-Means Algorithm)
 
-k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
+k-means算法，也被称为k-平均或k-均值，是一种得到最广泛使用的聚类算法。 通常它把n个点（可以是样本的一次观察或一个实例）划分到k个聚类中，使得每个点都属于离他最近的均值（此即聚类中心）对应的聚类，以之作为聚类的标准。
 
 k-means算法属于无监督学习方法。此算法以k为参数，把n 个对象分为k个簇，以使簇内具有较高的相似度，而且簇间的相似度较低。相似度的计算根据一个簇中对象的平均值（被看作簇的重心）来进行。此算法首先随机选择k个对象，每个对象代表一个聚类的质心。对于其余的每一个对象，根据该对象与各聚类质心之间的距离，把它分配到与之最相似的聚类中。然后，计算每个聚类的新质心。重复上述过程，直到准则函数收敛。k-means算法是一种较典型的逐点修改迭代的动态聚类算法，其要点是以误差平方和为准则函数。逐点修改类中心：一个象元样本按某一原则，归属于某一组类后，就要重新计算这个组类的均值，并且以新的均值作为凝聚中心点进行下一次象元素聚类；逐批修改类中心：在全部象元样本按某一组的类中心分类之后，再计算修改各类的均值，作为下一次分类的凝聚中心点
 

From 00da4cf6d3da172b93ed92dbff408bc98423d668 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 12 Nov 2018 09:50:42 +0800
Subject: [PATCH 1277/1406] Update BNS.0.6.md

---
 assets/src/BNS/BNS.0.6.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.0.6.md b/assets/src/BNS/BNS.0.6.md
index 1673b0bc..49e29537 100644
--- a/assets/src/BNS/BNS.0.6.md
+++ b/assets/src/BNS/BNS.0.6.md
@@ -6,7 +6,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络(Bayesian network)，又称信念网络(Belief Network)，或有向无环图模型(directed acyclic graphical model)，是一种概率图模型，于1985年由Judea Pearl首先提出，它是基于概率推理的图形化网络，可以模拟人类推理过程中因果关系的不确定性处理模型，其网络拓朴结构是一个有向无环图。而贝叶斯公式则是这个概率网络的基础。贝叶斯网络是基于概率推理的数学模型，所谓概率推理就是通过一些变量的信息来获取其他的概率信息的过程，基于概率推理的贝叶斯网络(Bayesian network)是为了解决不定性和不完整性问题而提出的，它对于解决复杂设备不确定性和关联性引起的故障有很大的优势，在多个领域中获得广泛应用。
 
-贝叶斯网络的有向无环图(Directed Acyclic Graph,DAG)中的节点表示随机变量<img width="120" align="center" src="../../images/218.jpg" />，,由代表变量节点及连接这些节点有向边构成。它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。节点代表随机变量，节点间的有向边代表了节点间的互相关系(由父节点指向其子节点)，用条件概率进行表达关系强度，没有父节点的用先验概率进行信息表达。节点变量可以是任何问题的抽象，如：测试值，观测现象，意见征询等。适用于表达和分析不确定性和概率性的事件，应用于有条件地依赖多种控制因素的决策，可以从不完全、不精确或不确定的知识或信息中做出推理。
+贝叶斯网络的有向无环图(Directed Acyclic Graph,DAG)中的节点表示随机变量<img width="130" align="center" src="../../images/218.jpg" />，,由代表变量节点及连接这些节点有向边构成。它们可以是可观察到的变量，或隐变量、未知参数等。认为有因果关系（或非条件独立）的变量或命题则用箭头来连接。若两个节点间以一个单箭头连接在一起，表示其中一个节点是“因(parents)”，另一个是“果(children)”，两节点就会产生一个条件概率值。节点代表随机变量，节点间的有向边代表了节点间的互相关系(由父节点指向其子节点)，用条件概率进行表达关系强度，没有父节点的用先验概率进行信息表达。节点变量可以是任何问题的抽象，如：测试值，观测现象，意见征询等。适用于表达和分析不确定性和概率性的事件，应用于有条件地依赖多种控制因素的决策，可以从不完全、不精确或不确定的知识或信息中做出推理。
 
 使用贝叶斯网络必须知道各个状态之间相关的概率。得到这些参数的过程叫做训练。和训练马尔可夫模型一样，训练贝叶斯网络要用一些已知的数据。比如在训练上面的网络，需要知道一些心血管疾病和吸烟、家族病史等有关的情况。相比马尔可夫链，贝叶斯网络的训练比较复杂，从理论上讲，它是一个 NP-complete问题，也就是说，现阶段没有可以在多项式时间内完成的算法。但是，对于某些应用，这个训练过程可以简化，并在计算上高效实现。
 

From 989f3207da8b8520f9c7bcc25bc395556366e9e8 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 23 Nov 2018 12:32:54 +0800
Subject: [PATCH 1278/1406] Update ABT.md

---
 assets/src/ABT/ABT.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ABT/ABT.md b/assets/src/ABT/ABT.md
index d7d47252..b8c46f79 100644
--- a/assets/src/ABT/ABT.md
+++ b/assets/src/ABT/ABT.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### AdaBoost
+
 自适应提升（AdaBoost：Adaptive Boosting）算法是基于概率近似正确的学习模型下提出的一种提升算法。在分类问题中，AdaBoost通过修改训练样本的权值分布，学习多个弱分类器，并将这些分类器进行线性组合，构成一个强分类器，提高分类性能。其中强分类器可理解为分类精确度高的算法，弱分类器可理解为分类精度低的算法，一般AdaBoost算法是弱分类器的线性组合为：
 <p align="center">
 <img width="160" align="center" src="../../images/74.jpg" />

From 66f6f7f7b5d937daf2d6ae72cf3114b181aaa079 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 23 Nov 2018 12:33:20 +0800
Subject: [PATCH 1279/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 84c24d55..1acae726 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 回归方法是对数值型连续随机变量进行预测和建模的监督学习算法。其特点是标注的数据集具有数值型的目标变量。回归的目的是预测数值型的目标值。
 
-
 常用的回归方法包括:
 * 线性回归：使用超平面拟合数据集 
 * 最近邻算法：通过搜寻最相似的训练样本来预测新样本的值

From 157c1462c5a24ef6c5329df92054d63f9b1eae05 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 23 Nov 2018 12:34:08 +0800
Subject: [PATCH 1280/1406] Update RAM.0.3.md

---
 assets/src/RAM/RAM.0.3.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/RAM/RAM.0.3.md b/assets/src/RAM/RAM.0.3.md
index 1acae726..649fc75c 100644
--- a/assets/src/RAM/RAM.0.3.md
+++ b/assets/src/RAM/RAM.0.3.md
@@ -27,7 +27,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 如果将$y$看作是样本$x$作为正例的可能性，那么可以得到反应$x$作为正例的相对可能性对数几率（logit）
 <p align="center">
-<img width="200" align="center" src="../../images/138.jpg" />
+<img width="190" align="center" src="../../images/138.jpg" />
 </p>
 
 #### 逻辑回归算法

From f7f76ba6ab29beb58476ab27e61afaed3c560e9a Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 2 Dec 2018 20:59:51 +0800
Subject: [PATCH 1281/1406] Update README.md

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index bcbbe450..f1ca466b 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 <p align='left'>
 <img src="https://img.shields.io/badge/build-passing-brightgreen.svg">
 <a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>

From 7049b98a9c31be103a3d7febb1354ddc1432012c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 2 Dec 2018 21:00:23 +0800
Subject: [PATCH 1282/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f1ca466b..ed8b7162 100644
--- a/README.md
+++ b/README.md
@@ -82,7 +82,7 @@
  * [关联规则](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
  * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/SVM/SVM.md)
 
-后面的算法和我们的算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
+后面的算法和算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
 
 #### 算法模型
  * [回归算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.1.md)

From 9cf19c507696eeac3d4900380aaec1fe12ab21ad Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 3 Dec 2018 09:57:31 +0800
Subject: [PATCH 1283/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index ed8b7162..bfc84b45 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,4 @@
 ### Deeplearning Algorithms tutorial
-
 <p align='left'>
 <img src="https://img.shields.io/badge/build-passing-brightgreen.svg">
 <a href="https://twitter.com/perfactsen"><img src="https://img.shields.io/badge/twitter-keke-green.svg?style=flat&colorA=009df2"></a>

From 47bbf26dd59c8bc471876aab18db2b8030d662d6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 3 Dec 2018 09:57:59 +0800
Subject: [PATCH 1284/1406] Update README.md

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index bfc84b45..48d39508 100644
--- a/README.md
+++ b/README.md
@@ -30,7 +30,6 @@
 * 用学习来的算法运用在测试集上累评估算法(可能要设计到调整参数(parameter tuning) 用来验证集(validation set))
 
 #### 机器学习
-
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   

From c04c5f7df85b7a907c7a6304c5b30f7c3e2bb167 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Dec 2018 08:52:21 +0800
Subject: [PATCH 1285/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index cd31cea0..02ccc489 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -3,7 +3,6 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 贝叶斯网络
-
 贝叶斯网络（Bayesian networks or Bayesnets）也称为因果概率网络（CPNs，Causal Probabilistic Networks）、贝叶斯信念网络（BNS，Bayesian belief Networks）或信念网络，是用来对那些带有不确定性问题的问题域进行建模的系统。
 
 从形式上说，贝叶斯网络是由一组以单向箭头相连的节点以及与每个节点相对应的概率函数所构成的网络。对于离散变量的贝叶斯网络，概率函数便具有了概率表的形式。这个网络必须是一个有向无环图，即其中不存在一条起始和终止于同一节点的通路。用图形的方法描述数据间的相互（因果）关系，语义清晰、可理解性强，有助于利用数据间的因果关系进行诊断、预测、分类等分析。因而贝叶斯方法具有独特的不确定性知识表达形式、丰富的概率表达能力、综合先验知识的增量学习特性等优点。

From f7684bb4db24543c8f0bcc3325a1431ad7ee6d82 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Dec 2018 08:52:38 +0800
Subject: [PATCH 1286/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index 02ccc489..2cdca7a0 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -15,7 +15,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络的分析流程通常由三个步骤组成，即(1)网络建立,(2)参数学习或参数设置,(3)网络推理，如图所示.
 <p align="center">
-<img width="400" align="center" src="../../images/25.jpg" />
+<img width="500" align="center" src="../../images/25.jpg" />
 </p>
 
 贝叶斯网络分析流程

From b3207b20f80a85d7133e30e99399f07e557652e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 4 Dec 2018 08:53:28 +0800
Subject: [PATCH 1287/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index 2cdca7a0..f15eb942 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -59,7 +59,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 如果要计算节点D的概率，由于节点D和节点A、B相关，根据边界概率的定义有:
 
 <p align="center">
-<img width="400" align="center" src="../../images/29.jpg" />
+<img width="500" align="center" src="../../images/29.jpg" />
 </p>
 
 在没有任何证据提供给网络的情况下有初始边界概率为

From 4dbf4e688510166ecd92730eab00c7fe50391207 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 5 Dec 2018 09:57:02 +0800
Subject: [PATCH 1288/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index e5d388b8..b0e3fc2b 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -12,6 +12,7 @@
 如今的机器学习领域主要的研究工作在三个方面进行：1）面向任务的研究，研究和分析改进一组预定任务的执行性能的学习系统；2）认知模型，研究人类学习过程并进行计算模拟；3）理论的分析，从理论的层面探索可能的算法和独立的应用领域算法。
 
 #### 卷积神经网络(Convolutional Neural Network)
+
 卷积神经网络（Convolutional Neural Network,CNN）是一种前馈神经网络，它的人工神经元可以响应一部分覆盖范围内的周围单元，对于大型图像处理有出色表现。 它包括卷积层(convolutional layer)和池化层(pooling layer)。
 
 卷积神经网络是近年发展起来，并引起广泛重视的一种高效识别方法。20世纪60年代，Hubel和Wiesel在研究猫脑皮层中用于局部敏感和方向选择的神经元时发现其独特的网络结构可以有效地降低反馈神经网络的复杂性，继而提出了卷积神经网络（Convolutional Neural Networks-简称CNN）。现在，CNN已经成为众多科学领域的研究热点之一，特别是在模式分类领域，由于该网络避免了对图像的复杂前期预处理，可以直接输入原始图像，因而得到了更为广泛的应用。 K.Fukushima在1980年提出的新识别机是卷积神经网络的第一个实现网络。随后，更多的科研工作者对该网络进行了改进。其中，具有代表性的研究成果是Alexander和Taylor提出的“改进认知机”，该方法综合了各种改进方法的优点并避免了耗时的误差反向传播。

From 1a256b3bb6bc0866195e0d50bd720d237c9e5813 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 5 Dec 2018 09:57:14 +0800
Subject: [PATCH 1289/1406] Update ANN.0.7.md

---
 assets/src/ANN/ANN.0.7.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/ANN/ANN.0.7.md b/assets/src/ANN/ANN.0.7.md
index b0e3fc2b..bcc81d07 100644
--- a/assets/src/ANN/ANN.0.7.md
+++ b/assets/src/ANN/ANN.0.7.md
@@ -24,8 +24,6 @@ CNN主要用来识别位移、缩放及其他形式扭曲不变性的二维图
 <p align="center">
 <img width="330" align="center" src="../../images/1.jpg" />
 </p>
-
-
 #### 应用示例
 ```python
 import numpy as np

From 7be9f48a043dc7598991845a6db821322f3cced3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 9 Dec 2018 18:04:35 +0800
Subject: [PATCH 1290/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index f15eb942..d34da37f 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 贝叶斯网络根据每个节点的概率表，在给定部分（一个或多个）节点状态值的前提下，对其余全部或部分节点的概率分布进行预测的过程即为网络的推理过程。
 
-分析流程
+分析流程:
 
 贝叶斯网络的分析流程通常由三个步骤组成，即(1)网络建立,(2)参数学习或参数设置,(3)网络推理，如图所示.
 <p align="center">

From 3aa579462791186fcd7cd9bd1537eec30eb1f2d2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 9 Dec 2018 18:04:52 +0800
Subject: [PATCH 1291/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index d34da37f..80093f59 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -62,7 +62,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 <img width="500" align="center" src="../../images/29.jpg" />
 </p>
 
-在没有任何证据提供给网络的情况下有初始边界概率为
+在没有任何证据提供给网络的情况下有初始边界概率为:
 
 P(D)＝0.8×0.1×0.4＋0.6×0.1×0.6＋0.6×0.9×0.4＋0.3×0.9＋0.6＝0.032＋0.036＋0.0216＋0.0162＝0. 446．
 

From dafac4211a343457e0a25ef9f532d9d6b0f3765f Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 11 Dec 2018 10:00:13 +0800
Subject: [PATCH 1292/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 3e7af32b..b1529b1d 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -3,4 +3,4 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### t－分布随机近邻嵌入(t-SNE)
-t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE)
+t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE).

From 8776cec69772c2919469178961feb819c7284640 Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@qutoutiao.net>
Date: Wed, 16 Jan 2019 10:02:09 +0800
Subject: [PATCH 1293/1406] change page of Readme

---
 README.md               | 5 +++--
 assets/src/EL/EL.0.1.md | 4 ++++
 assets/src/EL/EL.0.2.md | 4 ++++
 assets/src/EL/EL.0.3.md | 4 ++++
 assets/src/EL/EL.0.4.md | 4 ++++
 5 files changed, 19 insertions(+), 2 deletions(-)
 create mode 100644 assets/src/EL/EL.0.1.md
 create mode 100644 assets/src/EL/EL.0.2.md
 create mode 100644 assets/src/EL/EL.0.3.md
 create mode 100644 assets/src/EL/EL.0.4.md

diff --git a/README.md b/README.md
index 48d39508..dbf39039 100644
--- a/README.md
+++ b/README.md
@@ -30,6 +30,7 @@
 * 用学习来的算法运用在测试集上累评估算法(可能要设计到调整参数(parameter tuning) 用来验证集(validation set))
 
 #### 机器学习
+
 * 机器学习：机器学习是计算机科学的一个子领域，在人工智能领域，机器学习逐渐发展成模式识别和计算科学理论的研究。通俗的讲机器学习是一种能够赋予机器学习的能力，可以让它完成直接编程无法完成的功能的方法。但从实践的意义上来说，机器学习是一种通过利用数据，训练出模型，然后使用模型预测的一种方法。
 * 机器学习的应用：机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA序列测序、语音和手写识别、战略游戏和机器人等领域。下面开启我们的机器学习！
   
@@ -80,7 +81,7 @@
  * [关联规则](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/ARS/ARS.md)
  * [支持向量机（SVM）](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/SVM/SVM.md)
 
-后面的算法和算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
+后面的算法和我们的算法模型，我会持续更新整理，后续的算法章节会不断的补上，希望可以对新入门学习AI开发和算法的开发者有所帮助！
 
 #### 算法模型
  * [回归算法](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/RAM/RAM.0.1.md)
@@ -152,7 +153,7 @@
      * [拉普拉斯特征映射(Laplacian Eigenmaps)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.7.md)
      * [t－分布随机近邻嵌入(t-SNE)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.8.md)
      * [深度自动编码器(Deep Autoencoder Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.9.md)
- * [集成算法]()
+ * [集成算法(Ensemble Learning)]()
       * [Boosting]()
       * [Bagging]()
       * [AdaBoost]()
diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
new file mode 100644
index 00000000..758daf19
--- /dev/null
+++ b/assets/src/EL/EL.0.1.md
@@ -0,0 +1,4 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
new file mode 100644
index 00000000..758daf19
--- /dev/null
+++ b/assets/src/EL/EL.0.2.md
@@ -0,0 +1,4 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
diff --git a/assets/src/EL/EL.0.3.md b/assets/src/EL/EL.0.3.md
new file mode 100644
index 00000000..758daf19
--- /dev/null
+++ b/assets/src/EL/EL.0.3.md
@@ -0,0 +1,4 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
diff --git a/assets/src/EL/EL.0.4.md b/assets/src/EL/EL.0.4.md
new file mode 100644
index 00000000..758daf19
--- /dev/null
+++ b/assets/src/EL/EL.0.4.md
@@ -0,0 +1,4 @@
+### Deeplearning Algorithms tutorial
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+

From e887b42167c3c8c63cc9416978b66a85f0494d95 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 Jan 2019 10:04:32 +0800
Subject: [PATCH 1294/1406] Update README.md

---
 README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index dbf39039..c3307002 100644
--- a/README.md
+++ b/README.md
@@ -153,9 +153,9 @@
      * [拉普拉斯特征映射(Laplacian Eigenmaps)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.7.md)
      * [t－分布随机近邻嵌入(t-SNE)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.8.md)
      * [深度自动编码器(Deep Autoencoder Networks)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/DRA/DRA.0.9.md)
- * [集成算法(Ensemble Learning)]()
-      * [Boosting]()
-      * [Bagging]()
+ * [集成算法(Ensemble Learning)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/EL/EL.0.1.md)
+      * [Boosting](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/EL/EL.0.2.md)
+      * [Bagging](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/EL/EL.0.3.md)
       * [AdaBoost]()
       * [堆叠泛化（混合）]()
       * [GBM 算法]()

From ab3ba4458f4a49ca381e8c7d8c1de2460fa0efc7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 16 Jan 2019 10:05:31 +0800
Subject: [PATCH 1295/1406] Update EL.0.1.md

---
 assets/src/EL/EL.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
index 758daf19..8a8dbbba 100644
--- a/assets/src/EL/EL.0.1.md
+++ b/assets/src/EL/EL.0.1.md
@@ -2,3 +2,5 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+#### 集成算法(Ensemble Learning)
+

From fd154dd80a68d5140532f4140cafd012de4ec5bc Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 Jan 2019 18:40:31 +0800
Subject: [PATCH 1296/1406] Update EL.0.1.md

---
 assets/src/EL/EL.0.1.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
index 8a8dbbba..f6b383ce 100644
--- a/assets/src/EL/EL.0.1.md
+++ b/assets/src/EL/EL.0.1.md
@@ -4,3 +4,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 集成算法(Ensemble Learning)
 
+集成学习(Ensemble Learning)是使用一序列学习器进行学习，并使用某种规则把各个学习结果进行整合从而获得比单个学习器更好的学习效果的一种机器学习方法。集成学习中多个学习器被称为“弱学习器”，若这些弱学习器都是一个种类的，则被称为是同质的；若这些弱学习器不全是一个种类的，则被称为异质的。一般情况下，集成学习中的多个学习器都是同质的“弱学习器”
+

From f6905b84652089564ae7918512634abf7be4dfd9 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 Jan 2019 18:45:22 +0800
Subject: [PATCH 1297/1406] Update EL.0.1.md

---
 assets/src/EL/EL.0.1.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
index f6b383ce..522b1816 100644
--- a/assets/src/EL/EL.0.1.md
+++ b/assets/src/EL/EL.0.1.md
@@ -4,5 +4,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 集成算法(Ensemble Learning)
 
-集成学习(Ensemble Learning)是使用一序列学习器进行学习，并使用某种规则把各个学习结果进行整合从而获得比单个学习器更好的学习效果的一种机器学习方法。集成学习中多个学习器被称为“弱学习器”，若这些弱学习器都是一个种类的，则被称为是同质的；若这些弱学习器不全是一个种类的，则被称为异质的。一般情况下，集成学习中的多个学习器都是同质的“弱学习器”
+集成学习(Ensemble Learning)是使用一序列学习器进行学习，并使用某种规则把各个学习结果进行整合从而获得比单个学习器更好的学习效果的一种机器学习方法。集成学习中多个学习器被称为“弱学习器”，如果这些弱学习器都是一个种类的，则被称为是同质的；若这些弱学习器不全是一个种类的，则被称为异质的。一般情况下，集成学习中的多个学习器都是同质的“弱学习器”
+
+集成学习在各个规模的数据集上都有很好的策略。
+* 数据集大：划分成多个小数据集，学习多个模型进行组合
+* 数据集小：利用Bootstrap方法进行抽样，得到多个数据集，分别训练多个模型再进行组合
+
 

From fa084776a51ea62d63652971ad1a26608485a135 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 Jan 2019 18:46:14 +0800
Subject: [PATCH 1298/1406] Update EL.0.1.md

---
 assets/src/EL/EL.0.1.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
index 522b1816..6a6a1b28 100644
--- a/assets/src/EL/EL.0.1.md
+++ b/assets/src/EL/EL.0.1.md
@@ -10,4 +10,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 * 数据集大：划分成多个小数据集，学习多个模型进行组合
 * 数据集小：利用Bootstrap方法进行抽样，得到多个数据集，分别训练多个模型再进行组合
 
+集成算法(Ensemble Learning)主要包括:
+
+* Boosting
+* Bagging
+* AdaBoost
+* 堆叠泛化（混合）
+* GBM 算法
+* GBRT 算法
+* 随机森林
 

From 629211508936bdd8687e8f35cb37aa54ebb101bd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 Jan 2019 18:47:32 +0800
Subject: [PATCH 1299/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 758daf19..594201d6 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -2,3 +2,6 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+#### Bagging
+
+Bagging是bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。

From 1113a36f9adb46d5a20b1771d68bad85e24a36b2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 12 Feb 2019 10:20:27 +0800
Subject: [PATCH 1300/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 594201d6..4ac16608 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -4,4 +4,4 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Bagging
 
-Bagging是bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
+Bagging是Bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。

From 00199d6f26d80f21b44aadd196a23d7112b65cfd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 12 Feb 2019 10:25:41 +0800
Subject: [PATCH 1301/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 4ac16608..4e7ee2b3 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -5,3 +5,5 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 #### Bagging
 
 Bagging是Bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
+
+Baggging 和Boosting都是模型融合的方法，可以将弱分类器融合之后形成一个强分类器，而且融合之后的效果会比最好的弱分类器更好。

From b22c9435b3ae609805a3308961aded932a4f83f1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 12 Feb 2019 10:26:17 +0800
Subject: [PATCH 1302/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 4e7ee2b3..3558ee88 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -7,3 +7,11 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 Bagging是Bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
 
 Baggging 和Boosting都是模型融合的方法，可以将弱分类器融合之后形成一个强分类器，而且融合之后的效果会比最好的弱分类器更好。
+
+Bagging即套袋法，其算法过程如下：
+
+从原始样本集中抽取训练集。每轮从原始样本集中使用Bootstraping的方法抽取n个训练样本（在训练集中，有些样本可能被多次抽取到，而有些样本可能一次都没有被抽中）。共进行k轮抽取，得到k个训练集。（k个训练集之间是相互独立的）
+
+* 每次使用一个训练集得到一个模型，k个训练集共得到k个模型。（注：这里并没有具体的分类算法或回归方法，我们可以根据具体问题采用不同的分类或回归方法，如决策树、感知器等）
+
+* 对分类问题：将上步得到的k个模型采用投票的方式得到分类结果；对回归问题，计算上述模型的均值作为最后的结果。（所有模型的重要性相同）

From 02cc49caf7e6587050314ab8894b3a8cdd8f6b2c Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 12 Feb 2019 10:29:48 +0800
Subject: [PATCH 1303/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 3558ee88..7a812dce 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -2,7 +2,7 @@
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
-#### Bagging
+#### Boosting
 
 Bagging是Bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
 

From 6c9f61c049cc1d1fd807accc19ed49b99680c6f4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 14 Feb 2019 18:21:15 +0800
Subject: [PATCH 1304/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index a8e97b2e..c936d460 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -18,7 +18,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 聚类分析
 
-聚类分析（英语：Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
+聚类分析（Cluster analysis，亦称为群集分析）是对于统计数据分析的一门技术，在许多领域受到广泛应用，包括机器学习，数据挖掘，模式识别，图像分析以及生物信息。聚类是把相似的对象通过静态分类的方法分成不同的组别或者更多的子集（subset），这样让在同一个子集中的成员对象都有相似的一些属性，常见的包括在坐标系中更短的空间距离等。
 
 一般把数据聚类归纳为一种非监督学习。
 

From 409b4ff601ae48ea3f3a9975c164d028f6483db2 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 1 Mar 2019 10:27:13 +0800
Subject: [PATCH 1305/1406] Update EL.0.1.md

---
 assets/src/EL/EL.0.1.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/EL/EL.0.1.md b/assets/src/EL/EL.0.1.md
index 6a6a1b28..3cbe8ee5 100644
--- a/assets/src/EL/EL.0.1.md
+++ b/assets/src/EL/EL.0.1.md
@@ -7,6 +7,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 集成学习(Ensemble Learning)是使用一序列学习器进行学习，并使用某种规则把各个学习结果进行整合从而获得比单个学习器更好的学习效果的一种机器学习方法。集成学习中多个学习器被称为“弱学习器”，如果这些弱学习器都是一个种类的，则被称为是同质的；若这些弱学习器不全是一个种类的，则被称为异质的。一般情况下，集成学习中的多个学习器都是同质的“弱学习器”
 
 集成学习在各个规模的数据集上都有很好的策略。
+
 * 数据集大：划分成多个小数据集，学习多个模型进行组合
 * 数据集小：利用Bootstrap方法进行抽样，得到多个数据集，分别训练多个模型再进行组合
 

From f094d56154bbe021b132874f6f27bda36bf3c5b6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 11 Mar 2019 10:04:29 +0800
Subject: [PATCH 1306/1406] Update DRA.0.2.md

---
 assets/src/DRA/DRA.0.2.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.2.md b/assets/src/DRA/DRA.0.2.md
index 38dc3675..50574b30 100644
--- a/assets/src/DRA/DRA.0.2.md
+++ b/assets/src/DRA/DRA.0.2.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 

From d24e9ddc877af18386bfaa0e5569560085b36542 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 26 Mar 2019 20:01:25 +0800
Subject: [PATCH 1307/1406] Update DRA.0.6.md

---
 assets/src/DRA/DRA.0.6.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
index 9c0cea4e..97764db2 100644
--- a/assets/src/DRA/DRA.0.6.md
+++ b/assets/src/DRA/DRA.0.6.md
@@ -8,3 +8,14 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 从数据本身的的性质特征来看，数据降维可以大致分为线性降维和非线性降维两种技术方法。其中，线性降维技术仅对于数据维数相对较低、且具有全局线性结构的数据有着很好的降维效果。然而，在实际的科学研究中，科研工作者却需要面对海量的非线性高维数据。因此，能够有效处理高维非线性数据的方法亟待被提出，本文将介绍一种用于处理高维非线性数据的降维方法。
 
 局部线性嵌入（Locally linear embedding, LLE）是一种非线性的降维方法，该算法由 Sam T.Roweis等人于2000年提出并发表在《Science》杂志上。LLE试图保留原始高维数据的局部性质，通过假设局部原始数据近似位于一张超平面上，从而使得该局部的某一个数据可以由其邻域数据线性表示。
+
+Sam T.Roweis 和 Lawrence K.Saul提出局部线性嵌入（Locally linear embedding, LLE）算法，它是针对非线性数据的一种新的降维技术，并且能够使降维后的数据保持原有的拓扑结构。 LLE算法可以广泛的应用于非线性数据的降维、聚类以及图像分割等领域。 
+
+局部线性嵌入(Locally linear embedding, LLE)是最新提出的非线性降维方法。该算法即具有处理非线性数据的优点又有线性降维方法计算性能的优越性。 简单的讲，该方法是将高维流型用剪刀剪成很多的小块，每一小块可以用平面代替，然后再低维中重新拼合出来， 且要求保留各点之间的拓扑关系不变。整个问题最后被转化为两个二次规划问题。
+
+局部线性嵌入(Locally linear embedding, LLE)算法可以归结为三步:
+1. 寻找每个样本点的k个近邻点；
+2. 由每个样本点的近邻点计算出该样本点的局部重建权值矩阵；
+3. 由该样本点的局部重建权值矩阵和其近邻点计算出该样本点的输出值。
+
+局部线性嵌入算法的第一步是计算出每个样本点的k个近邻点。把相对于所求样本点距离最近的k个样本点规定为所求样本点的k个近邻点。k是一个预先给定值。Sam T.Roweis 和 Lawrence K.Saul算法采用的是欧氏距离，则减轻复杂的计算。然而本文是假定高维空间中的数据是非线性分布的，采用了diijstra距离。Dijkstra 距离是一种测地距离，它能够保持样本点之间的曲面特性，在ISOMAP算法中有广泛的应用。针对样本点多的情况，普通的dijkstra算法不能满足LLE算法的要求。

From b6073935ed5216ce3f4258226dd3e04b7e906fb6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 4 Apr 2019 15:46:34 +0800
Subject: [PATCH 1308/1406] Update DRA.0.6.md

---
 assets/src/DRA/DRA.0.6.md | 335 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 335 insertions(+)

diff --git a/assets/src/DRA/DRA.0.6.md b/assets/src/DRA/DRA.0.6.md
index 97764db2..41683bc3 100644
--- a/assets/src/DRA/DRA.0.6.md
+++ b/assets/src/DRA/DRA.0.6.md
@@ -19,3 +19,338 @@ Sam T.Roweis 和 Lawrence K.Saul提出局部线性嵌入（Locally linear embedd
 3. 由该样本点的局部重建权值矩阵和其近邻点计算出该样本点的输出值。
 
 局部线性嵌入算法的第一步是计算出每个样本点的k个近邻点。把相对于所求样本点距离最近的k个样本点规定为所求样本点的k个近邻点。k是一个预先给定值。Sam T.Roweis 和 Lawrence K.Saul算法采用的是欧氏距离，则减轻复杂的计算。然而本文是假定高维空间中的数据是非线性分布的，采用了diijstra距离。Dijkstra 距离是一种测地距离，它能够保持样本点之间的曲面特性，在ISOMAP算法中有广泛的应用。针对样本点多的情况，普通的dijkstra算法不能满足LLE算法的要求。
+
+
+应用示例：
+```python
+
+import numpy
+import sources
+
+from sklearn import manifold
+from sklearn.utils.extmath import randomized_svd
+from sklearn.neighbors import NearestNeighbors
+
+
+from wordreps import WordReps
+from scipy.sparse import csr_matrix, eye
+from scipy.sparse.linalg import eigsh
+from scipy.sparse.linalg.eigen.arpack.arpack import ArpackNoConvergence
+
+from scipy.io import savemat, loadmat
+
+import sys
+import time
+import argparse
+import collections
+
+
+class MetaEmbed():
+
+    def __init__(self, wordreps, words):
+        self.words = words
+        self.ids = {}
+        for (i,word) in enumerate(words):
+            self.ids[word] = i
+
+        self.reps = wordreps
+        self.dims = [x.dim for x in self.reps]
+        self.embeds = []
+        N = len(words)
+
+        # Create the source embedding matrices
+        write("Creating source embedding matrices...")
+        for i in range(len(self.reps)):
+            M = numpy.zeros((self.reps[i].dim, N), dtype=numpy.float64)
+            for j in range(N):
+                M[:,j] = self.reps[i].vects[self.words[j]]
+            self.embeds.append(M)
+        write("done\n")
+        pass
+
+    def compute_neighbours(self, nns):
+        """
+        Compute the nearest neighbours for each embedding.
+        """
+        self.NNS = []
+        for i in range(len(self.embeds)):
+            start_time = time.clock()
+            write("Computing nearest neighbours for embedding no = %d ..." % i)
+            nbrs = NearestNeighbors(n_neighbors=nns, algorithm='ball_tree').fit(self.embeds[i].T)
+            distances, indices = nbrs.kneighbors(self.embeds[i].T)
+            self.NNS.append(indices[:,1:])
+            end_time = time.clock()
+            write("Done (%s sec.)\n" % str(end_time - start_time))
+        pass
+
+    def show_nns(self, word ,nns):
+        """
+        Print nearest neigbours for a word in different embeddings.
+        """
+        for i in range(len(self.embeds)):
+            print "Showing nearest neighbours for = %s" % word
+            print "\nEmbedding no = %d" % i
+            for s in self.NNS[i][self.ids[word], :][:nns]:
+                print self.words[s]
+        pass
+
+    def compute_weights(self):
+        """
+        Computes the reconstruction weights.
+        """
+        start_time = time.clock()
+        T = 10  # no. of iterations.
+        alpha = 0.01  # learning rate.
+        N = len(self.words)
+        self.W = numpy.zeros((N, N), dtype=numpy.float64)
+
+        # initialise the weights.
+        for i in range(N):
+            nns = set()
+            for j in range(len(self.embeds)):
+                for x in self.NNS[j][i,:]:
+                    nns.add(x)
+            val = 1.0 / float(len(nns))
+            for j in nns:
+                self.W[i,j] = val
+
+        # iterate
+        for i in range(N):
+            write("\x1b[2K\rLearning weights for (%d of %d) = %s" % (i, N, self.words[i]))
+            for t in range(T):                       
+                d = [self.embeds[j][:,i] - numpy.sum([self.W[i,k] * self.embeds[j][:,k] for k in self.NNS[j][i,:]], axis=0) for j in range(len(self.embeds))]
+                #for j in range(len(self.embeds)):
+                #    d.append(self.embeds[j][:,i] - numpy.sum([self.W[i,k] * self.embeds[j][:,k] for k in self.NNS[j][i,:]], axis=0))
+                
+                grad = numpy.zeros(N, dtype=numpy.float64)
+                for j in range(len(self.embeds)):
+                    for k in self.NNS[j][i,:]:
+                        grad[k] += -2.0 * numpy.dot(d[j], self.embeds[j][:,k])
+        
+                self.W[i,:] -= (alpha * grad)
+        
+            total = numpy.sum(self.W[i,:])
+            if total != 0:
+                self.W[i,:] = self.W[i,:] / total
+        write("\n")
+        end_time = time.clock()
+        write("Done (took %s seconds)\n" % str(end_time - start_time))
+        pass
+
+    def save_weights(self, fname):
+        """
+        Save the weight matrix to a disk file.
+        """
+        savemat(fname, {"W":self.W})
+        pass
+
+    def load_weights(self, fname):
+        """
+        Load the weight matrix from a disk file.
+        """
+        self.W = loadmat(fname)["W"]
+        pass
+
+    def test_compute_weights(self):
+        """
+        Check whether the weights are computed correctly
+        """
+        N = len(self.words)
+        # Check whether non-neighbours have weights equal to zero.
+        write("Checking whether non-neighbours have zero weights...\n")
+        for i in range(N):
+            pred_nns = set(numpy.where(self.W[i,:] != 0)[0])
+            nns = set()
+            for j in range(len(self.embeds)):
+                nns = nns.union(set(self.NNS[j][i,:]))
+            assert(pred_nns == nns)
+
+        # Check whether reconstruction weights add upto one.
+        write("Checking whether weights add to 1...\n")
+        for i in range(N):
+            assert(numpy.allclose(numpy.sum(self.W[i,:]), 1)) 
+
+        # print nearest neighbours and their weights
+        nn_file = open("../work/nn.csv", 'w')
+        for i in range(N):
+            nn_file.write("%s, " % self.words[i])
+            L = []
+            for j in range(N):
+                if self.W[i,j] != 0:
+                    L.append((self.words[j], self.W[i,j]))
+            L.sort(lambda x, y: -1 if x[1] > y[1] else 1)
+            for (w, val) in L:
+                nn_file.write("%s, %f, " % (w, val))
+            nn_file.write("\n")
+        nn_file.close()
+        pass
+
+    def compute_M(self):
+        """
+        Compute the smallest eigenvectors of M = (I - W')\T(I - W').
+        """
+        # Building W'
+        N = len(self.words)
+        start_time = time.clock()
+        write("Computing W'...")
+        for i in range(N):
+            z = numpy.zeros(N)
+            write("Completed %d of %d\r" % (i, N))
+            for nns in self.NNS:
+                z[nns[i,:]] += 1
+            self.W[i,:] = z * self.W[i,:]
+        end_time = time.clock()
+        write("Done (took %s seconds)\n" % str(end_time - start_time))
+
+        # Computing M.
+        start_time = time.clock()
+        write("Computing M....")
+        self.W = csr_matrix(self.W)
+        M = eye(N, format=self.W.format) - self.W
+        M = (M.T * M).tocsr()
+        end_time = time.clock()
+        write("Done (took %s seconds)\n" % str(end_time - start_time))
+        return M
+
+    def compute_embeddings(self, k, M, embed_fname):
+        """
+        Perform eigen decomposition.
+        """
+        N = len(self.words)
+        start_time = time.clock()
+        write("Computing Eigen decomposition...")
+        s, V =  eigsh(M, k+1, tol=1E-6, which="SA", maxiter=100)
+        end_time = time.clock()
+        write("Done (took %s seconds)\n" % str(end_time - start_time))
+        P = V[:, 1:]
+        err = numpy.sum(s[1:])
+        write("Projection error = %f\n" % err)
+        
+        write("Writing embeddings to file...")
+        # Write embeddings to file.
+        with open(embed_fname, 'w') as embed_file:
+            for i in range(N):
+                embed_file.write("%s %s\n" % (self.words[i], " ".join([str(x) for x in P[i,:]])))
+        write("Done\n")
+        pass
+
+
+def write(msg):
+    sys.stdout.write(msg)
+    sys.stdout.flush()
+    pass
+
+
+def meta_embed(embeddings, words, nns, comps, embed_path):
+    """
+    Perform meta-embedding using LLE.
+    """
+    ME = MetaEmbed(embeddings, words)
+    ME.compute_neighbours(nns)
+    #ME.show_nns("king", 5)
+
+    #ME.compute_weights_parallel()
+    ME.compute_weights()
+
+    #ME.save_weights("../work/weights_%d" % nns)
+    #ME.load_weights("../work/weights+n=%d.meta" % nns)
+    #ME.test_compute_weights()
+    M = ME.compute_M()
+    for k in comps:
+        embed_fname = "%s/n=%d+k=%d" % (embed_path, nns, k)
+        write("Embedding NNS = %d, Components (k) = %d\n" % (nns, k))
+        try:
+            ME.compute_embeddings(k, M, embed_fname)
+        except ArpackNoConvergence as e:
+            print e
+    return ME
+
+
+def baseline_concatenate(embeddings, words, embed_fname):
+    """
+    Concatenate embeddings to create co-embeddings.
+    """
+    dim = sum([x.dim for x in embeddings])
+
+    print "Concatenation dimension =", dim
+    # concatenate the vectors.
+    with open(embed_fname, 'w') as embed_file:
+        for (i,word) in enumerate(words):
+            L = []
+            for x in embeddings:
+                w = 8 if x.dim == 300 else 1
+                #w = 1
+                L.append(w * x.vects[word])
+                
+            z = numpy.concatenate(L)            
+            embed_file.write("%s %s\n" % (word, " ".join([str(x) for x in z])))
+    pass
+
+def get_common_words(embeddings):
+    words = set(embeddings[0].vocab)
+    for i in range(1, len(embeddings)):
+        words = words.intersection(set(embeddings[i].vocab))
+    return words
+
+
+def get_selected_words(fname):
+    words = []
+    with open(fname) as F:
+        for line in F:
+            words.append(line.strip())
+    return words
+
+def perform_embedding(nns, comps):
+    print "Neigbourhood size = %d" % nns
+    
+    #embed_sett
+    embed_settings = sources.embed_settings
+    embeddings = []
+    for (embd_fname, dim) in embed_settings:
+        start_time = time.clock()
+        sys.stdout.write("Loading %s -- (%d dim) ..." % (embd_fname, dim))
+        sys.stdout.flush()        
+        WR = WordReps()
+        WR.read_model(embd_fname, dim)
+        end_time = time.clock()
+        sys.stdout.write("\nDone. took %s seconds\n" % str(end_time - start_time))
+        sys.stdout.flush()
+        embeddings.append(WR)
+
+    common_words = get_common_words(embeddings)
+    selected_words = get_selected_words("../work/selected-words")
+    words = []
+    for word in selected_words:
+        if word in common_words and word not in words:
+            words.append(word)
+    print "No. of common words =", len(common_words)
+    print "Vocabulary size =", len(words)
+    ME = meta_embed(embeddings, words, nns, comps, "../work/meta-embeds")
+    pass
+
+def save_embedding(words, WR, fname):
+    F = open(fname, 'w')
+    for w in words:
+        if w in WR.vects:
+            F.write("%s " % w)
+            F.write("%s\n" % " ".join([str(x) for x in WR.vects[w]]))
+        # elif w.lower() in WR.vects:
+        #     F.write("%s " % w.lower())
+        #     F.write("%s\n" % " ".join([str(x) for x in WR.vects[w.lower()]]))
+    F.close()
+    pass
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("-nns", type=int, help="number of nearest neighbours")
+    parser.add_argument("-comps", type=str, help="components for the projection")
+    args = parser.parse_args()
+    comps = [int(x) for x in args.comps.split(',')]
+    perform_embedding(args.nns, comps)
+    pass
+
+if __name__ == '__main__':
+    main()
+    pass
+
+```

From 5be22aef8fb806d1add1f019e6e36246f97b69b5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 11 Oct 2019 09:44:32 +0800
Subject: [PATCH 1309/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 7a812dce..36d0ff16 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -15,3 +15,6 @@ Bagging即套袋法，其算法过程如下：
 * 每次使用一个训练集得到一个模型，k个训练集共得到k个模型。（注：这里并没有具体的分类算法或回归方法，我们可以根据具体问题采用不同的分类或回归方法，如决策树、感知器等）
 
 * 对分类问题：将上步得到的k个模型采用投票的方式得到分类结果；对回归问题，计算上述模型的均值作为最后的结果。（所有模型的重要性相同）
+
+
+Boosting这其实思想相当的简单，大概是，对一份数据，建立M个模型（比如分类），一般这种模型比较简单，称为弱分类器(weak learner)每次分类都将上一次分错的数据权重提高一点再进行分类，这样最终得到的分类器在测试数据与训练数据上都可以得到比较好的成绩。

From 6178e97fbfc3208d88927a37b127dbf1cd5fb2a3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 Oct 2019 11:07:45 +0800
Subject: [PATCH 1310/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 0a29994c..797cd61c 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -3,3 +3,9 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 拉普拉斯特征映射(Laplacian Eigenmaps)
+
+拉普拉斯特征映射（Laplacian Eigenmaps，LE），就是将核函数方法应用在局部保持投影的非监督降维方法，也是无监督降维的一种方法，LE方法的直观思想是希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近。LE可以反映出数据内在的流形结构。
+
+拉普拉斯特征映射是一种基于图的降维算法，它希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近，从而在降维后仍能保持原有的数据结构。 借鉴了图论里面的Laplacian矩阵，把每个样本点看成图中的一个节点，通过样本距离或者邻接矩阵得到W（可以表征样本间的相似关系，用来重构数据流形的局部结构特征），再通过D = diag(sum(W,2))，得到对角的度矩阵（每个元素都是行和或者列和），然后通过L = D - W 得到Laplacian矩阵。
+
+Laplacian Eigenmaps算法的主要思想是，如果两个数据实例i和j很相似，那么i和j在降维后目标子空间中应该尽量接近。设数据实例的数目为n，目标子空间即最终的降维目标的维度为m。定义n×m大小的矩阵Y，其中每一个行向量yTi是数据实例i在目标m维子空间中的向量表示（即降维后的数据实例i）。

From 94c034864a629d7453965649d8528dcbeb170cfa Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@innotechx.com>
Date: Fri, 18 Oct 2019 11:30:38 +0800
Subject: [PATCH 1311/1406] change page of images

---
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 assets/images/446.jpg | Bin 0 -> 4595 bytes
 assets/images/447.jpg | Bin 0 -> 6825 bytes
 assets/images/448.jpg | Bin 0 -> 6231 bytes
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From 67e0fbaa0b1b1ae0356e852d254c44e6b62bd494 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 Oct 2019 11:52:01 +0800
Subject: [PATCH 1312/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 48 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 797cd61c..0d533a9d 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -9,3 +9,51 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 拉普拉斯特征映射是一种基于图的降维算法，它希望相互间有关系的点（在图中相连的点）在降维后的空间中尽可能的靠近，从而在降维后仍能保持原有的数据结构。 借鉴了图论里面的Laplacian矩阵，把每个样本点看成图中的一个节点，通过样本距离或者邻接矩阵得到W（可以表征样本间的相似关系，用来重构数据流形的局部结构特征），再通过D = diag(sum(W,2))，得到对角的度矩阵（每个元素都是行和或者列和），然后通过L = D - W 得到Laplacian矩阵。
 
 Laplacian Eigenmaps算法的主要思想是，如果两个数据实例i和j很相似，那么i和j在降维后目标子空间中应该尽量接近。设数据实例的数目为n，目标子空间即最终的降维目标的维度为m。定义n×m大小的矩阵Y，其中每一个行向量yTi是数据实例i在目标m维子空间中的向量表示（即降维后的数据实例i）。
+
+
+Laplacian Eigenmap算法主要步骤:
+
+1. 建立邻接图：这里采用ϵ−最近邻图和K−最近邻图都能够解决问题。两种方法各有利弊，前者几何解释清楚，并且邻接矩阵天然是对称的，然而参数选择有困难，并且图的连通性未必有好的保证；后者参数选择容易，且图的连接性较好，但是几何解释不清晰。
+
+
+2. 赋权：我们常用热核来赋给权重，即对于连通的两个点i,i′,令<img width="200" align="center" src="../../images/440.jpg" />；而对其它点对权值赋0. 最终我们可以用邻接矩阵W来表示这个图.
+
+3. 计算Laplace算子矩阵：完成建图后，我们定义顶点vi的度是:
+<p align="center">
+<img width="200" align="center" src="../../images/441.jpg" />
+</p>
+
+并构造一个度矩阵:
+
+<p align="center">
+<img width="200" align="center" src="../../images/442.jpg" />
+</p>
+
+由此即可得到未归一化的图Laplace矩阵:
+
+<p align="center">
+<img width="200" align="center" src="../../images/443.jpg" />
+</p>
+
+容易说明, L是对称半正定矩阵，特征值是非负实数，且0是L的特征值，而特征向量是常1向量。值得说明的是我们经常采用的是经过归一化的L矩阵，规范化的方法是:
+
+<p align="center">
+<img width="200" align="center" src="../../images/444.jpg" />
+</p>
+
+4. 计算特征向量：即解以下问题：
+
+<p align="center">
+<img width="200" align="center" src="../../images/445.jpg" />
+</p>
+
+得到特征值<img width="200" align="center" src="../../images/446.jpg" />
+
+5. 特征映射：（先验地）假定低维流形维数d的值，并将数据映射到特征空间上，即
+
+<p align="center">
+<img width="200" align="center" src="../../images/447.jpg" />
+</p>
+
+这就是拉普拉斯特征映射(Laplacian Eigenmaps)算法进行数据降维处理的全过程。
+

From 1518b01dffb75401a40ae22891c030bba5ef210e Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@innotechx.com>
Date: Fri, 18 Oct 2019 11:54:08 +0800
Subject: [PATCH 1313/1406] change page of images

---
 assets/images/446.jpg | Bin 4595 -> 6825 bytes
 assets/images/447.jpg | Bin 6825 -> 6231 bytes
 assets/images/448.jpg | Bin 6231 -> 0 bytes
 3 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 assets/images/448.jpg

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diff --git a/assets/images/447.jpg b/assets/images/447.jpg
index 45c0ec5d92f637321f8124e54cfbbd88846bddf9..7c0f737268cafad34367a59bd8d9d3bc714612a1 100644
GIT binary patch
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B9ohf@


From b2d75c72b3292ca9b0dde3f244b02697d6229712 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 Oct 2019 12:07:52 +0800
Subject: [PATCH 1314/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 0d533a9d..2f114ed1 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -47,7 +47,7 @@ Laplacian Eigenmap算法主要步骤:
 <img width="200" align="center" src="../../images/445.jpg" />
 </p>
 
-得到特征值<img width="200" align="center" src="../../images/446.jpg" />
+得到特征值<img width="200" align="center" src="../../images/445.jpg" />
 
 5. 特征映射：（先验地）假定低维流形维数d的值，并将数据映射到特征空间上，即
 

From 07948652f8030f3bfecef083ab5f122aa0be2b3d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Fri, 18 Oct 2019 12:08:11 +0800
Subject: [PATCH 1315/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 2f114ed1..0d533a9d 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -47,7 +47,7 @@ Laplacian Eigenmap算法主要步骤:
 <img width="200" align="center" src="../../images/445.jpg" />
 </p>
 
-得到特征值<img width="200" align="center" src="../../images/445.jpg" />
+得到特征值<img width="200" align="center" src="../../images/446.jpg" />
 
 5. 特征映射：（先验地）假定低维流形维数d的值，并将数据映射到特征空间上，即
 

From 0f6f9d1fa336eba337bd6d39daf20637997b41e4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 19 Oct 2019 17:44:57 +0800
Subject: [PATCH 1316/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 0d533a9d..8952f4e9 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -57,3 +57,36 @@ Laplacian Eigenmap算法主要步骤:
 
 这就是拉普拉斯特征映射(Laplacian Eigenmaps)算法进行数据降维处理的全过程。
 
+应用示例:
+```python
+  # import libraries
+  import numpy as np
+  import matplotlib.pyplot as plt
+  %matplotlib inline
+  from mpl_toolkits.mplot3d import Axes3D
+  from IPython.core.pylabtools import figsize
+  from IPython.core.interactiveshell import InteractiveShell
+  InteractiveShell.ast_node_interactivity = "all";
+  np.random.seed(8888)
+  plt.style.use('default')
+  plt.rcParams['figure.facecolor'] = 'white'
+  # ignore warnings
+  import warnings
+  warnings.filterwarnings('ignore');
+
+  # draw samples to create the grid
+  x = np.linspace(-2, 2, 50)
+  y = np.linspace(-2, 2, 50)
+  x,y = np.meshgrid(x,y)
+
+  # scalar function
+  z = x*np.exp(-1*(x**2 + y**2))
+
+  # plot 3d surface
+  fig = plt.figure(figsize = (6, 6))
+  ax = fig.gca(projection = '3d')
+  colors = plt.cm.jet(z*4)
+  ax.plot_surface(x, y, z, rstride=1, cstride=1, facecolors=colors, cmap=plt.cm.coolwarm, linewidth=1.4, alpha=0.8)
+  ax.set_title(r'$f(x, y)=x e^{-\left(x^{2}+y^{2}\right)}$', size=14);
+  
+```

From 92f7fdaf3f76b658461b415d026d617b89511eff Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 20 Oct 2019 19:29:01 +0800
Subject: [PATCH 1317/1406] Update DRA.0.7.md

---
 assets/src/DRA/DRA.0.7.md | 171 +++++++++++++++++++++++++++++++-------
 1 file changed, 141 insertions(+), 30 deletions(-)

diff --git a/assets/src/DRA/DRA.0.7.md b/assets/src/DRA/DRA.0.7.md
index 8952f4e9..082ec559 100644
--- a/assets/src/DRA/DRA.0.7.md
+++ b/assets/src/DRA/DRA.0.7.md
@@ -59,34 +59,145 @@ Laplacian Eigenmap算法主要步骤:
 
 应用示例:
 ```python
-  # import libraries
-  import numpy as np
-  import matplotlib.pyplot as plt
-  %matplotlib inline
-  from mpl_toolkits.mplot3d import Axes3D
-  from IPython.core.pylabtools import figsize
-  from IPython.core.interactiveshell import InteractiveShell
-  InteractiveShell.ast_node_interactivity = "all";
-  np.random.seed(8888)
-  plt.style.use('default')
-  plt.rcParams['figure.facecolor'] = 'white'
-  # ignore warnings
-  import warnings
-  warnings.filterwarnings('ignore');
-
-  # draw samples to create the grid
-  x = np.linspace(-2, 2, 50)
-  y = np.linspace(-2, 2, 50)
-  x,y = np.meshgrid(x,y)
-
-  # scalar function
-  z = x*np.exp(-1*(x**2 + y**2))
-
-  # plot 3d surface
-  fig = plt.figure(figsize = (6, 6))
-  ax = fig.gca(projection = '3d')
-  colors = plt.cm.jet(z*4)
-  ax.plot_surface(x, y, z, rstride=1, cstride=1, facecolors=colors, cmap=plt.cm.coolwarm, linewidth=1.4, alpha=0.8)
-  ax.set_title(r'$f(x, y)=x e^{-\left(x^{2}+y^{2}\right)}$', size=14);
-  
+  from numpy import exp, median
+from scipy.sparse.csgraph import laplacian
+from sklearn.manifold.locally_linear import (
+    null_space, LocallyLinearEmbedding)
+from sklearn.metrics.pairwise import pairwise_distances, rbf_kernel
+from sklearn.neighbors import kneighbors_graph, NearestNeighbors
+
+
+def ler(X, Y, n_components=2, affinity='nearest_neighbors',
+        n_neighbors=None, gamma=None, mu=1.0, y_gamma=None,
+        eigen_solver='auto', tol=1e-6, max_iter=100, 
+        random_state=None):
+    """
+    Laplacian Eigenmaps for Regression (LER)
+
+    Parameters
+    ----------
+    X : ndarray, 2-dimensional
+        The data matrix, shape (num_points, num_dims)
+
+    Y : ndarray, 1 or 2-dimensional
+        The response matrix, shape (num_points, num_responses).
+
+    n_components : int
+        Number of dimensions for embedding. Default is 2.
+
+    affinity : string or callable, default : "nearest_neighbors"
+        How to construct the affinity matrix.
+         - 'nearest_neighbors' : construct affinity matrix by knn graph
+         - 'rbf' : construct affinity matrix by rbf kernel
+
+    n_neighbors : int, optional, default=None
+        Number of neighbors for kNN graph construction on X.
+
+    gamma : float, optional, default=None
+        Scaling factor for RBF kernel on X.
+
+    mu : float, optional, default=1.0
+        Influence of the Y-similarity penalty.
+
+    y_gamma : float, optional
+        Scaling factor for RBF kernel on Y.
+        Defaults to the inverse of the median distance between rows of Y.
+
+    Returns
+    -------
+    embedding : ndarray, 2-dimensional
+        The embedding of X, shape (num_points, n_components)
+    """
+
+    if eigen_solver not in ('auto', 'arpack', 'dense'):
+        raise ValueError("unrecognized eigen_solver '%s'" % eigen_solver)
+
+    nbrs = NearestNeighbors(n_neighbors=n_neighbors + 1)
+    nbrs.fit(X)
+    X = nbrs._fit_X
+
+    Nx, d_in = X.shape
+    Ny = Y.shape[0]
+
+    if n_components > d_in:
+        raise ValueError("output dimension must be less than or equal "
+                         "to input dimension")
+    if Nx != Ny:
+        raise ValueError("X and Y must have same number of points")
+    if affinity == 'nearest_neighbors':
+        if n_neighbors >= Nx:
+            raise ValueError("n_neighbors must be less than number of points")
+        if n_neighbors == None or n_neighbors <= 0:
+            raise ValueError("n_neighbors must be positive")
+    elif affinity == 'rbf':
+        if gamma != None and gamma <= 0:
+            raise ValueError("n_neighbors must be positive")
+    else:
+        raise ValueError("affinity must be 'nearest_neighbors' or 'rbf' must be positive")
+
+    if Y.ndim == 1:
+        Y = Y[:, None]
+
+    if y_gamma is None:
+        dists = pairwise_distances(Y)
+        y_gamma = 1.0 / median(dists)
+
+    if affinity == 'nearest_neighbors':
+        affinity = kneighbors_graph(X, n_neighbors, include_self=True)
+    else:
+        if gamma == None:
+            dists = pairwise_distances(X)
+            gamma = 1.0 / median(dists)
+        affinity = kneighbors_graph(X, n_neighbors, mode='distance', include_self=True)
+        affinity.data = exp(-gamma * affinity.data ** 2)
+
+    K = rbf_kernel(Y, gamma=y_gamma)
+    lap = laplacian(affinity, normed=True)
+    lapK = laplacian(K, normed=True)
+    embedding, _ = null_space(lap + mu * lapK, n_components,
+                              k_skip=1, eigen_solver=eigen_solver,
+                              tol=tol, max_iter=max_iter,
+                              random_state=random_state)
+
+    return embedding
+
+
+class LER(LocallyLinearEmbedding):
+    """Scikit-learn compatible class for LER."""
+
+    def __init__(self, n_components=2, affinity='nearest_neighbors',
+                 n_neighbors=2, gamma=None, mu=1.0, y_gamma=None, 
+                 eigen_solver='auto', tol=1E-6, max_iter=100, 
+                 random_state=None, neighbors_algorithm='auto'):
+
+        self.n_components = n_components
+        self.affinity = affinity
+        self.n_neighbors = n_neighbors
+        self.gamma = gamma
+        self.mu = mu
+        self.y_gamma = y_gamma
+        self.eigen_solver = eigen_solver
+        self.tol = tol
+        self.max_iter = max_iter
+        self.random_state = random_state
+        self.neighbors_algorithm = neighbors_algorithm
+
+    def fit_transform(self, X, Y):
+        self.fit(X, Y)
+        return self.embedding_
+
+    def fit(self, X, Y):
+        # NN necessary for out-of-sample extensions
+        self.nbrs_ = NearestNeighbors(self.n_neighbors,
+                                      algorithm=self.neighbors_algorithm)
+        self.nbrs_.fit(X)
+
+        self.embedding_ = ler(
+            X, Y, n_components=self.n_components, 
+            affinity=self.affinity, n_neighbors=self.n_neighbors,
+            gamma=self.gamma, mu=self.mu, y_gamma=self.y_gamma,
+            eigen_solver=self.eigen_solver, tol=self.tol, 
+            max_iter=self.max_iter, random_state=self.random_state)
+
+        return self
 ```

From 558e6244bc12a0232e57f7e3429b65b55a399402 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 21 Oct 2019 13:39:55 +0800
Subject: [PATCH 1318/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 90 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 89 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index b1529b1d..48b57db4 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -3,4 +3,92 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### t－分布随机近邻嵌入(t-SNE)
-t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE).
+
+t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE) 是用于降维的一种机器学习算法，是由 Laurens van der Maaten 和 Geoffrey Hinton在08年提出来。此外，t-SNE 是一种非线性降维算法，非常适用于高维数据降维到2维或者3维，进行可视化。
+
+降维（dimension reduction）的基本作用：
+
+★缓解维数灾难。即提高样本密度，以及使基于欧氏距离的算法重新生效。
+
+★数据预处理。对数据去冗余、降低信噪比。
+
+★方便可视化。
+
+降维的概念中有两对直觉性的概念会反复出现：高维/低维空间、高维/低维数据。在文献中他们有若干别称：
+
+★高维空间（high-dimensional space），又叫原空间（original space）
+
+★高维数据（low-dimensional data），也直接叫数据点（data points），用于和下述的映射点对应。
+
+★低维空间（low-dimensional space），又叫嵌入空间（embedded space）、低维映射（low-dimensional map，map在此做名词用）等。
+
+★低维数据（low-dimensional data），又叫低维嵌入（low-dimensional embeddings）、低维表示（low-dimensional representations）、映射点（map points）等。
+
+嵌入（embedding）：数学上，嵌入是指一个数学结构经映射包含在另一个结构中。
+
+★NLP目前所使用的词嵌入（word embedding）一词的本意可能就是这个意思。最初所使用的词向量是one-hot向量，维度等于词表大小（约几十万）。后来采用分布式表示的词向量，维度一般取几百维。因此我们认为分布式表示的词向量是更高维度语义空间的低维嵌入（embedding）。
+
+★"Embed Everything！" 嵌入的思想不仅可以用在词（word）上，还能用于许多其他技术上。如知识图谱中可以把原先的网络结构也做嵌入，有实体嵌入、关系嵌入等。
+
+降维技术可以分为线性和非线性两大类：
+
+★线性降维技术。侧重让不相似的点在低维表示中分开。
+
+①PCA（Principle Components Analysis，主成分分析）.
+
+②MDS（Multiple Dimensional Scaling，多维缩放）等.
+
+★非线性降维技术（广义上“非线性降维技术”≈“流形学习”，狭义上后者是前者子集）。这类技术假设高维数据实际上处于一个比所处空间维度低的非线性流形上，因此侧重让相似的近邻点在低维表示中靠近。
+
+①Sammon mapping.
+
+②SNE（Stochastic Neighbor Embedding，随机近邻嵌入），t-SNE是基于SNE的。
+
+③Isomap（Isometric Mapping，等度量映射）.
+
+④MVU（Maximum Variance Unfolding）.
+
+⑤LLE（Locally Linear Embedding，局部线性嵌入）等.
+
+
+流形（manifold）：
+
+★机器学习中指的流形指本征维度较低但嵌入在高维空间中的空间（a manifold haslow intrinsic dimensions, and is embedded within a space of much higher dimensionality）。比如上图中的S-curve数据集，本征维度=2（摊开来是一个二维空间），但被嵌在三维空间中。
+
+★数学中提到流形，强调其具有局部欧式空间的性质，可以在局部应用欧几里得距离。但是在机器学习（流形学习）中，这个假设基本不成立。原因是高维空间由于维数灾难的存在，没有足够稠密的数据能在足够小的局部去近似该流形。
+
+★但是流形概念中局部的思想仍可以借鉴。它为降维提供了另一个视角：从微观角度去探索高维数据结构。
+
+距离：想象你是一只蚂蚁，在图中的二维曲面流形上行走。
+
+★高维直线距离：左图黑线。这个距离没有意义！
+
+★测地线距离：左图红线，右图红虚线。这个距离才有意义！
+
+★近邻距离：右图黑折线。用近邻距离可以拟合测地线距离。
+
+学习：流形学习之所以叫学习，因为它不像PCA一类的纯线性代数降维方法，而是更像一个类似神经网络的学习算法。
+
+★神经网络大部分是有监督学习；流形学习大部分是无监督学习。
+
+★神经网络拟合一个分类函数；流形学习（以t-SNE为例）拟合高维数据的分布。
+
+★神经网络学习参数；流形学习（以t-SNE为例）直接学习低维数据的表达。
+
+★两者均有损失函数、梯度下降、迭代轮数等学习算法的特点。
+
+t-SNE优点:
+
+流形学习中其他方法如Isomap、LLE等，主要用于展开单个连续的低维流形（比如“瑞士卷”数据集），而t-SNE主要用于数据的局部结构，并且会倾向于提取出局部的簇，这种能力对于可视化同时包含多个流形的高维数据（比如MNIST数据集）很有效。
+
+t-SNE缺点:
+
+* 时间、空间复杂度为O(n^2)，计算代价昂贵。百万量级的数据需要几小时，对于PCA可能只需要几分钟。
+
+* 升级版Barnes-Hut t-SNE可以让复杂度降为O(nlogn)，但只限于获得二维和三维的嵌入。（sklearn中可以直接使用参数method='barnes_hut'）
+
+* 由于代价函数非凸，多次执行算法的结果是随机的（名字中“Stochatsic”的由来？），需要多次运行选取最好的结果。
+
+* 全局结构不能很清楚的保留。这个问题可以通过先用PCA降维到一个合理的维度（如50）后再用t-SNE来缓解，前置的PCA步骤也可以起到去除噪声等功能。（sklearn中可以直接使用参数init='pca'）.
+
+

From 779c15bc21fcd4023653e5faf231aed9911e038b Mon Sep 17 00:00:00 2001
From: lisensen <lisensen@innotechx.com>
Date: Thu, 24 Oct 2019 20:50:37 +0800
Subject: [PATCH 1319/1406] change page of images

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From 32598aa10c48db07dcb7ed5d876a07be54e785e6 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 20:51:23 +0800
Subject: [PATCH 1320/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 48b57db4..507033e0 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -6,6 +6,10 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE) 是用于降维的一种机器学习算法，是由 Laurens van der Maaten 和 Geoffrey Hinton在08年提出来。此外，t-SNE 是一种非线性降维算法，非常适用于高维数据降维到2维或者3维，进行可视化。
 
+t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不懂流形学习并不影响我们理解t-SNE，这里只是对其做一个简单的介绍，完全可以跳过。
+
+流形(Manifold)是局部具有欧式空间性质的空间，包括各种纬度的曲线曲面，例如球体、弯曲的平面等。流形的局部和欧式空间是同构的。但是在全局尺度下不能简单的用欧式几何计算。一个好理解的例子就是地球，我们在几米的尺度下计算三角形的内角和是180度，但是在几百公里的尺度下会大于180度。因为地球上有意义的数据点是分布在球面上的，此时需要引入黎曼几何来描述问题。可见流形空间在真实世界中其实是大量存在的，所以我们对数据进行了一个假设，假设数据都是在高维欧式空间中的低维流形，如果我们能将其降维到低维，就能直观的发现其本质和一些内在规律。t-SNE就是基于这样的一个假设。
+
 降维（dimension reduction）的基本作用：
 
 ★缓解维数灾难。即提高样本密度，以及使基于欧氏距离的算法重新生效。
@@ -92,3 +96,5 @@ t-SNE缺点:
 * 全局结构不能很清楚的保留。这个问题可以通过先用PCA降维到一个合理的维度（如50）后再用t-SNE来缓解，前置的PCA步骤也可以起到去除噪声等功能。（sklearn中可以直接使用参数init='pca'）.
 
 
+
+

From 1551ac94de2fdd7f7826784e6cbb673754541f76 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:01:40 +0800
Subject: [PATCH 1321/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 40 +++++++++++++++++++++++++++++++++++----
 1 file changed, 36 insertions(+), 4 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 507033e0..1aa04032 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -81,11 +81,45 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 ★两者均有损失函数、梯度下降、迭代轮数等学习算法的特点。
 
-t-SNE优点:
+
+#### t-分布
+学生t-分布（t-distribution）用于根据小样本来估计呈正态分布且方差未知的总体的均值。其曲线形态与自由度有关，自由度越小，t分布越平坦；自由度为无穷时，t分布等同于标准正态分布。本文主要目的是理解t-SNE，所以只需要知道t-分布的解析式和曲线形状（见下图）即可，更多的内容请自行Wiki。
+
+<p align="center">
+<img width="260" align="center" src="../../images/448.jpg" />
+</p>
+
+#### SNE
+t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心思路可以概括如下：
+
+在高维空间相似的数据点，映射到低维空间距离也是相似的。常规的做法是用欧式距离表示这种相似性，而SNE把这种距离关系转换为一种条件概率来表示相似性。并使高维和低维下每个数据点对于其他数据点的相似性分布尽量接近。
+
+对于高维空间中每一个数据点 xi来说，xj是剩下的每个数据点，我们可以算出 xi 和每一个 xj 的欧式距离 dj 。但是不同维度下的欧式距离没有可比性，所以SNE的想法是构造一个概率来表征出这种距离的相似度来，一个合适易求导的分布就是高斯分布。构造一个 μ=xi 的高斯分布，并假设 σ=σi 是已知的（方差如何选择会在后面讨论）。那么每个 xj 和 xj 的距离对应的概率就可以作为相似度的度量。如下图，显然距离远的点相似度很底，距离近的点相似度很高。
+
+那么这个“高斯相似度”可以定义如下:
+
+<p align="center">
+<img width="260" align="center" src="../../images/449.jpg" />
+</p>
+
+另外因为我们只考虑不同数据点之间的相似度，所以定义 sim(xi,xi)=0.
+
+对 xi 和所有的 xj 计算相似度，我们就可以得到 xi 的相似度分布了，这个分布每一点的概率可以写成条件概率的形式，为了保证概率和为1，需要做归一化。即：
+
+<p align="center">
+<img width="260" align="center" src="../../images/450.jpg" />
+</p>
+
+
+相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="260" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="260" align="center" src="../../images/452.jpg" /> 。于是有
+
+
+
+#### t-SNE优点:
 
 流形学习中其他方法如Isomap、LLE等，主要用于展开单个连续的低维流形（比如“瑞士卷”数据集），而t-SNE主要用于数据的局部结构，并且会倾向于提取出局部的簇，这种能力对于可视化同时包含多个流形的高维数据（比如MNIST数据集）很有效。
 
-t-SNE缺点:
+#### t-SNE缺点:
 
 * 时间、空间复杂度为O(n^2)，计算代价昂贵。百万量级的数据需要几小时，对于PCA可能只需要几分钟。
 
@@ -96,5 +130,3 @@ t-SNE缺点:
 * 全局结构不能很清楚的保留。这个问题可以通过先用PCA降维到一个合理的维度（如50）后再用t-SNE来缓解，前置的PCA步骤也可以起到去除噪声等功能。（sklearn中可以直接使用参数init='pca'）.
 
 
-
-

From 155545f1ca26bd194469f9cf9afb2417bbbe640d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:03:36 +0800
Subject: [PATCH 1322/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 44 ++++++++++++++++++++-------------------
 1 file changed, 23 insertions(+), 21 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 1aa04032..e93529a1 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -12,37 +12,37 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 降维（dimension reduction）的基本作用：
 
-★缓解维数灾难。即提高样本密度，以及使基于欧氏距离的算法重新生效。
+* 缓解维数灾难。即提高样本密度，以及使基于欧氏距离的算法重新生效。
 
-★数据预处理。对数据去冗余、降低信噪比。
+* 数据预处理。对数据去冗余、降低信噪比。
 
-★方便可视化。
+* 方便可视化。
 
 降维的概念中有两对直觉性的概念会反复出现：高维/低维空间、高维/低维数据。在文献中他们有若干别称：
 
-★高维空间（high-dimensional space），又叫原空间（original space）
+* 高维空间（high-dimensional space），又叫原空间（original space）
 
-★高维数据（low-dimensional data），也直接叫数据点（data points），用于和下述的映射点对应。
+* 高维数据（low-dimensional data），也直接叫数据点（data points），用于和下述的映射点对应。
 
-★低维空间（low-dimensional space），又叫嵌入空间（embedded space）、低维映射（low-dimensional map，map在此做名词用）等。
+* 低维空间（low-dimensional space），又叫嵌入空间（embedded space）、低维映射（low-dimensional map，map在此做名词用）等。
 
-★低维数据（low-dimensional data），又叫低维嵌入（low-dimensional embeddings）、低维表示（low-dimensional representations）、映射点（map points）等。
+* 低维数据（low-dimensional data），又叫低维嵌入（low-dimensional embeddings）、低维表示（low-dimensional representations）、映射点（map points）等。
 
 嵌入（embedding）：数学上，嵌入是指一个数学结构经映射包含在另一个结构中。
 
-★NLP目前所使用的词嵌入（word embedding）一词的本意可能就是这个意思。最初所使用的词向量是one-hot向量，维度等于词表大小（约几十万）。后来采用分布式表示的词向量，维度一般取几百维。因此我们认为分布式表示的词向量是更高维度语义空间的低维嵌入（embedding）。
+* NLP目前所使用的词嵌入（word embedding）一词的本意可能就是这个意思。最初所使用的词向量是one-hot向量，维度等于词表大小（约几十万）。后来采用分布式表示的词向量，维度一般取几百维。因此我们认为分布式表示的词向量是更高维度语义空间的低维嵌入（embedding）。
 
-★"Embed Everything！" 嵌入的思想不仅可以用在词（word）上，还能用于许多其他技术上。如知识图谱中可以把原先的网络结构也做嵌入，有实体嵌入、关系嵌入等。
+* "Embed Everything！" 嵌入的思想不仅可以用在词（word）上，还能用于许多其他技术上。如知识图谱中可以把原先的网络结构也做嵌入，有实体嵌入、关系嵌入等。
 
 降维技术可以分为线性和非线性两大类：
 
-★线性降维技术。侧重让不相似的点在低维表示中分开。
+* 线性降维技术。侧重让不相似的点在低维表示中分开。
 
 ①PCA（Principle Components Analysis，主成分分析）.
 
 ②MDS（Multiple Dimensional Scaling，多维缩放）等.
 
-★非线性降维技术（广义上“非线性降维技术”≈“流形学习”，狭义上后者是前者子集）。这类技术假设高维数据实际上处于一个比所处空间维度低的非线性流形上，因此侧重让相似的近邻点在低维表示中靠近。
+* 非线性降维技术（广义上“非线性降维技术”≈“流形学习”，狭义上后者是前者子集）。这类技术假设高维数据实际上处于一个比所处空间维度低的非线性流形上，因此侧重让相似的近邻点在低维表示中靠近。
 
 ①Sammon mapping.
 
@@ -57,32 +57,33 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 流形（manifold）：
 
-★机器学习中指的流形指本征维度较低但嵌入在高维空间中的空间（a manifold haslow intrinsic dimensions, and is embedded within a space of much higher dimensionality）。比如上图中的S-curve数据集，本征维度=2（摊开来是一个二维空间），但被嵌在三维空间中。
+* 机器学习中指的流形指本征维度较低但嵌入在高维空间中的空间（a manifold haslow intrinsic dimensions, and is embedded within a space of much higher dimensionality）。比如上图中的S-curve数据集，本征维度=2（摊开来是一个二维空间），但被嵌在三维空间中。
 
-★数学中提到流形，强调其具有局部欧式空间的性质，可以在局部应用欧几里得距离。但是在机器学习（流形学习）中，这个假设基本不成立。原因是高维空间由于维数灾难的存在，没有足够稠密的数据能在足够小的局部去近似该流形。
+* 数学中提到流形，强调其具有局部欧式空间的性质，可以在局部应用欧几里得距离。但是在机器学习（流形学习）中，这个假设基本不成立。原因是高维空间由于维数灾难的存在，没有足够稠密的数据能在足够小的局部去近似该流形。
 
-★但是流形概念中局部的思想仍可以借鉴。它为降维提供了另一个视角：从微观角度去探索高维数据结构。
+* 但是流形概念中局部的思想仍可以借鉴。它为降维提供了另一个视角：从微观角度去探索高维数据结构。
 
 距离：想象你是一只蚂蚁，在图中的二维曲面流形上行走。
 
-★高维直线距离：左图黑线。这个距离没有意义！
+*  高维直线距离：左图黑线。这个距离没有意义！
 
-★测地线距离：左图红线，右图红虚线。这个距离才有意义！
+* 测地线距离：左图红线，右图红虚线。这个距离才有意义！
 
-★近邻距离：右图黑折线。用近邻距离可以拟合测地线距离。
+* 近邻距离：右图黑折线。用近邻距离可以拟合测地线距离。
 
 学习：流形学习之所以叫学习，因为它不像PCA一类的纯线性代数降维方法，而是更像一个类似神经网络的学习算法。
 
-★神经网络大部分是有监督学习；流形学习大部分是无监督学习。
+* 神经网络大部分是有监督学习；流形学习大部分是无监督学习。
 
-★神经网络拟合一个分类函数；流形学习（以t-SNE为例）拟合高维数据的分布。
+* 神经网络拟合一个分类函数；流形学习（以t-SNE为例）拟合高维数据的分布。
 
-★神经网络学习参数；流形学习（以t-SNE为例）直接学习低维数据的表达。
+* 神经网络学习参数；流形学习（以t-SNE为例）直接学习低维数据的表达。
 
-★两者均有损失函数、梯度下降、迭代轮数等学习算法的特点。
+* 两者均有损失函数、梯度下降、迭代轮数等学习算法的特点。
 
 
 #### t-分布
+
 学生t-分布（t-distribution）用于根据小样本来估计呈正态分布且方差未知的总体的均值。其曲线形态与自由度有关，自由度越小，t分布越平坦；自由度为无穷时，t分布等同于标准正态分布。本文主要目的是理解t-SNE，所以只需要知道t-分布的解析式和曲线形状（见下图）即可，更多的内容请自行Wiki。
 
 <p align="center">
@@ -90,6 +91,7 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 </p>
 
 #### SNE
+
 t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心思路可以概括如下：
 
 在高维空间相似的数据点，映射到低维空间距离也是相似的。常规的做法是用欧式距离表示这种相似性，而SNE把这种距离关系转换为一种条件概率来表示相似性。并使高维和低维下每个数据点对于其他数据点的相似性分布尽量接近。

From 2163785b274354f7bdab49bf2c1417c339d7d4e1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:08:20 +0800
Subject: [PATCH 1323/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 75 ++++++++++++++++++++++++++++++++++-----
 1 file changed, 66 insertions(+), 9 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index e93529a1..4889b737 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -36,23 +36,23 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 降维技术可以分为线性和非线性两大类：
 
-* 线性降维技术。侧重让不相似的点在低维表示中分开。
+线性降维技术。侧重让不相似的点在低维表示中分开。
 
-①PCA（Principle Components Analysis，主成分分析）.
+* PCA（Principle Components Analysis，主成分分析）.
 
-②MDS（Multiple Dimensional Scaling，多维缩放）等.
+* MDS（Multiple Dimensional Scaling，多维缩放）等.
 
-* 非线性降维技术（广义上“非线性降维技术”≈“流形学习”，狭义上后者是前者子集）。这类技术假设高维数据实际上处于一个比所处空间维度低的非线性流形上，因此侧重让相似的近邻点在低维表示中靠近。
+非线性降维技术（广义上“非线性降维技术”≈“流形学习”，狭义上后者是前者子集）。这类技术假设高维数据实际上处于一个比所处空间维度低的非线性流形上，因此侧重让相似的近邻点在低维表示中靠近。
 
-①Sammon mapping.
+* Sammon mapping.
 
-②SNE（Stochastic Neighbor Embedding，随机近邻嵌入），t-SNE是基于SNE的。
+* SNE（Stochastic Neighbor Embedding，随机近邻嵌入），t-SNE是基于SNE的。
 
-③Isomap（Isometric Mapping，等度量映射）.
+* Isomap（Isometric Mapping，等度量映射）.
 
-④MVU（Maximum Variance Unfolding）.
+* MVU（Maximum Variance Unfolding）.
 
-⑤LLE（Locally Linear Embedding，局部线性嵌入）等.
+* LLE（Locally Linear Embedding，局部线性嵌入）等.
 
 
 流形（manifold）：
@@ -116,6 +116,63 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="260" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="260" align="center" src="../../images/452.jpg" /> 。于是有
 
 
+<p align="center">
+<img width="260" align="center" src="../../images/453.jpg" />
+</p>
+
+此时就很明朗了，如果 yi 和 yj 能真实反映 xi 和 xj 的关系，那么 pj|i 和 qj|i 就应该是完全相等的。我们对所有j计算条件概率，就能得到这个条件概率的完整分布 Pi 。同理可以得到低维下的分布 Qi 。我们的目标就是使两个分布尽量接近，自然而然想到了KL散度。于是SNE的代价函数就可以写出来了，用梯度下降求解即可。
+
+
+<p align="center">
+<img width="260" align="center" src="../../images/454.jpg" />
+</p>
+
+求梯度的过程参考softmax函数的梯度，这里不重要，省略过程。对 yi 求梯度得到:
+
+<p align="center">
+<img width="260" align="center" src="../../images/455.jpg" />
+</p>
+
+其实这个梯度是有一定物理意义的，可以把 yi 看做一个分子，它最终的受力方向是由所有其他分子对它的合力决定的。对其中一个分子j来说， (pj∣i−qj∣i+pi∣j−qi∣j) 决定了力的大小，(yi−yj) 决定了力的方向。在初始化中，可以用较小的 σ 下的高斯分布来进行初始化。为了加速优化过程和避免陷入局部最优解，梯度中需要使用一个相对较大的动量(momentum)。即参数更新中除了当前的梯度，还要引入之前的梯度累加的指数衰减项，如下:
+
+
+<p align="center">
+<img width="260" align="center" src="../../images/457.jpg" />
+</p>
+
+这里的 Y(t) 表示迭代t次的解，η 表示学习速率, α(t) 表示迭代t次的动量。另外SNE在超参数的选择上需要做多次优化才可以。
+
+
+#### 困惑度（Perplexity）
+
+刚才在构建 qj|i 时，我们假设已知了每个 xi 的高斯相似度分布的 σ 。那 σ 究竟应该怎么设置呢？SNE的唯一参数困惑度就是用来为每个数据点 xi 寻找合适的 σi 的。困惑度可以定义为:
+
+<p align="center">
+<img width="260" align="center" src="../../images/458.jpg" />
+</p>
+
+其中 H(Pi) 是 Pi 的香农熵。从直观上是可以理解这个式子的，数据越混乱，熵越大，为了使每个数据点的困惑度都满足给定的困惑度，就需要一个很大的 σi使高斯分布尽量平坦，这样得到的每个 pj|i 就更接近一些。实际上我们经常将Perp设置为近邻数，因为增大 σ 就相当于增加近邻数据点。困惑度通常会被设置为 5 - 50 之间，并且在这个范围内具有良好的鲁棒性。
+
+因为 σi 和 Perp(Pi)是线性相关的，所以当设置好Perp后，我们可以简单的用 Binary Search 去为每个高斯分布找一个对应的 σi 。
+
+#### Symmetric SNE
+
+SNE设计出来之后，效果其实并没有想象的那么好。在人们尝试着去寻找优化方案时发现了这样一个问题， pj|i 和 pi|j 是不对称的。这违背了相似度这个概念的初衷，Symmetric SNE 就是来解决这个问题的。
+
+Symmetric SNE 把条件概率转换为了联合概率去度量相似度，这样就确保了对称性。在实践中联合概率采用了一种简单直观的定义方式:
+
+<p align="center">
+<img width="260" align="center" src="../../images/459.jpg" />
+</p>
+
+其中n为数据点总数。这样定义既保证了对称性，又保证了每个点对总代价的贡献都不会太小（因为 ∑jpij≥12n ）。此外，由联合分布计算出的梯度拥有更简单的形式，计算效率更高了。
+
+<p align="center">
+<img width="260" align="center" src="../../images/460.jpg" />
+</p>
+
+
+
 
 #### t-SNE优点:
 

From 6a8e27a6093be872a6c1eaedcb84359542808509 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:09:18 +0800
Subject: [PATCH 1324/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 4889b737..cf157801 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -113,7 +113,7 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 </p>
 
 
-相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="260" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="260" align="center" src="../../images/452.jpg" /> 。于是有
+相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="30" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="30" align="center" src="../../images/452.jpg" /> 。于是有
 
 
 <p align="center">

From b08530622a92d0e8197249c03758a23d9c335988 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:11:02 +0800
Subject: [PATCH 1325/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index cf157801..d8ee51df 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -113,7 +113,7 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 </p>
 
 
-相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="30" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="30" align="center" src="../../images/452.jpg" /> 。于是有
+相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="60" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="60" align="center" src="../../images/452.jpg" /> 。于是有
 
 
 <p align="center">

From addf1d5fc91f3658705367833f6f070c296d5af1 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:17:12 +0800
Subject: [PATCH 1326/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 49 +++++++++++++++++++++++++++++++++++++--
 1 file changed, 47 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index d8ee51df..d9a94a41 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -113,7 +113,7 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 </p>
 
 
-相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="60" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="60" align="center" src="../../images/452.jpg" /> 。于是有
+相应的，在低维度我们做同样的处理，设 xi 在低维的映射是 yi ，则可以得到低维下拟合每对数据点相似度的条件概率 <img width="30" align="center" src="../../images/451.jpg" />。另外由于我们可以任意假设低维下数据点的分布，为了方便和好看就设置每个数据点的相似度分布（同样是高斯分布）的 <img width="60" align="center" src="../../images/452.jpg" /> 。于是有
 
 
 <p align="center">
@@ -165,13 +165,58 @@ Symmetric SNE 把条件概率转换为了联合概率去度量相似度，这样
 <img width="260" align="center" src="../../images/459.jpg" />
 </p>
 
-其中n为数据点总数。这样定义既保证了对称性，又保证了每个点对总代价的贡献都不会太小（因为 ∑jpij≥12n ）。此外，由联合分布计算出的梯度拥有更简单的形式，计算效率更高了。
+其中n为数据点总数。这样定义既保证了对称性，又保证了每个点对总代价的贡献都不会太小（因为 <img width="260" align="center" src="../../images/461.jpg" /> ）。此外，由联合分布计算出的梯度拥有更简单的形式，计算效率更高了。
 
 <p align="center">
 <img width="260" align="center" src="../../images/460.jpg" />
 </p>
 
+#### 拥挤问题（The Crowding Problem）
 
+虽然 Symmetric SNE 解决了不对称问题，但是其得到的结果类边界也还是有一些模糊。这里涉及到了一个从高维降到低维所面临的拥挤问题。举个例子，我们假设在10维空间中有11个点两两距离相等，但是其降到可以可视化的二维后，我们是没有办法保存它们距离两两相等的信息的，因为在二维空间中最多只有三个点的距离可以两两相等。
+
+再假设在三维空间里有一个球体，数据点在球体内均匀分布。如果想把它降到二维，根据各个点到球心的距离，会得到一个圆形范围，且越靠近球面的数据点越密集。同理，越是高维的“球体”，降到低维后边缘越拥挤，因为高维球体的体积是呈 rd 增长的。这就是所谓的拥挤问题，降维后的簇会拥挤在一起无法区分，SNE 和 Symmetric SNE 都不能很好地解决这个问题。
+
+#### t-SNE
+
+然后t-SNE出现了，t-SNE在SNE的基础上做出了如下两个改进：
+
+* 使用联合概率代替条件概率（同 Symmetric SNE）
+* 在低维空间使用t分布代替高斯分布（高维空间不变）
+
+其中第一个改进保证了对称性和代价函数的下限，第二个改进一定程度上解决了拥挤问题。那么t分布是怎么解决拥挤问题的呢？
+
+<p align="center">
+<img width="260" align="center" src="../../images/462.jpg" />
+</p>
+
+t分布有一个重要的特点：属于长尾分布。我们看上图，高斯分布在3sigma后的概率密度就变得特别小，因此为了迎合长尾部分的数据，它会主动变得平坦，从而导致拟合不准确。或者可以说，高斯分布对异常值较为敏感。而t分布的长尾特性使其既能兼顾均值周围的数据点，又能兼顾边缘的数据点，更好的捕获了数据的特征。
+
+<p align="center">
+<img width="260" align="center" src="../../images/463.jpg" />
+</p>
+
+除此之外，高斯分布和t分布的差异也有助于缓解拥挤问题。我们看上图，横轴表示距离，纵轴表示相似度, 可以看到，对于较大相似度的点，t分布在低维空间中的距离需要稍小一点；而对于低相似度的点，t分布在低维空间中的距离需要更远。这恰好满足了我们的需求，即同一簇内的点(距离较近)聚合的更紧密，不同簇之间的点(距离较远)更加疏远。
+
+使用了自由度为1的t分布后， qij 变成了：
+
+<p align="center">
+<img width="260" align="center" src="../../images/464.jpg" />
+</p>
+可以看出公式里少了指数函数，计算上会方便很多。最终得到t-SNE的更新梯度（推导见原论文Appendix）是:
+<p align="center">
+<img width="260" align="center" src="../../images/465.jpg" />
+</p>
+
+然后再利用梯度下降求解 yi 即可。
+
+####  t-SNE效果
+
+t-SNE降维后的效果，总体是完爆其他可视化降维方法的。
+
+<p align="center">
+<img width="260" align="center" src="../../images/466.jpg" />
+</p>
 
 
 #### t-SNE优点:

From 9cf989ca4a1eeb8adc20ec4cb45e2a380b957bfd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:19:27 +0800
Subject: [PATCH 1327/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index d9a94a41..d734501c 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -218,6 +218,7 @@ t-SNE降维后的效果，总体是完爆其他可视化降维方法的。
 <img width="260" align="center" src="../../images/466.jpg" />
 </p>
 
+t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，从代价函数的公式中可以看出，当 pj|i 较大， qj|i 较小时，代价较高；而当 qj|i 较大， pj|i 较小时，代价较低。什么意思呢？就是当高维空间距离远，低维空间距离近的时候，代价函数会很高，模型会尽量避免这种事情发生，所以会加大低维的距离，这没问题。但是当高维近低维远的时候，代价会变低，模型也就不会在乎这个问题，导致低维空间距离较远的点始终拉不近。换句话说，t-SNE的代价函数更关注局部结构，而忽视了全局结构。所以假设数据集是在高维空间中的低维流形这一点是比较重要的，如果数据集的本征维度本身就很高，那么是不可能完整的映射到2-3维空间的。
 
 #### t-SNE优点:
 

From 49d7a5c51b23a3a0f113044bda2d305386674e35 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:19:42 +0800
Subject: [PATCH 1328/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index d734501c..f74e2b18 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -220,11 +220,11 @@ t-SNE降维后的效果，总体是完爆其他可视化降维方法的。
 
 t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，从代价函数的公式中可以看出，当 pj|i 较大， qj|i 较小时，代价较高；而当 qj|i 较大， pj|i 较小时，代价较低。什么意思呢？就是当高维空间距离远，低维空间距离近的时候，代价函数会很高，模型会尽量避免这种事情发生，所以会加大低维的距离，这没问题。但是当高维近低维远的时候，代价会变低，模型也就不会在乎这个问题，导致低维空间距离较远的点始终拉不近。换句话说，t-SNE的代价函数更关注局部结构，而忽视了全局结构。所以假设数据集是在高维空间中的低维流形这一点是比较重要的，如果数据集的本征维度本身就很高，那么是不可能完整的映射到2-3维空间的。
 
-#### t-SNE优点:
+#### t-SNE优点
 
 流形学习中其他方法如Isomap、LLE等，主要用于展开单个连续的低维流形（比如“瑞士卷”数据集），而t-SNE主要用于数据的局部结构，并且会倾向于提取出局部的簇，这种能力对于可视化同时包含多个流形的高维数据（比如MNIST数据集）很有效。
 
-#### t-SNE缺点:
+#### t-SNE缺点
 
 * 时间、空间复杂度为O(n^2)，计算代价昂贵。百万量级的数据需要几小时，对于PCA可能只需要几分钟。
 

From 47cdf86c41fd94800010a1059363d4b573249297 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:21:41 +0800
Subject: [PATCH 1329/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index f74e2b18..5633564e 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -130,14 +130,14 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 求梯度的过程参考softmax函数的梯度，这里不重要，省略过程。对 yi 求梯度得到:
 
 <p align="center">
-<img width="260" align="center" src="../../images/455.jpg" />
+<img width="300" align="center" src="../../images/455.jpg" />
 </p>
 
 其实这个梯度是有一定物理意义的，可以把 yi 看做一个分子，它最终的受力方向是由所有其他分子对它的合力决定的。对其中一个分子j来说， (pj∣i−qj∣i+pi∣j−qi∣j) 决定了力的大小，(yi−yj) 决定了力的方向。在初始化中，可以用较小的 σ 下的高斯分布来进行初始化。为了加速优化过程和避免陷入局部最优解，梯度中需要使用一个相对较大的动量(momentum)。即参数更新中除了当前的梯度，还要引入之前的梯度累加的指数衰减项，如下:
 
 
 <p align="center">
-<img width="260" align="center" src="../../images/457.jpg" />
+<img width="300" align="center" src="../../images/457.jpg" />
 </p>
 
 这里的 Y(t) 表示迭代t次的解，η 表示学习速率, α(t) 表示迭代t次的动量。另外SNE在超参数的选择上需要做多次优化才可以。

From bcdacef92e7ca06e56be8e1cff659d26fa513a67 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 24 Oct 2019 21:22:57 +0800
Subject: [PATCH 1330/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 5633564e..26be552b 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -165,7 +165,7 @@ Symmetric SNE 把条件概率转换为了联合概率去度量相似度，这样
 <img width="260" align="center" src="../../images/459.jpg" />
 </p>
 
-其中n为数据点总数。这样定义既保证了对称性，又保证了每个点对总代价的贡献都不会太小（因为 <img width="260" align="center" src="../../images/461.jpg" /> ）。此外，由联合分布计算出的梯度拥有更简单的形式，计算效率更高了。
+其中n为数据点总数。这样定义既保证了对称性，又保证了每个点对总代价的贡献都不会太小（因为 <img width="60" align="center" src="../../images/461.jpg" /> ）。此外，由联合分布计算出的梯度拥有更简单的形式，计算效率更高了。
 
 <p align="center">
 <img width="260" align="center" src="../../images/460.jpg" />

From acebddfa38ad6e8806ab5023cec11138634cec6d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 Oct 2019 11:10:54 +0800
Subject: [PATCH 1331/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 26be552b..8036c14e 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -201,11 +201,13 @@ t分布有一个重要的特点：属于长尾分布。我们看上图，高斯
 使用了自由度为1的t分布后， qij 变成了：
 
 <p align="center">
-<img width="260" align="center" src="../../images/464.jpg" />
+<img width="300" align="center" src="../../images/464.jpg" />
 </p>
+
 可以看出公式里少了指数函数，计算上会方便很多。最终得到t-SNE的更新梯度（推导见原论文Appendix）是:
+
 <p align="center">
-<img width="260" align="center" src="../../images/465.jpg" />
+<img width="300" align="center" src="../../images/465.jpg" />
 </p>
 
 然后再利用梯度下降求解 yi 即可。
@@ -215,10 +217,12 @@ t分布有一个重要的特点：属于长尾分布。我们看上图，高斯
 t-SNE降维后的效果，总体是完爆其他可视化降维方法的。
 
 <p align="center">
-<img width="260" align="center" src="../../images/466.jpg" />
+<img width="300" align="center" src="../../images/466.jpg" />
 </p>
 
-t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，从代价函数的公式中可以看出，当 pj|i 较大， qj|i 较小时，代价较高；而当 qj|i 较大， pj|i 较小时，代价较低。什么意思呢？就是当高维空间距离远，低维空间距离近的时候，代价函数会很高，模型会尽量避免这种事情发生，所以会加大低维的距离，这没问题。但是当高维近低维远的时候，代价会变低，模型也就不会在乎这个问题，导致低维空间距离较远的点始终拉不近。换句话说，t-SNE的代价函数更关注局部结构，而忽视了全局结构。所以假设数据集是在高维空间中的低维流形这一点是比较重要的，如果数据集的本征维度本身就很高，那么是不可能完整的映射到2-3维空间的。
+t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，从代价函数的公式中可以看出，当 pj|i 较大， qj|i 较小时，代价较高；而当 qj|i 较大， pj|i 较小时，代价较低。什么意思呢？就是当高维空间距离远，低维空间距离近的时候，代价函数会很高，模型会尽量避免这种事情发生，所以会加大低维的距离，这没问题。
+
+但是当高维近低维远的时候，代价会变低，模型也就不会在乎这个问题，导致低维空间距离较远的点始终拉不近。换句话说，t-SNE的代价函数更关注局部结构，而忽视了全局结构。所以假设数据集是在高维空间中的低维流形这一点是比较重要的，如果数据集的本征维度本身就很高，那么是不可能完整的映射到2-3维空间的。
 
 #### t-SNE优点
 

From acbd9162f1e9c6bc8c181a67d36b683bb50a5bc0 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 28 Oct 2019 10:08:11 +0800
Subject: [PATCH 1332/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 8036c14e..03436b6b 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -187,7 +187,7 @@ Symmetric SNE 把条件概率转换为了联合概率去度量相似度，这样
 其中第一个改进保证了对称性和代价函数的下限，第二个改进一定程度上解决了拥挤问题。那么t分布是怎么解决拥挤问题的呢？
 
 <p align="center">
-<img width="260" align="center" src="../../images/462.jpg" />
+<img width="300" align="center" src="../../images/462.jpg" />
 </p>
 
 t分布有一个重要的特点：属于长尾分布。我们看上图，高斯分布在3sigma后的概率密度就变得特别小，因此为了迎合长尾部分的数据，它会主动变得平坦，从而导致拟合不准确。或者可以说，高斯分布对异常值较为敏感。而t分布的长尾特性使其既能兼顾均值周围的数据点，又能兼顾边缘的数据点，更好的捕获了数据的特征。

From 325a3bfc955f886d1dce9af72c79b1025338ec5d Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 29 Oct 2019 10:23:01 +0800
Subject: [PATCH 1333/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 8 --------
 1 file changed, 8 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 03436b6b..7781142a 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -63,14 +63,6 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 * 但是流形概念中局部的思想仍可以借鉴。它为降维提供了另一个视角：从微观角度去探索高维数据结构。
 
-距离：想象你是一只蚂蚁，在图中的二维曲面流形上行走。
-
-*  高维直线距离：左图黑线。这个距离没有意义！
-
-* 测地线距离：左图红线，右图红虚线。这个距离才有意义！
-
-* 近邻距离：右图黑折线。用近邻距离可以拟合测地线距离。
-
 学习：流形学习之所以叫学习，因为它不像PCA一类的纯线性代数降维方法，而是更像一个类似神经网络的学习算法。
 
 * 神经网络大部分是有监督学习；流形学习大部分是无监督学习。

From 65c2afed13d792ef61bf1a960bc66307c1ec8539 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 Oct 2019 09:54:25 +0800
Subject: [PATCH 1334/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 7781142a..ad0042ad 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -54,7 +54,6 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 * LLE（Locally Linear Embedding，局部线性嵌入）等.
 
-
 流形（manifold）：
 
 * 机器学习中指的流形指本征维度较低但嵌入在高维空间中的空间（a manifold haslow intrinsic dimensions, and is embedded within a space of much higher dimensionality）。比如上图中的S-curve数据集，本征维度=2（摊开来是一个二维空间），但被嵌在三维空间中。
@@ -73,7 +72,6 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 
 * 两者均有损失函数、梯度下降、迭代轮数等学习算法的特点。
 
-
 #### t-分布
 
 学生t-分布（t-distribution）用于根据小样本来估计呈正态分布且方差未知的总体的均值。其曲线形态与自由度有关，自由度越小，t分布越平坦；自由度为无穷时，t分布等同于标准正态分布。本文主要目的是理解t-SNE，所以只需要知道t-分布的解析式和曲线形状（见下图）即可，更多的内容请自行Wiki。
@@ -114,7 +112,6 @@ t-SNE可以看做是SNE的改进，所以我们从SNE开始说起。SNE的核心
 
 此时就很明朗了，如果 yi 和 yj 能真实反映 xi 和 xj 的关系，那么 pj|i 和 qj|i 就应该是完全相等的。我们对所有j计算条件概率，就能得到这个条件概率的完整分布 Pi 。同理可以得到低维下的分布 Qi 。我们的目标就是使两个分布尽量接近，自然而然想到了KL散度。于是SNE的代价函数就可以写出来了，用梯度下降求解即可。
 
-
 <p align="center">
 <img width="260" align="center" src="../../images/454.jpg" />
 </p>
@@ -229,5 +226,3 @@ t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，
 * 由于代价函数非凸，多次执行算法的结果是随机的（名字中“Stochatsic”的由来？），需要多次运行选取最好的结果。
 
 * 全局结构不能很清楚的保留。这个问题可以通过先用PCA降维到一个合理的维度（如50）后再用t-SNE来缓解，前置的PCA步骤也可以起到去除噪声等功能。（sklearn中可以直接使用参数init='pca'）.
-
-

From 12e7db89c9cb52b9136da3997860b9acfd7c1418 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 3 Nov 2019 15:43:17 +0800
Subject: [PATCH 1335/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index ad0042ad..71cc7272 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -6,8 +6,6 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE) 是用于降维的一种机器学习算法，是由 Laurens van der Maaten 和 Geoffrey Hinton在08年提出来。此外，t-SNE 是一种非线性降维算法，非常适用于高维数据降维到2维或者3维，进行可视化。
 
-t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不懂流形学习并不影响我们理解t-SNE，这里只是对其做一个简单的介绍，完全可以跳过。
-
 流形(Manifold)是局部具有欧式空间性质的空间，包括各种纬度的曲线曲面，例如球体、弯曲的平面等。流形的局部和欧式空间是同构的。但是在全局尺度下不能简单的用欧式几何计算。一个好理解的例子就是地球，我们在几米的尺度下计算三角形的内角和是180度，但是在几百公里的尺度下会大于180度。因为地球上有意义的数据点是分布在球面上的，此时需要引入黎曼几何来描述问题。可见流形空间在真实世界中其实是大量存在的，所以我们对数据进行了一个假设，假设数据都是在高维欧式空间中的低维流形，如果我们能将其降维到低维，就能直观的发现其本质和一些内在规律。t-SNE就是基于这样的一个假设。
 
 降维（dimension reduction）的基本作用：
@@ -77,7 +75,7 @@ t-SNE是流形学习（Manifold Learning）分支下的一种模型。其实不
 学生t-分布（t-distribution）用于根据小样本来估计呈正态分布且方差未知的总体的均值。其曲线形态与自由度有关，自由度越小，t分布越平坦；自由度为无穷时，t分布等同于标准正态分布。本文主要目的是理解t-SNE，所以只需要知道t-分布的解析式和曲线形状（见下图）即可，更多的内容请自行Wiki。
 
 <p align="center">
-<img width="260" align="center" src="../../images/448.jpg" />
+<img width="300" align="center" src="../../images/448.jpg" />
 </p>
 
 #### SNE
@@ -206,7 +204,7 @@ t分布有一个重要的特点：属于长尾分布。我们看上图，高斯
 t-SNE降维后的效果，总体是完爆其他可视化降维方法的。
 
 <p align="center">
-<img width="300" align="center" src="../../images/466.jpg" />
+<img width="500" align="center" src="../../images/466.jpg" />
 </p>
 
 t-SNE得到的是局部最优解。因为KL散度是一个不对称的度量，从代价函数的公式中可以看出，当 pj|i 较大， qj|i 较小时，代价较高；而当 qj|i 较大， pj|i 较小时，代价较低。什么意思呢？就是当高维空间距离远，低维空间距离近的时候，代价函数会很高，模型会尽量避免这种事情发生，所以会加大低维的距离，这没问题。

From 1caef607c418ff425d23f08348dcada119993ceb Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 Dec 2019 09:48:09 +0800
Subject: [PATCH 1336/1406] Update DRA.0.9.md

---
 assets/src/DRA/DRA.0.9.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/DRA/DRA.0.9.md b/assets/src/DRA/DRA.0.9.md
index 1780af93..c9bf8de9 100644
--- a/assets/src/DRA/DRA.0.9.md
+++ b/assets/src/DRA/DRA.0.9.md
@@ -3,3 +3,5 @@
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### 深度自动编码器(Deep Autoencoder Networks)
+
+自动编码器是一种无监督的神经网络模型，它可以学习到输入数据的隐含特征，这称为编码(coding)，同时用学习到的新特征可以重构出原始输入数据，称之为解码(decoding)。从直观上来看，自动编码器可以用于特征降维，类似主成分分析PCA，但是其相比PCA其性能更强，这是由于神经网络模型可以提取更有效的新特征。除了进行特征降维，自动编码器学习到的新特征可以送入有监督学习模型中，所以自动编码器可以起到特征提取器的作用。作为无监督学习模型，自动编码器还可以用于生成与训练样本不同的新数据，这样自动编码器（变分自动编码器，Variational Autoencoders）就是生成式模型。

From 0965fcfd91d8bcc3e5551372b4ff0178904c62a3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 9 May 2020 19:12:19 +0800
Subject: [PATCH 1337/1406] Update DRA.0.8.md

---
 assets/src/DRA/DRA.0.8.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/DRA/DRA.0.8.md b/assets/src/DRA/DRA.0.8.md
index 71cc7272..33f9d169 100644
--- a/assets/src/DRA/DRA.0.8.md
+++ b/assets/src/DRA/DRA.0.8.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
@@ -32,7 +33,7 @@ t－分布随机近邻嵌入(t-Distributed Stochastic Neighbor Embedding,t-SNE)
 
 * "Embed Everything！" 嵌入的思想不仅可以用在词（word）上，还能用于许多其他技术上。如知识图谱中可以把原先的网络结构也做嵌入，有实体嵌入、关系嵌入等。
 
-降维技术可以分为线性和非线性两大类：
+降维技术可以分为线性和非线性两大类.
 
 线性降维技术。侧重让不相似的点在低维表示中分开。
 

From 484583e578384c7a16a1f2860701a6f2f2e2cbd5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 14 May 2020 10:17:24 +0800
Subject: [PATCH 1338/1406] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index c3307002..4a83353c 100644
--- a/README.md
+++ b/README.md
@@ -194,7 +194,7 @@
 
 ### 机器学习
 
-觉得此文章不错，支持我的话可以给我star ，:star:！如果有问题可以加我的微信**Sen0676**,加入我们的交流群一起交流机器学习！
+如果觉得此文章不错，支持我的话可以给我star ，:star:！有问题也可以给我直接提issues,我会及时回复的.
 
 ### License
 This is free software distributed under the terms of the MIT license

From 0a295701be4d491704c94df49275ccafa4edffbd Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 27 Jun 2020 00:37:02 +0800
Subject: [PATCH 1339/1406] Update README.md

---
 README.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 4a83353c..517ff82c 100644
--- a/README.md
+++ b/README.md
@@ -194,7 +194,10 @@
 
 ### 机器学习
 
-如果觉得此文章不错，支持我的话可以给我star ，:star:！有问题也可以给我直接提issues,我会及时回复的.
+觉得此文章不错，支持我的话可以给我star ，:star:！ 如果有问题可以加我的微信,也可以加入我们的交流群一起交流技术！
+<p align="center">
+<img width="300" align="center" src="https://github.com/KeKe-Li/micro-Services-Tutorial/blob/master/src/images/12.jpg" />
+</p>
 
 ### License
 This is free software distributed under the terms of the MIT license

From f12d4dc9308af54e02906caf3259435f78ccd8c7 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 26 Sep 2020 11:13:44 +0800
Subject: [PATCH 1340/1406] Update EL.0.2.md

---
 assets/src/EL/EL.0.2.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/EL/EL.0.2.md b/assets/src/EL/EL.0.2.md
index 36d0ff16..b25fa577 100644
--- a/assets/src/EL/EL.0.2.md
+++ b/assets/src/EL/EL.0.2.md
@@ -4,9 +4,9 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 #### Boosting
 
-Bagging是Bootstrap aggregating的简写。先说一下bootstrap，bootstrap也称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
+Bagging是Bootstrap aggregating的简写。这里先说一下`bootstrap`，`bootstrap` 也被称为自助法，它是一种有放回的抽样方法，目的为了得到统计量的分布以及置信区间。
 
-Baggging 和Boosting都是模型融合的方法，可以将弱分类器融合之后形成一个强分类器，而且融合之后的效果会比最好的弱分类器更好。
+Baggging 和 Boosting都是模型融合的方法，可以将弱分类器融合之后形成一个强分类器，而且融合之后的效果会比最好的弱分类器更好。
 
 Bagging即套袋法，其算法过程如下：
 

From 0bcbf0b084e545b9ded37aa71a2eddc7e86f8b46 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 14 Oct 2020 10:02:41 +0800
Subject: [PATCH 1341/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 2d533d11..2d4de632 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -9,6 +9,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 学习矢量量化是一种结构简单、功能强大的有监督式神经网络分类方法。作为一种最近邻原型分类器，LVQ在训练过程中通过对神经元权向量（原型向量）的不断更新，对其学习率的不断调整，能够使不同类别权向量之间的边界逐步收敛至贝叶斯分类边界。算法中，对获胜神经元（最近邻权向量）的选取是通过计算输入样本和权向量之间的距离的大小来判断的。与矢量量化（VQ）相比，LVQ最突出的特点就是其具有自适应性 
 
 1.向量量化
+
 向量量化的思路是，将高维输入空间分成若干不同的区域，对每个区域确定一个中心向量作为聚类的中心，与其处于同一区域的输入向量可用该中心向量来代表，从而形成了以各中心向量为聚类中心的点集。在图像处理领域常用各区域中心点（向量）的编码代替区域内的点来存储或传输，从而提出了各种基于向量量化的有损压缩技术，在二维输入平面上表示的中心向量分布称为Voronoi图，如图所示：
 <p align="center">
 <img width="400" align="center" src="../../images/147.jpg" />
@@ -18,24 +19,31 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 自组织映射可以起到聚类作用，但无法直接分类或识别，因此它只是自适应解决模式分类问题两步中的第一步。第二步：学习向量量化，采用监督机制，在训练中加入信号作为分类信息对权值进行细调，并对输出神经元预先指定其类别。
 
 2.学习矢量量化网络结构与工作原理
+
 学习矢量量化神经网络有三层组成：输入层，竞争层，线性输出层。
+
 <p align="center">
 <img width="400" align="center" src="../../images/148.jpg" />
 </p>
+
 竞争层有m个神经元，输入层有n个神经元，两层之间完全连接。输出层每个神经元只与竞争层中的一组神经元连接，连接权重固定为1，训练过程中输入层和竞争层之间的权值逐渐被调整为聚类中心。当一个样本输入LVQ网络时，竞争层的神经元通过胜者为王学习规则产生获胜神经元，容许其输出为1，其它神经元输出为0。与获胜神经元所在组相连的输出神经元输出为1，而其它输出神经元为0，从而给出当前输入样本的模式类。将竞争层学习得到的类成为子类，而将输出层学习得到的类成为目标类。
 
 3.学习矢量量化网络学习算法
+
 学习矢量量化学习规则结合了竞争学习规则和有导师学习规则，所以样本集应当为{(xi，di)}。其中di为l维，对应输出层的l个神经元，它只有一个分量为1，其他分量均为0。通常把竞争层的每个神经元指定给一个输出神经元，相应的权值为1，从而得到输出层的权值。比如某LVQ网络竞争层6个神经元，输出层3个神经元，代表3类。若将竞争层的1，3指定为第一个输出神经元，2，5指定为第二个输出神经元，3，6指定为第三个输出神经元。则竞争层到输出层的权值矩阵为:
+
 <p align="center">
 <img width="300" align="center" src="../../images/149.jpg" />
 </p>
 
 训练前预先定义好竞争层到输出层权重，从而指定了输出神经元类别，训练中不再改变。网络的学习通过改变输入层到竞争层的权重来进行。根据输入样本类别和获胜神经元所属类别，可判断当前分类是否正确。若分类正确，则将获胜神经元的权向量向输入向量方向调整，分类错误则向相反方向调整。
+
 <p align="center">
 <img width="400" align="center" src="../../images/150.jpg" />
 </p>
 
 学习矢量量化网络学习算法的步骤如下:
+
 * 初始化。竞争层各神经元权值向量随机赋值小随机数，确定初始学习速率和训练次数。
 * 输入样本向量。
 * 寻找激活神经元。

From abd1200c43e1b928280b93786826eb125eeaa821 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 25 Jan 2021 09:57:46 +0800
Subject: [PATCH 1342/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index a62b663b..711f1574 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -40,6 +40,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 </p>
 
 当k=1时，模型变为:
+
 <p align="center">
 <img width="500" align="center" src="../../images/294.jpg" />
 </p>
@@ -98,6 +99,7 @@ RNN训练困难的主要原因在于隐藏层参数w的传播：由于误差传
 <p align="center">
 <img width="380" align="center" src="../../images/305.jpg" />
 </p>
+
 而对梯度消失问题，则有很多不同的方案：
 
 * 有效初始化+ReLU激活函数能够得到较好效果
@@ -106,7 +108,7 @@ RNN训练困难的主要原因在于隐藏层参数w的传播：由于误差传
 * 在BPTT算法中加入skip connection，此时误差可以间歇的向前传播。
 * 加入一些Leaky Units，思路类似于skip connection
 
-LSTM 全称叫 Long Short-Term Memory networks，它和传统 RNN 唯一的不同就在与其中的神经元（感知机）的构造不同。传统的 RNN 每个神经元和一般神经网络的感知机没啥区别，但在 LSTM 中，每个神经元是一个“记忆细胞”（元胞状态，Cell State），将以前的信息连接到当前的任务中来。每个LSTM细胞里面都包含:
+LSTM 全称叫 `Long Short-Term Memory networks`，它和传统 RNN 唯一的不同就在与其中的神经元（感知机）的构造不同。传统的 RNN 每个神经元和一般神经网络的感知机没啥区别，但在 LSTM 中，每个神经元是一个“记忆细胞”（元胞状态，Cell State），将以前的信息连接到当前的任务中来。每个LSTM细胞里面都包含:
 
 * 输入门（input gate）: 一个Sigmoid层，观察<img width="60" align="center" src="../../images/299.jpg" />和<img width="50" align="center" src="../../images/298.jpg" />,对于元胞状态<img width="50" align="center" src="../../images/306.jpg" />中的每一个元素，输出一个0~1之间的数。1表示“完全保留该信息”，0表示“完全丢弃该信息”：
 
@@ -146,6 +148,7 @@ LSTM 全称叫 Long Short-Term Memory networks，它和传统 RNN 唯一的不
 如果我们把LSTM的forget gate全部置0（总是忘记之前的信息），input gate全部 置1，output gate全部置1（把cell state中的信息全部输出），这样LSTM就变成一个标准的RNN。
 
 目前 LSTM 模型在实践中取得了非常好的效果， 只需要训练一个两三层的LSTM, 它就可以:
+
 * 模仿保罗·格雷厄姆进行写作
 * 生成维基百科的 markdown 页面
 * 手写识别

From b52a502e67bc76904a128049b520a16adb86c441 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 25 Jan 2021 09:58:30 +0800
Subject: [PATCH 1343/1406] Update ANN.0.4.md

---
 assets/src/ANN/ANN.0.4.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/ANN/ANN.0.4.md b/assets/src/ANN/ANN.0.4.md
index 711f1574..74d0df6d 100644
--- a/assets/src/ANN/ANN.0.4.md
+++ b/assets/src/ANN/ANN.0.4.md
@@ -57,7 +57,7 @@ RNN主要解决序列数据的处理，比如文本、语音、视频等等。
 <img width="380" align="center" src="../../images/297.jpg" />
 </p>
 
-把序列视作时间序列，隐含层h的自连接边实际上是和上一时刻的h相连.在每一个时刻t，<img width="60" align="center" src="../../images/299.jpg" />的取值是当前时刻的输入<img width="50" align="center" src="../../images/298.jpg" />,和上一时刻的隐含层值<img width="30" align="center" src="../../images/301.jpg" />的一个函数:
+把序列视作时间序列，隐含层h的自连接边实际上是和上一时刻的h相连.在每一个时刻t，<img width="60" align="center" src="../../images/299.jpg" />的取值是当前时刻的输入<img width="30" align="center" src="../../images/298.jpg" />,和上一时刻的隐含层值<img width="30" align="center" src="../../images/301.jpg" />的一个函数:
 
 <p align="center">
 <img width="380" align="center" src="../../images/300.jpg" />

From a88cbc44ad00e9322a7cb9c7635c1d8b41b14023 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 14 Feb 2021 20:37:00 +0800
Subject: [PATCH 1344/1406] Update BA.0.3.md

---
 assets/src/BA/BA.0.3.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/BA/BA.0.3.md b/assets/src/BA/BA.0.3.md
index 2d4de632..758d9c33 100644
--- a/assets/src/BA/BA.0.3.md
+++ b/assets/src/BA/BA.0.3.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
@@ -54,10 +55,13 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 </p>
 
 当网络分类结果与教师信号不一致时，向输入样本反方向调整权值：
+
 <p align="center">
 <img width="300" align="center" src="../../images/152.jpg" />
 </p>
+
 其他非激活神经元权值保持不变。
+
 * 更新学习速率
 <p align="center">
 <img width="300" align="center" src="../../images/153.jpg" />

From 906e51e037368f32c88fc9dd027515e38c3e5a20 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Mon, 14 Feb 2022 09:44:46 +0800
Subject: [PATCH 1345/1406] Update OTR.md

---
 assets/src/OTR/OTR.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/OTR/OTR.md b/assets/src/OTR/OTR.md
index 35606c69..a86b6646 100644
--- a/assets/src/OTR/OTR.md
+++ b/assets/src/OTR/OTR.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
@@ -34,7 +35,9 @@ Hawkins(1980)给出孤立点（outlier）的定义：孤立点是在数据集中
 孤立点的挖掘方法主要有：基于统计学的、基于距离的、基于密度的局部离群点方法和基于深度偏差的方法。
 
 马克威孤立点算法是基于距离的：设<img width="50" align="center" src="../../images/51.jpg" />表示p点和它的第k个最近邻居的距离。直观地看，<img width="50" align="center" src="../../images/52.jpg" />越大，p越有可能成为孤立点。
+
 给定d维空间中包含N个点的数据集、参数N（孤立点个数）和k（偏差距离）,如果满足<img width="50" align="center" src="../../images/55.jpg" />的点<img width="20" align="center" src="../../images/53.jpg" />不超过n-1个,那么称p为<img width="20" align="center" src="../../images/54.jpg" />孤立点。
+
 如果对所有数据点根据其<img width="50" align="center" src="../../images/51.jpg" />距离进行从大到小排序，那么前n个点就被看作是孤立点。
 
 算法步骤如下，对每个p点，计算它的第k个最近邻居的距离<img width="50" align="center" src="../../images/51.jpg" />，把具有极大<img width="50" align="center" src="../../images/54.jpg" />值的前个n点作为孤立点。该算法每次处理一个点p，就需要扫描一遍数据库，总共需要扫描N遍（N为数据点数）。

From 764da7d2ce2ea4b04307c35cd1e4ed0696b520c5 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sun, 20 Mar 2022 20:50:18 +0800
Subject: [PATCH 1346/1406] Update BNS.md

---
 assets/src/BNS/BNS.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/BNS/BNS.md b/assets/src/BNS/BNS.md
index 80093f59..69b7ef51 100644
--- a/assets/src/BNS/BNS.md
+++ b/assets/src/BNS/BNS.md
@@ -64,7 +64,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 在没有任何证据提供给网络的情况下有初始边界概率为:
 
-P(D)＝0.8×0.1×0.4＋0.6×0.1×0.6＋0.6×0.9×0.4＋0.3×0.9＋0.6＝0.032＋0.036＋0.0216＋0.0162＝0. 446．
+P(D)＝0.8×0.1×0.4＋0.6×0.1×0.6＋0.6×0.9×0.4＋0.3×0.9＋0.6＝0.032＋0.036＋0.0216＋0.0162＝0.446．
 
 同样，考虑节点C发生了的情况，亦即C＝TRUE，知道P(A)从0.1变成0.471，P(notA)也就从0.9变成0.529，将这些值重新代入式(2)，得到修改后的边界概率，即条件概率P(D| C)＝0.542．给网络输入新的证据以更新各个节点的概率，这个过程称为概率繁殖．贝叶斯网络的作用就在于对不确定性系统进行知识表达并利用概率繁殖来对其进行推理．
 

From 16f3d861e742500417ed7aaf3ec930c42623c257 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 30 Mar 2022 20:19:15 +0800
Subject: [PATCH 1347/1406] Update OTR.md

---
 assets/src/OTR/OTR.md | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/assets/src/OTR/OTR.md b/assets/src/OTR/OTR.md
index a86b6646..47213017 100644
--- a/assets/src/OTR/OTR.md
+++ b/assets/src/OTR/OTR.md
@@ -11,7 +11,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 机器学习主要有三种方式：监督学习，无监督学习与半监督学习。
 
-（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，SVM，ID3，C4.5以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
+（1）监督学习：从给定的训练数据集中学习出一个函数，当新的数据输入时，可以根据函数预测相应的结果。监督学习的训练集要求是包括输入和输出，也就是特征和目标。训练集中的目标是有标注的。如今机器学习已固有的监督学习算法有可以进行分类的，例如贝叶斯分类，`SVM`，ID3，`C4.5` 以及分类决策树，以及现在最火热的人工神经网络，例如BP神经网络，RBF神经网络，Hopfield神经网络、深度信念网络和卷积神经网络等。人工神经网络是模拟人大脑的思考方式来进行分析，在人工神经网络中有显层，隐层以及输出层，而每一层都会有神经元，神经元的状态或开启或关闭，这取决于大数据。同样监督机器学习算法也可以作回归，最常用便是逻辑回归。
 
 （2）无监督学习：与有监督学习相比，无监督学习的训练集的类标号是未知的，并且要学习的类的个数或集合可能事先不知道。常见的无监督学习算法包括聚类和关联，例如K均值法、Apriori算法。
 
@@ -28,6 +28,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 Hawkins(1980)给出孤立点（outlier）的定义：孤立点是在数据集中与众不同的数据，使人怀疑这些数据并非随机孤立点，而是产生于完全不同的机制。孤立点可能在聚集运行或者检测的时候被发现，比如一个人的年龄是999，这在对数据库进行检测的时候就会被发现。还有就是outlier可能是本身就固有的，而不是一个错误，比如CEO的工资就比一般员工的工资高出很多。
 
 2.算法原理
+
 <p align="center">
 <img width="300" align="center" src="../../images/50.jpg" />
 </p>
@@ -43,14 +44,16 @@ Hawkins(1980)给出孤立点（outlier）的定义：孤立点是在数据集中
 算法步骤如下，对每个p点，计算它的第k个最近邻居的距离<img width="50" align="center" src="../../images/51.jpg" />，把具有极大<img width="50" align="center" src="../../images/54.jpg" />值的前个n点作为孤立点。该算法每次处理一个点p，就需要扫描一遍数据库，总共需要扫描N遍（N为数据点数）。
 
 #### 算法应用
+
 孤立点分析被广泛地应用于各种行业，如电信和信用卡欺骗（如检查购买金额或购买次数异常等）、贷款审批、药物研究（如用于发现对多种治疗方式的不寻常的反应）、气象预报、金融领域（如检查洗钱等异常行为）、客户分类（如确定极低或极高收入的客户的消费行为）、网络入侵检测等。
 
 
 #### 相关应用
+
 聚类分析、异常监测、异常欺诈、行为异常
 
 #### 优点和缺点
+
 优点：应用领域广泛，对异常检测、极端情况的事件发生尤其有用。
 
 缺点：孤立点分析时，有时候得到的结果并不是我们想要的，是数据本身固有的一种属性，如总经理的工资待遇比员工高很多；在时间序列中寻找孤立点时，难度比较大，因为时间序列的数据可能隐藏在趋势、季节性或者其他循环规则变化中。对非整型的数值型数据，孤立点定义及分析需要特殊考虑。
-

From 402430c899c44f7742c04327b154d152c623def4 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 16 Apr 2022 20:26:01 +0800
Subject: [PATCH 1348/1406] Update HPD.md

---
 assets/src/HPD/HPD.md | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

diff --git a/assets/src/HPD/HPD.md b/assets/src/HPD/HPD.md
index 7952183e..5df2bb20 100644
--- a/assets/src/HPD/HPD.md
+++ b/assets/src/HPD/HPD.md
@@ -1,7 +1,8 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
-AI的开发离不开算法那我们就接下来开始学习算法吧！
 
+AI的开发离不开算法那我们就接下来开始学习算法吧！
 
 所谓的人工神经网络 （Artificial Neural Network，ANN）简称神经网络(NN)，是基于生物学中神经网络的基本原理，在理解和抽象了人脑结构和外界刺激响应机制后，以网络拓扑知识为理论基础，模拟人脑的神经系统对复杂信息的处理机制的一种数学模型，根植于神经科学、数学、思维科学、人工智能、统计学、物理学、计算机科学以及工程科学的一门技术，通常用于解决分类和回归问题。具有并行分布的处理能力、高容错性、智能化和自学习等能力的特征，本质上是一个有大量简单元件相互连接而成的复杂网络，具有高度的非线性，能够进行复杂的逻辑操作和非线性关系实现的系统。
 
@@ -67,17 +68,25 @@ Hopfield网络按网络输入和输出的数字形式不同可分为离散型和
 
 DHNN结构：它是一种单层全反馈网络,共有n个神经元。每个神经元都通过连接权接收所有其它神经元输出反馈来的信息，其目的是为了让任一神经元的输出能接受所有神经元输出的控制,从而使各神经元能相互制约。
 
-DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）决定的，设计吸引子的核心就是如何设计一组合适的权值。为了使所设计的权值满足要求，权值矩阵应符合以下要求：(1)为保证异步方式工作时网络收敛，W应为对称阵；(2)为保证同步方式工作时网络收敛，W应为非负定对称阵；(3)保证给定的样本是网络的吸引子，并且要有一定的吸引域。
+DHNN的设计原则：吸引子的分布是由网络的权值（包括阀值）决定的，设计吸引子的核心就是如何设计一组合适的权值。为了使所设计的权值满足要求，权值矩阵应符合以下要求：
 
-具体设计时，可以采用不同的方法：(1)联立方程法；(2)外积和法。
+(1)为保证异步方式工作时网络收敛，W应为对称阵；
 
-CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
+(2)为保证同步方式工作时网络收敛，W应为非负定对称阵；
+
+(3)保证给定的样本是网络的吸引子，并且要有一定的吸引域。
 
+具体设计时，可以采用不同的方法：
+
+(1)联立方程法；
+
+(2)外积和法。
+
+CHNN：在连续型Hopfield神经网络中，所有神经元都随时间t并行更新，网络状态随时间连续改变。
 
 #### 应用领域
 Hopfield是反馈归神经网络，主要应用于联想记忆、聚类以及优化计算等方面。
 
-
 #### 优缺点
 
 Hopfield网络是一种非线性的动力网络，可通过反复的网络动态迭代来求解问题，这是符号逻辑方法所不具有的特性。在求解某些问题时，其求解问题的方法与人类求解问题的方法很相似，虽然所求得的解不是最佳解，但其求解速度快，更符合人们日常解决问题的策略。

From a40859dfc2c23b123b20b988000a0e3e8235c653 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Sat, 30 Apr 2022 20:08:29 +0800
Subject: [PATCH 1349/1406] Update CART.md

---
 assets/src/CART/CART.md | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/assets/src/CART/CART.md b/assets/src/CART/CART.md
index 7c750743..e6c6444a 100644
--- a/assets/src/CART/CART.md
+++ b/assets/src/CART/CART.md
@@ -31,19 +31,26 @@ CART算法原理:CART决策树是结构简洁的二叉树，采用一种二分
 </p>
 
 对于给定样本集合D，其基尼指数的计算为：
+
 <p align="center">
 <img width="200" align="center" src="../../images/57.jpg" />
 </p>
+
 如果样本集合D根据特征A是否取某一可能值a被分割成D1和D2两部分，即：<img width="300" align="center" src="../../images/60.jpg" />,D2=D-D1
 则在特征A的条件下，集合D的基尼指数计算公式为：
+
 <p align="center">
 <img width="200" align="center" src="../../images/58.jpg" />
 </p>
+
 基尼指数Gini(D)表示集合D的不确定性，基尼指数Gini(D,A)表示经A=a分割后集合D的不确定性。基尼指数值越大，样本集合的不确定性也就越大。
-（2）回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：
+
+(2)回归树原理：回归树用平方误差最小化准则，进行特征选择，生成二叉树。将输入空间划分为M个区域R1，R2，…，Rm，则生成的回归树模型表示为：
+
 <p align="center">
 <img width="200" align="center" src="../../images/59.jpg" />
 </p>
+
 其中cm表示单元Rm上的最小误差平方的最优解.
 
 2、决策树的剪枝

From 6e69473dbacd4939a1351759cb258c3198bca029 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Tue, 31 May 2022 11:14:42 +0800
Subject: [PATCH 1350/1406] Update RST.md

---
 assets/src/RST/RST.md | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/assets/src/RST/RST.md b/assets/src/RST/RST.md
index 426b31da..69c8d75b 100644
--- a/assets/src/RST/RST.md
+++ b/assets/src/RST/RST.md
@@ -1,4 +1,5 @@
 ### Deeplearning Algorithms tutorial
+
 谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
 AI的开发离不开算法那我们就接下来开始学习算法吧！
 
@@ -39,9 +40,9 @@ D在C上的依赖度定义为：<img width="200" align="center" src="../../image
 
 优点：
 1. 除数据集外，无需任何先验知识（或信息）
-2. 对不确定性的描述和处理相对客观
+2. 对不确定性的描述和处理相对客观.
 
 缺点：
-1. 缺乏处理不精确或不确定原始数据的机制
-2. 对含糊概念的刻画过于简单
-3. 无法解决所有含糊的、模糊的不确定性问题
+1. 缺乏处理不精确或不确定原始数据的机制.
+2. 对含糊概念的刻画过于简单.
+3. 无法解决所有含糊的、模糊的不确定性问题.

From 2ebfafe03f68239273bdb1808dfdbde8b3b1c625 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Wed, 1 Nov 2023 19:12:51 +0800
Subject: [PATCH 1351/1406] Update CAS.md

---
 assets/src/CAS/CAS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/CAS/CAS.md b/assets/src/CAS/CAS.md
index c936d460..7fefbfc0 100644
--- a/assets/src/CAS/CAS.md
+++ b/assets/src/CAS/CAS.md
@@ -64,6 +64,7 @@ AI的开发离不开算法那我们就接下来开始学习算法吧！
 1.可以选取前K个观测变量值为初始中心点；
 
 2.最小最大原则：先选择所有样本数据中距离最远的两个值；并且选择第三个值，使得与前两个聚点的距离最小者等于所有其余数据的较小距离中最大的，依次按这个原则选取，直到最终确定K个中心点；用公式可以表示为：
+
 <p align="center">
 <img width="500" align="center" src="../../images/111.jpg" />
 </p>

From d73d9e29947ff353a8b06d93dd21b33dca9bf25f Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 26 Feb 2024 09:07:41 +0800
Subject: [PATCH 1352/1406] feat: update llm

---
 README.md             | 20 ++++++++++++++++++++
 assets/src/LLM/llm.md |  6 ++++++
 2 files changed, 26 insertions(+)
 create mode 100644 assets/src/LLM/llm.md

diff --git a/README.md b/README.md
index 517ff82c..7c278c21 100644
--- a/README.md
+++ b/README.md
@@ -171,7 +171,27 @@
       * [迁移学习]()
 
 算法模型的整体基本就是这样目录，后续的算法模型我会不断完善和补充，更新！
+
+#### 大模型LLM
+
+大型语言模型（LLM,Large Language Model）伴随着chatgpt的诞生，走进了我们的视野，GPT 3.0它不仅仅是一项具体的技术，其实体现的是LLM应该往何处去的一个发展理念。
+
+自此之后，差距拉得越来越远，ChatGPT只是这种发展理念差异的一个自然结果。
+
+那么什么是大语言模型呢， 我们深入探索和学习下。
+
+大型语言模型（LLM）是基于大量数据进行预训练的超大型深度学习模型。底层转换器是一组神经网络，这些神经网络由具有自注意力功能的编码器和解码器组成。编码器和解码器从一系列文本中提取含义，并理解其中的单词和短语之间的关系。
+
+转换器 LLM 能够进行无监督的训练，但更精确的解释是转换器可以执行自主学习。通过此过程，转换器可学会理解基本的语法、语言和知识。
+
+与早期按顺序处理输入的循环神经网络（RNN）不同，转换器并行处理整个序列。这可让数据科学家使用 GPU 训练基于转换器的 LLM，从而大幅度缩短训练时间。
+
+借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
+
+* [走进大语言模型LLM)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/LLM/llm.0.1.md)
+
 #### 机器学习的基础
+
 * 机器学习需要的理论基础：数学，线性代数，数理统计，概率论，高等数学、凸优化理论，形式逻辑等
 
 #### 参考书籍
diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
new file mode 100644
index 00000000..c84bb2d6
--- /dev/null
+++ b/assets/src/LLM/llm.md
@@ -0,0 +1,6 @@
+### Deeplearning Algorithms tutorial
+
+谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
+AI的开发离不开算法那我们就接下来开始学习算法吧！
+
+#### LLM
\ No newline at end of file

From 7ea3d67308b8b7f429697e259fda43d4de1c5496 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 26 Feb 2024 09:14:04 +0800
Subject: [PATCH 1353/1406] feat: update timeline of llm

---
 assets/images/467.jpg | Bin 0 -> 126562 bytes
 assets/src/LLM/llm.md |  26 ++++++++++++++++++++++----
 2 files changed, 22 insertions(+), 4 deletions(-)
 create mode 100644 assets/images/467.jpg

diff --git a/assets/images/467.jpg b/assets/images/467.jpg
new file mode 100644
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diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index c84bb2d6..9a9cc950 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -1,6 +1,24 @@
-### Deeplearning Algorithms tutorial
+#### 为什么大型语言模型如此重要？
 
-谷歌的人工智能位于全球前列，在图像识别、语音识别、无人驾驶等技术上都已经落地。而百度实质意义上扛起了国内的人工智能的大旗，覆盖无人驾驶、智能助手、图像识别等许多层面。苹果业已开始全面拥抱机器学习，新产品进军家庭智能音箱并打造工作站级别Mac。另外，腾讯的深度学习平台Mariana已支持了微信语音识别的语音输入法、语音开放平台、长按语音消息转文本等产品，在微信图像识别中开始应用。全球前十大科技公司全部发力人工智能理论研究和应用的实现，虽然入门艰难，但是一旦入门，高手也就在你的不远处！
-AI的开发离不开算法那我们就接下来开始学习算法吧！
+大型语言模型非常灵活。一个模型可以执行完全不同的任务，例如回答问题、总结文档、翻译语言和完成语句。LLM 有可能破坏内容创作以及人们使用搜索引擎和虚拟助手的方式。
 
-#### LLM
\ No newline at end of file
+尽管并不完美，但 LLM 表现出根据相对较少量的提示或输入做出预测的非凡能力。LLM 可用于生成式人工智能，以根据采用人类语言的输入提示生成内容。
+
+LLM 非常庞大。它们可以考虑数十亿个参数，并且有许多可能的用途。下面是一些示例：
+
+Open AI 的 GPT-3 模型有 1750 亿个参数。类似的产品 ChatGPT 可以从数据中识别模式并生成自然且可读的输出。
+
+虽然我们不知道 Claude 2 的规模，但该模型可以在每个提示中输入多达 10 万个令牌，这意味着它可以处理数百页的技术文档，甚至可以处理整本书。
+
+AI21 Labs 的 Jurassic-1 模型具有 1780 亿个参数和由 25 万单词部分组成的令牌词汇表以及类似的对话功能。
+
+Cohere 的 Command 模型具有类似的功能，并且可以使用 100 多种不同的语言开展工作。
+
+LightOn 的 Paradigm 提供根基模型，并且宣称该模型的功能超过 GPT-3。所有这些 LLM 都带有 API，可让开发人员打造独特的生成式人工智能应用程序。
+
+
+Timeline of LLMs:
+
+<p align="center">
+<img width="400" align="center" src="../../images/467.jpg" />
+</p>
\ No newline at end of file

From 2f0a581e41ee2301538e78384a6e5f70894fffcc Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 27 Feb 2024 09:23:40 +0800
Subject: [PATCH 1354/1406] feat: update llm

---
 assets/src/LLM/llm.md | 80 ++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 79 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 9a9cc950..cc028741 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -1,3 +1,13 @@
+#### 什么是大型语言模型？
+
+大型语言模型（LLM）是基于大量数据进行预训练的超大型深度学习模型。底层转换器是一组神经网络，这些神经网络由具有自注意力功能的编码器和解码器组成。编码器和解码器从一系列文本中提取含义，并理解其中的单词和短语之间的关系。
+
+转换器 LLM 能够进行无监督的训练，但更精确的解释是转换器可以执行自主学习。通过此过程，转换器可学会理解基本的语法、语言和知识。
+
+与早期按顺序处理输入的循环神经网络（RNN）不同，转换器并行处理整个序列。这可让数据科学家使用 GPU 训练基于转换器的 LLM，从而大幅度缩短训练时间。
+
+借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
+
 #### 为什么大型语言模型如此重要？
 
 大型语言模型非常灵活。一个模型可以执行完全不同的任务，例如回答问题、总结文档、翻译语言和完成语句。LLM 有可能破坏内容创作以及人们使用搜索引擎和虚拟助手的方式。
@@ -21,4 +31,72 @@ Timeline of LLMs:
 
 <p align="center">
 <img width="400" align="center" src="../../images/467.jpg" />
-</p>
\ No newline at end of file
+</p>
+
+#### 大型语言模型如何运作？
+
+LLM 运作原理的一个关键因素是它们表示单词的方式。
+
+早期的机器学习使用数字表来表示每个单词。但是，这种表示形式无法识别单词之间的关系，例如具有相似含义的单词。
+
+人们采用如下方式克服此限制：使用多维向量（通常称为单词嵌入）来表示单词，从而使具有相似上下文含义或其他关系的单词在向量空间中彼此接近。
+
+使用单词嵌入，转换器可以通过编码器将文本预处理为数字表示，并理解含义相似的单词和短语的上下文以及单词之间的其他关系，例如语音部分。然后，LLM 就可以通过解码器应用这些语言知识来生成独特的输出。
+
+#### 大型语言模型有哪些应用？
+
+LLM 有很多实际应用。
+
+* 文案写作
+
+除了 GPT-3 和 ChatGPT 之外，Claude、Llama 2、Cohere Command 和 Jurassic 也可编写原件。AI21 Wordspice 建议修改原始语句以改善风格和语音。
+
+* 知识库回答
+
+该技术通常称为知识密集型自然语言处理（KI-NLP），是指可以根据数字存档中的信息帮助回答特定问题的 LLM。AI21 Studio playground 能够回答常识性问题就是此类示例。
+
+* 文本分类
+
+使用集群，LLM 可以对含义或情绪相似的文本进行分类。用途包括衡量客户情绪、确定文本之间的关系和文档搜索。
+
+* 代码生成
+
+LLM 擅长根据自然语言提示生成代码。示例包括 Amazon CodeWhisperer 和 GitHub Copilot 中使用的 Open AI Codex，它们可以用 Python、JavaScript、Ruby 和其他几种编程语言编码。其他编码应用包括创建 SQL 查询、编写 Shell 命令和进行网站设计。
+
+* 文本生成
+
+与代码生成类似，文本生成可以完成不完整的语句，编写产品文档，或者像 Alexa Create 一样创作简短的儿童故事。
+
+#### 如何训练大型语言模型？
+
+基于转换器的神经网络非常庞大。这些网络包含多个节点和层。层中的每个节点都有指向后续层中所有节点的连接，并且每个节点都有权重和偏差。权重和偏差以及嵌入称为模型参数。基于转换器的大型神经网络可以有数十亿个参数。模型的大小通常由模型大小、参数数量和训练数据规模之间的经验关系决定。
+
+使用大量高质量数据执行训练。在训练过程中，模型会迭代调整参数值，直到模型可根据前一个输入令牌序列正确预测下一个令牌。为此，模型使用自学技术，这些技术教导模型调整参数，以最大限度地提高训练示例中正确预测下一个令牌的可能性。
+
+经过训练，LLM 可以很容易地适应使用相对较小的有监督数据集执行多项任务，这一过程称为微调。
+
+存在三种常见的学习模型：
+
+* 零样本学习；Base LLM 无需明确训练即可响应各种请求，通常是通过提示，但是答案的准确性各不相同。
+* 少量样本学习：通过提供一些相关的训练示例，基础模型在该特定领域的表现显著提升。
+* 微调：这是少量样本学习的扩展，其中数据科学家训练基础模型，使模型使用与特定应用相关的其他数据来调整其参数。
+
+#### LLM 的未来前景是什么？
+
+随着 ChatGPT、Claude 2 和 Llama 2 等可以回答问题和生成文本的大型语言模型的引入，我们可以预见令人兴奋的未来前景。可以肯定的是，LLM 会越来越接近人性化的表现，尽管这一过程会较为漫长。这些 LLM 即时取得的成功表明人们对机器人类型 LLM 的浓厚兴趣，这些 LLM 可模仿人类大脑的思维，在某些情况下表现甚至优于人类大脑。以下是一些关于 LLM 未来前景的想法：
+
+* 增强的功能
+
+尽管 LLM 给人们留下了深刻的印象，但当前的技术水平并不完善，LLM 也并非绝对可靠。然而，随着开发人员学习如何在减少偏见和消除错误答案的同时提高性能，较新的 LLM 版本将提高准确性和增强功能。
+
+* 视听训练
+
+开发人员使用文本训练大多数 LLM，但有些人已经开始使用视频和音频输入来训练模型。这种形式的训练应该可以加快模型开发速度，并为将 LLM 用于自动驾驶汽车开辟新的可能性。
+
+* 工作场所转型
+
+LLM 是颠覆性的因素，它将转变工作场所。LLM 可能会采用机器人处理重复性制造任务的相同方式来减少单调和重复的任务。可能减少的任务包括重复的文书任务、客户服务聊天机器人和简单的自动文案写作。
+
+* 对话式人工智能
+
+LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的性能。这些虚拟助手将能够更妥善地解释用户意图并响应复杂的命令。
\ No newline at end of file

From 491a841a94e3d5e8b67c3473e2164f9f1aa9ba2f Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 28 Feb 2024 09:31:55 +0800
Subject: [PATCH 1355/1406] feat: update llm

---
 assets/src/LLM/llm.md | 34 ++++++++++++++++++++++++++++++++--
 1 file changed, 32 insertions(+), 2 deletions(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index cc028741..37cfe348 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -49,7 +49,9 @@ LLM 有很多实际应用。
 
 * 文案写作
 
-除了 GPT-3 和 ChatGPT 之外，Claude、Llama 2、Cohere Command 和 Jurassic 也可编写原件。AI21 Wordspice 建议修改原始语句以改善风格和语音。
+除了 GPT-3 和 ChatGPT 之外，Claude、Llama 2、Cohere Command 和 Jurassic 也可编写原件。
+
+AI21 Wordspice 建议修改原始语句以改善风格和语音。
 
 * 知识库回答
 
@@ -99,4 +101,32 @@ LLM 是颠覆性的因素，它将转变工作场所。LLM 可能会采用机器
 
 * 对话式人工智能
 
-LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的性能。这些虚拟助手将能够更妥善地解释用户意图并响应复杂的命令。
\ No newline at end of file
+LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的性能。这些虚拟助手将能够更妥善地解释用户意图并响应复杂的命令。
+
+#### 学习大语言模型指南
+
+* 入门篇：
+
+1. 了解大语言模型的基础知识和常见术语。
+
+2. 学会使用编程语言访问 OpenAI API 等常见大语言模型接口。
+
+* 提高篇：
+
+1. 了解机器学习、神经网络、NLP 的基础知识。
+2. 了解 Transformer 以及典型 Decoder-only 语言模型的基础结构和简单原理。
+3. 了解大语言模型发展历史，以及业界主流模型（含开源模型）进展。
+
+* 应用篇：
+
+1. 可以在本地环境搭建开源模型的推理环境。
+2. Prompt 工程。
+3. 使用已有框架（如Langchain）或自行开发，结合大语言模型结果，开发生产应用。
+
+* 深入篇：（本文涉及少量资料）
+
+1. 掌握 Continue Pre-train、Fine-tuning 已有开源模型的能力。
+2. 掌握 Lora、QLora 等低资源高效模型训练的能力。
+3. 掌握大语言模型微调以及预训练数据准备的能力。
+4. 深入了解大模型背后的技术原理。
+5. 了解生产环境部署大模型的相关技术点。
\ No newline at end of file

From 8f45bc2e320ae8857840265b64abaa23577560d2 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 29 Feb 2024 09:32:22 +0800
Subject: [PATCH 1356/1406] feat: update llm

---
 .DS_Store             | Bin 0 -> 6148 bytes
 assets/src/LLM/llm.md |  16 +++++++++++++++-
 2 files changed, 15 insertions(+), 1 deletion(-)
 create mode 100644 .DS_Store

diff --git a/.DS_Store b/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..80e0543a3322e73d099ce46f7c09c789419e089c
GIT binary patch
literal 6148
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zNm{&#=uDV-o7tJo<|Sk@MC9_ja!8aCQ37S`?ZT`Po@ebyPdz;8;u_=G)o^rKSMyG+
zIesSt{Oq>rfNrRyDYc&8;H)`Y)kQIx)f0G=!}G`V?c@EZ9Z`N0F~44YLr#%SJ2a*R
zjw#*JqVWbjJ)gAaSNHJpaGwuk4~;dd`fC@PVjBB+4ZIH%W55_N2L1~JsM##Zo}gJ{
zz!)$FmJIOs!9y7{#UL0z9Wb#40QTXIf-(0JoZ}TU#UO|oh?7*Hq&jUeoTS6=H7-*O
zf|5>7n-8Z~cG{u1cy+ArV>r1?(5x|F3^W<olGBvy|MBMjznNrb#(**Krx<YkVpQa~
zC9SQUo8wyRp%+jVjthdz6bxc1Ml6@&eP|T;Jr97HVi1G}Vm|_r1~bOMk23HH|D8%z

literal 0
HcmV?d00001

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 37cfe348..e6b5a6a3 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -129,4 +129,18 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 2. 掌握 Lora、QLora 等低资源高效模型训练的能力。
 3. 掌握大语言模型微调以及预训练数据准备的能力。
 4. 深入了解大模型背后的技术原理。
-5. 了解生产环境部署大模型的相关技术点。
\ No newline at end of file
+5. 了解生产环境部署大模型的相关技术点。
+
+#### 学习资料
+
+1. 入门篇
+
+* [大语言模型](https://github.com/RUCAIBox/LLMSurvey)
+
+Prompt 工程:
+
+* [ChatGPT Prompt Engineering for Developers](https://learn.deeplearning.ai/courses/chatgpt-prompt-eng/lesson/1/introduction)
+* [Prompt中英双语字幕](https://github.com/GitHubDaily/ChatGPT-Prompt-Engineering-for-Developers-in-Chinese)
+* [OpenAI 官方 Quickstart 文档](https://platform.openai.com/docs/api-reference)
+* [GPT的训练和应用](https://www.youtube.com/watch?v=bZQun8Y4L2A)
+* [GPT的训练和应用稳定](https://karpathy.ai/stateofgpt.pdf)
\ No newline at end of file

From 3e8575d783abc5d932807df43c27ede92281c0a0 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 29 Feb 2024 11:37:31 +0800
Subject: [PATCH 1357/1406] feat: update readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 7c278c21..29aa84ad 100644
--- a/README.md
+++ b/README.md
@@ -188,7 +188,7 @@
 
 借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
 
-* [走进大语言模型LLM)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/LLM/llm.0.1.md)
+* [走进大语言模型LLM)](https://github.com/KeKe-Li/tutorial/blob/master/assets/src/LLM/llm.md)
 
 #### 机器学习的基础
 

From 8d52118aa69e0dc2761b0b5e999f06d4dcf07ee3 Mon Sep 17 00:00:00 2001
From: keke <2536485681li@gmail.com>
Date: Thu, 29 Feb 2024 11:38:32 +0800
Subject: [PATCH 1358/1406] Update llm.md

---
 assets/src/LLM/llm.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index e6b5a6a3..415f6786 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -30,7 +30,7 @@ LightOn 的 Paradigm 提供根基模型，并且宣称该模型的功能超过 G
 Timeline of LLMs:
 
 <p align="center">
-<img width="400" align="center" src="../../images/467.jpg" />
+<img width="700" align="center" src="../../images/467.jpg" />
 </p>
 
 #### 大型语言模型如何运作？
@@ -143,4 +143,4 @@ Prompt 工程:
 * [Prompt中英双语字幕](https://github.com/GitHubDaily/ChatGPT-Prompt-Engineering-for-Developers-in-Chinese)
 * [OpenAI 官方 Quickstart 文档](https://platform.openai.com/docs/api-reference)
 * [GPT的训练和应用](https://www.youtube.com/watch?v=bZQun8Y4L2A)
-* [GPT的训练和应用稳定](https://karpathy.ai/stateofgpt.pdf)
\ No newline at end of file
+* [GPT的训练和应用稳定](https://karpathy.ai/stateofgpt.pdf)

From a110697e9cca1fd77d829fa383a75e4a20299b7a Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 29 Feb 2024 11:40:47 +0800
Subject: [PATCH 1359/1406] feat: update llm

---
 assets/src/LLM/llm.md | 38 +++++++++++++++++---------------------
 1 file changed, 17 insertions(+), 21 deletions(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 415f6786..30301a08 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -105,40 +105,36 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 
 #### 学习大语言模型指南
 
-* 入门篇：
+1. 入门篇：
 
-1. 了解大语言模型的基础知识和常见术语。
+* 了解大语言模型的基础知识和常见术语。
+* 学会使用编程语言访问 OpenAI API 等常见大语言模型接口。
 
-2. 学会使用编程语言访问 OpenAI API 等常见大语言模型接口。
+2. 提高篇：
 
-* 提高篇：
+* 了解机器学习、神经网络、NLP 的基础知识。
+* 了解 Transformer 以及典型 Decoder-only 语言模型的基础结构和简单原理。
+* 了解大语言模型发展历史，以及业界主流模型（含开源模型）进展。
 
-1. 了解机器学习、神经网络、NLP 的基础知识。
-2. 了解 Transformer 以及典型 Decoder-only 语言模型的基础结构和简单原理。
-3. 了解大语言模型发展历史，以及业界主流模型（含开源模型）进展。
+3. 应用篇：
 
-* 应用篇：
+*  可以在本地环境搭建开源模型的推理环境。
+* Prompt 工程。
+* 使用已有框架（如Langchain）或自行开发，结合大语言模型结果，开发生产应用。
 
-1. 可以在本地环境搭建开源模型的推理环境。
-2. Prompt 工程。
-3. 使用已有框架（如Langchain）或自行开发，结合大语言模型结果，开发生产应用。
+4. 深入篇：
 
-* 深入篇：（本文涉及少量资料）
-
-1. 掌握 Continue Pre-train、Fine-tuning 已有开源模型的能力。
-2. 掌握 Lora、QLora 等低资源高效模型训练的能力。
-3. 掌握大语言模型微调以及预训练数据准备的能力。
-4. 深入了解大模型背后的技术原理。
-5. 了解生产环境部署大模型的相关技术点。
+* 掌握 Continue Pre-train、Fine-tuning 已有开源模型的能力。
+* 掌握 Lora、QLora 等低资源高效模型训练的能力。
+* 掌握大语言模型微调以及预训练数据准备的能力。
+* 深入了解大模型背后的技术原理。
+* 了解生产环境部署大模型的相关技术点。
 
 #### 学习资料
 
 1. 入门篇
 
 * [大语言模型](https://github.com/RUCAIBox/LLMSurvey)
-
-Prompt 工程:
-
 * [ChatGPT Prompt Engineering for Developers](https://learn.deeplearning.ai/courses/chatgpt-prompt-eng/lesson/1/introduction)
 * [Prompt中英双语字幕](https://github.com/GitHubDaily/ChatGPT-Prompt-Engineering-for-Developers-in-Chinese)
 * [OpenAI 官方 Quickstart 文档](https://platform.openai.com/docs/api-reference)

From fbe6c75759e6bb2a2334c299dbbc41c9f2835414 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 1 Mar 2024 09:12:00 +0800
Subject: [PATCH 1360/1406] feat: update llm

---
 assets/src/LLM/llm.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 30301a08..692bfc25 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -140,3 +140,13 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 * [OpenAI 官方 Quickstart 文档](https://platform.openai.com/docs/api-reference)
 * [GPT的训练和应用](https://www.youtube.com/watch?v=bZQun8Y4L2A)
 * [GPT的训练和应用稳定](https://karpathy.ai/stateofgpt.pdf)
+
+
+2. 提高篇
+* [清华大模型公开课](https://www.bilibili.com/video/BV1UG411p7zv/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8) ,从NLP到大模型的综合课程。
+* [深度学习：台湾大学李宏毅](https://www.bilibili.com/video/BV1J94y1f7u5/)
+* [The Illustrated GPT-2 (Visualizing Transformer Language Models](https://jalammar.github.io/illustrated-gpt2/),图解 GPT2 。
+* [图解 GPT2 中文翻译](https://zhuanlan.zhihu.com/p/139840113)
+* [InstructGPT: Training language models to follow instructions with human feedback](https://cdn.openai.com/papers/Training_language_models_to_follow_instructions_with_human_feedback.pdf), 著名的 InstructGPT 论文。
+* [RLHF技术详解](https://huggingface.co/blog/zh/rlhf)
+* [NLP 入门课程](https://huggingface.co/learn/nlp-course/chapter1/1)
\ No newline at end of file

From dce5d2589f87f419e1a1c6423817d5fa4f617d1d Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 2 Mar 2024 13:52:23 +0800
Subject: [PATCH 1361/1406] feat: update llm

---
 assets/src/LLM/llm.md | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 692bfc25..4685830a 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -149,4 +149,15 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 * [图解 GPT2 中文翻译](https://zhuanlan.zhihu.com/p/139840113)
 * [InstructGPT: Training language models to follow instructions with human feedback](https://cdn.openai.com/papers/Training_language_models_to_follow_instructions_with_human_feedback.pdf), 著名的 InstructGPT 论文。
 * [RLHF技术详解](https://huggingface.co/blog/zh/rlhf)
-* [NLP 入门课程](https://huggingface.co/learn/nlp-course/chapter1/1)
\ No newline at end of file
+* [NLP 入门课程](https://huggingface.co/learn/nlp-course/chapter1/1)
+
+3. 应用篇
+
+* [Building Systems with the ChatGPT API](https://learn.deeplearning.ai/courses/chatgpt-building-system/lesson/1/introduction)
+* [使用 ChatGPT API 构建系统](https://www.bilibili.com/video/BV1gj411X72B/)
+* [Langchain 是大语言模型框架](https://python.langchain.com/docs/get_started/introduction)
+* [LangChain for LLM Application Development](https://learn.deeplearning.ai/courses/langchain/lesson/1/introduction)
+* [LLM应用开发实践](https://www.bilibili.com/video/BV1Ku411x78m/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8)
+* [OpenAI 官方出的最佳实践](https://platform.openai.com/docs/guides/gpt-best-practices/gpt-best-practices)
+* [OpenAI 官方 Cookbook](https://github.com/openai/openai-cookbook)
+* [Prompt 工程简介](https://github.com/brexhq/prompt-engineering)

From 007186f542a53b5913a454e846d76d235220c224 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 4 Mar 2024 09:15:38 +0800
Subject: [PATCH 1362/1406] feat: update llm transformer

---
 assets/src/LLM/llm.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 4685830a..170423da 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -161,3 +161,11 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 * [OpenAI 官方出的最佳实践](https://platform.openai.com/docs/guides/gpt-best-practices/gpt-best-practices)
 * [OpenAI 官方 Cookbook](https://github.com/openai/openai-cookbook)
 * [Prompt 工程简介](https://github.com/brexhq/prompt-engineering)
+
+
+4. 深入篇
+
+* [Transformer 官方文档](https://huggingface.co/docs/transformers/index)
+* [大语言模型的北极星能力](https://yaofu.notion.site/6dafe3f8d11445ca9dcf8a2ca1c5b199)
+* [GPT，GPT-2，GPT-3 论文精读](https://www.bilibili.com/video/BV1AF411b7xQ/)
+* [在生产环境中构建 LLM 应用](https://huyenchip.com/2023/04/11/llm-engineering.html)
\ No newline at end of file

From d4c2cfa4ad0104a3e9282c0c45d72687886eaf90 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 5 Mar 2024 09:21:29 +0800
Subject: [PATCH 1363/1406] feat: update llm

---
 assets/src/LLM/llm.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 170423da..c98732b3 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -143,11 +143,11 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 
 
 2. 提高篇
-* [清华大模型公开课](https://www.bilibili.com/video/BV1UG411p7zv/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8) ,从NLP到大模型的综合课程。
+* [清华大模型公开课:从NLP到大模型的综合课程](https://www.bilibili.com/video/BV1UG411p7zv/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8) 
 * [深度学习：台湾大学李宏毅](https://www.bilibili.com/video/BV1J94y1f7u5/)
-* [The Illustrated GPT-2 (Visualizing Transformer Language Models](https://jalammar.github.io/illustrated-gpt2/),图解 GPT2 。
+* [The Illustrated GPT-2 (Visualizing Transformer Language Models](https://jalammar.github.io/illustrated-gpt2/)
 * [图解 GPT2 中文翻译](https://zhuanlan.zhihu.com/p/139840113)
-* [InstructGPT: Training language models to follow instructions with human feedback](https://cdn.openai.com/papers/Training_language_models_to_follow_instructions_with_human_feedback.pdf), 著名的 InstructGPT 论文。
+* [InstructGPT: Training language models to follow instructions with human feedback](https://cdn.openai.com/papers/Training_language_models_to_follow_instructions_with_human_feedback.pdf)
 * [RLHF技术详解](https://huggingface.co/blog/zh/rlhf)
 * [NLP 入门课程](https://huggingface.co/learn/nlp-course/chapter1/1)
 

From cd70a069bdd97230ede5e70e47dd1b448a74d420 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 6 Mar 2024 09:11:34 +0800
Subject: [PATCH 1364/1406] feat: update llm

---
 assets/src/LLM/llm.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index c98732b3..796b6e86 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -154,7 +154,7 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 3. 应用篇
 
 * [Building Systems with the ChatGPT API](https://learn.deeplearning.ai/courses/chatgpt-building-system/lesson/1/introduction)
-* [使用 ChatGPT API 构建系统](https://www.bilibili.com/video/BV1gj411X72B/)
+* [使用ChatGPT API构建系统](https://www.bilibili.com/video/BV1gj411X72B/)
 * [Langchain 是大语言模型框架](https://python.langchain.com/docs/get_started/introduction)
 * [LangChain for LLM Application Development](https://learn.deeplearning.ai/courses/langchain/lesson/1/introduction)
 * [LLM应用开发实践](https://www.bilibili.com/video/BV1Ku411x78m/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8)

From d856e6ce646e8a7876920cf2686ccbcd0feb35e1 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 7 Mar 2024 09:05:29 +0800
Subject: [PATCH 1365/1406] feat: update llm

---
 assets/src/LLM/llm.md   | 1 +
 assets/src/LLM/llm01.md | 9 +++++++++
 2 files changed, 10 insertions(+)
 create mode 100644 assets/src/LLM/llm01.md

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index 796b6e86..c97d890c 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -143,6 +143,7 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 
 
 2. 提高篇
+
 * [清华大模型公开课:从NLP到大模型的综合课程](https://www.bilibili.com/video/BV1UG411p7zv/?vd_source=66c6e275fb1f3c8315a531e1a1b051d8) 
 * [深度学习：台湾大学李宏毅](https://www.bilibili.com/video/BV1J94y1f7u5/)
 * [The Illustrated GPT-2 (Visualizing Transformer Language Models](https://jalammar.github.io/illustrated-gpt2/)
diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
new file mode 100644
index 00000000..75afb880
--- /dev/null
+++ b/assets/src/LLM/llm01.md
@@ -0,0 +1,9 @@
+#### 什么是大型语言模型？
+
+大型语言模型（LLM）是基于大量数据进行预训练的超大型深度学习模型。底层转换器是一组神经网络，这些神经网络由具有自注意力功能的编码器和解码器组成。编码器和解码器从一系列文本中提取含义，并理解其中的单词和短语之间的关系。
+
+转换器 LLM 能够进行无监督的训练，但更精确的解释是转换器可以执行自主学习。通过此过程，转换器可学会理解基本的语法、语言和知识。
+
+与早期按顺序处理输入的循环神经网络（RNN）不同，转换器并行处理整个序列。这可让数据科学家使用 GPU 训练基于转换器的 LLM，从而大幅度缩短训练时间。
+
+借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。

From 06bdc328a91f26ee96133c2dd1425eadb2172051 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 8 Mar 2024 09:10:13 +0800
Subject: [PATCH 1366/1406] feat: update llm

---
 assets/src/LLM/llm.md   | 2 +-
 assets/src/LLM/llm01.md | 1 +
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm.md b/assets/src/LLM/llm.md
index c97d890c..1f32b023 100644
--- a/assets/src/LLM/llm.md
+++ b/assets/src/LLM/llm.md
@@ -118,7 +118,7 @@ LLM 无疑将提高 Alexa、Google Assistant 和 Siri 等自动虚拟助手的
 
 3. 应用篇：
 
-*  可以在本地环境搭建开源模型的推理环境。
+* 可以在本地环境搭建开源模型的推理环境。
 * Prompt 工程。
 * 使用已有框架（如Langchain）或自行开发，结合大语言模型结果，开发生产应用。
 
diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 75afb880..dc200e5e 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -7,3 +7,4 @@
 与早期按顺序处理输入的循环神经网络（RNN）不同，转换器并行处理整个序列。这可让数据科学家使用 GPU 训练基于转换器的 LLM，从而大幅度缩短训练时间。
 
 借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
+

From 83ec1930fb6fef90e28a1e721c0ea19d0f57696e Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 9 Mar 2024 10:23:27 +0800
Subject: [PATCH 1367/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index dc200e5e..d2244a22 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -8,3 +8,41 @@
 
 借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
 
+
+#### 大型语言模型工作原理
+
+LLM 通过利用深度学习技术和大量文本数据来运行。这些模型通常基于转换器架构，如生成式预训练转换器，它擅长处理文本输入等顺序数据。LLM 由多层神经网络组成，每层神经网络的参数都可以在训练过程中进行微调，而被称为注意力机制的众多神经网络层则进一步增强了这些神经网络的功能，这些神经网络层可以对数据集的特定部分进行调整。
+
+在训练过程中，这些模型学习根据前面单词提供的上下文来预测句子中的下一个单词。该模型通过将概率分数归因于重复的已标记单词（分解为较小的字符序列）来实现这一点。然后，这些标记被转换为嵌入，嵌入是该上下文的数字表示。
+
+为了确保准确性，这个过程涉及在大量文本语料库（数十亿页）上训练 LLM，使 LLM 能够通过零样本和自我监督学习来学习语法、语义和概念关系。经过这些训练数据的训练后，LLM 就可以根据它们收到的输入自动预测下一个单词，并利用它们获得的模式和知识来生成文本。其结果是生成连贯且与上下文相关的语言，可用于广泛的 NLU 和内容生成任务。
+
+还可以通过即时工程、即时调优、微调和其他策略来提高模型性能，例如基于人类反馈的强化学习 (RLHF)，以消除偏见、仇恨言论和被称为“幻觉”的事实错误答案，这些通常是对如此多的非结构化数据进行训练的有害副产品。这是确保企业级 LLM 随时可用，不会使组织承担不必要的责任或对组织声誉造成损害的最重要的方面之一。
+
+
+#### LLM 用例
+
+LLM 正在重新定义越来越多的业务流程，并已在各个行业的无数用例和任务中证明了它们的多功能性。LLM 可以增强聊天机器人和虚拟助理（例如 IBM watsonx Assistant 和 Google 的 BARD）中的会话式 AI，以增强支持卓越客户服务的交互，提供模仿与人工客服交互的情境感知响应。
+
+LLM 还擅长内容生成，可以自动创建内容，包括博客文章、营销或销售资料以及其他写作任务。在研究和学术界，它们帮助从大量数据集中总结和提取信息，加速知识发现。LLM 在语言翻译中也发挥着至关重要的作用，通过提供准确且与上下文相关的翻译来打破语言障碍。它们甚至可以用来编写代码，或者在编程语言之间进行“翻译”。
+
+此外，它们还通过提供文字转语音应用以及以无障碍格式生成内容等功能，帮助残障人员，为无障碍访问功能做出了贡献。从医疗保健到金融，LLM 正在通过简化流程、改善客户体验以及实现更高效和数据驱动的决策来推动行业发展和变革。
+
+最令人兴奋的是，所有这些功能都很容易访问，在某些情况下，实际上只需 API 集成即可。
+
+以下是 LLM 为组织带来益处的一些最重要的领域：
+
+* 文本生成：语言生成能力，如根据提示撰写电子邮件、博客文章或其他中长篇内容，并加以提炼和润色。检索增强生成 (RAG) 就是一个很好的例子。
+
+* 内容摘要：将长文章、新闻报道、研究报告、公司文档甚至客户历史记录汇总成根据输出格式定制长度的完整文本。
+
+* AI 助手：聊天机器人，可以回答客户询问、执行后端任务并以自然语言提供详细信息，作为集成式自助客户服务解决方案的一部分。
+
+* 代码生成：帮助开发人员构建应用程序，查找代码中的错误并发现多种编程语言中的安全问题，甚至在它们之间进行“翻译”。
+
+* 情感分析：分析文本，确定客户的语气，以便大规模了解客户反馈并帮助进行品牌声誉管理。
+
+* 语言翻译：通过流畅的翻译和多语言功能，为各语言和地域的组织提供更广泛的覆盖范围。
+
+LLM 将通过实现客户自助服务自动化、加快对越来越多任务的响应以及提高准确性、增强路由和智能上下文收集，影响从金融到保险、人力资源到医疗保健等各个行业。
+

From 4ef1ac3319a3c6129a4f8e02b50650244a73d150 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sun, 10 Mar 2024 10:59:41 +0800
Subject: [PATCH 1368/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index d2244a22..5f80693e 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -19,7 +19,6 @@ LLM 通过利用深度学习技术和大量文本数据来运行。这些模型
 
 还可以通过即时工程、即时调优、微调和其他策略来提高模型性能，例如基于人类反馈的强化学习 (RLHF)，以消除偏见、仇恨言论和被称为“幻觉”的事实错误答案，这些通常是对如此多的非结构化数据进行训练的有害副产品。这是确保企业级 LLM 随时可用，不会使组织承担不必要的责任或对组织声誉造成损害的最重要的方面之一。
 
-
 #### LLM 用例
 
 LLM 正在重新定义越来越多的业务流程，并已在各个行业的无数用例和任务中证明了它们的多功能性。LLM 可以增强聊天机器人和虚拟助理（例如 IBM watsonx Assistant 和 Google 的 BARD）中的会话式 AI，以增强支持卓越客户服务的交互，提供模仿与人工客服交互的情境感知响应。

From d08f78288c41387835227482963a1bbf7fd84aed Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 11 Mar 2024 10:06:50 +0800
Subject: [PATCH 1369/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 5f80693e..dc69301b 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -45,3 +45,32 @@ LLM 还擅长内容生成，可以自动创建内容，包括博客文章、营
 
 LLM 将通过实现客户自助服务自动化、加快对越来越多任务的响应以及提高准确性、增强路由和智能上下文收集，影响从金融到保险、人力资源到医疗保健等各个行业。
 
+#### 增加大语言模型推理能力的方案
+
+目前，推理的方案与构建通用大型语言模型和聊天机器人的方案密切相关。总共有三个阶段：
+
+- 预训练或持续训练：在这个阶段，我们通常在大型数据集（如科学文献或代码数据）上训练大型模型。
+- 有监督微调：在这个阶段，我们对模型进行微调，以便完成复杂任务的指令。
+- 强化学习：在这个阶段，我们使用诸如任务是否已全部/部分完成的信号作为奖励。
+
+因此，在我们的文献分析中，我们同时考虑推理和编码。我们将看到，就学习方法而言，这两者之间存在惊人的相关性。
+
+* 预训练与持续训练
+
+分析以下几项研究：
+
+1. Lewkowycz et. al. 2022. Minerva: [Solving Quantitative Reasoning Problems with Language Models](https://arxiv.org/abs/2206.14858)
+
+* 在来自 Arxiv 论文的 38.5B 的 token 上继续训练 PaLM 540B。 
+* 在 MATH （一个需要使用 LaTeX 格式回答问题的困难数据集），上的得分为 33.6（[GPT-4 的得分是 42.5](https://github.com/FranxYao/chain-of-thought-hub)）
+
+2. Taylor et. al. 2022. [Galactica: A Large Language Model for Science](https://arxiv.org/abs/2211.09085)
+
+* 在包含论文、代码、参考资料、知识库和其他内容的 106B token 上预训练一个120B语言模型。
+* 在MATH上的表现为 20.4（Minerva 33.6，GPT-4 42.5） 
+ 
+3. Chen et. al. 2021. [Codex: Evaluating Large Language Models Trained on Code](https://arxiv.org/abs/2107.03374)
+
+* 在159GB代码数据上继续训练 12B GPT-3 模型，提高了 HumanEval 数据集上的代码性能。
+
+这些研究发现，在大量科学文献代码上进行训练可以显著提高基础模型的推理编码能力。
\ No newline at end of file

From 9725d7092a318d9749139ec1fe38ff3e7a018c44 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 12 Mar 2024 09:12:14 +0800
Subject: [PATCH 1370/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index dc69301b..3c6341b0 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -73,4 +73,12 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 * 在159GB代码数据上继续训练 12B GPT-3 模型，提高了 HumanEval 数据集上的代码性能。
 
-这些研究发现，在大量科学文献代码上进行训练可以显著提高基础模型的推理编码能力。
\ No newline at end of file
+这些研究发现，在大量科学文献代码上进行训练可以显著提高基础模型的推理编码能力。
+
+####  监督微调
+
+1.  Chung et. al. 2022. [Scaling Instruction-Finetuned Language Models](https://arxiv.org/abs/2210.11416)
+- 使用多样化的指令显著提高了模型零样本泛化的能力
+- 在指令集合中混合思维链数据（[the flan collection](https://arxiv.org/abs/2301.13688) 文章中进一步讨论了这个问题）明显提高了模型的思维链能力
+- 注意：尽管 the flan collection 数据集从多个维度激发了基础模型的能力，但这些指令并非来自真实的聊天机器人用户互动，因此可能无法直接转化为更好的聊天性能。
+

From af914248d1014317aeecb0ee1a8cf75ec72a6161 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 13 Mar 2024 09:08:27 +0800
Subject: [PATCH 1371/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 19 ++++++++++++++++++-
 1 file changed, 18 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 3c6341b0..b951217a 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -78,7 +78,24 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 ####  监督微调
 
 1.  Chung et. al. 2022. [Scaling Instruction-Finetuned Language Models](https://arxiv.org/abs/2210.11416)
+
 - 使用多样化的指令显著提高了模型零样本泛化的能力
 - 在指令集合中混合思维链数据（[the flan collection](https://arxiv.org/abs/2301.13688) 文章中进一步讨论了这个问题）明显提高了模型的思维链能力
-- 注意：尽管 the flan collection 数据集从多个维度激发了基础模型的能力，但这些指令并非来自真实的聊天机器人用户互动，因此可能无法直接转化为更好的聊天性能。
+- 注意：尽管 the flan collection 数据集从多个维度激发了基础模型的能力，但这些指令并非来自真实的聊天机器人用户互动，因此可能[无法直接转化为更好的聊天性能](https://www.yitay.net/blog/flan-ul2-20b)。
+
+2. Fu et. al. 2023. [Specializing Smaller Language Models towards Multi-Step Reasoning](https://arxiv.org/abs/2301.12726)
+
+- 将思维链推理能力提炼到较小规模（小于或等于 10B）的模型。通常，10B 规模的模型非常适合部署（更大的模型太贵了，更小的模型太弱了）。
+- 本文讨论了很多工程细节，如数据工程、能力平衡以及小型和大型模型之间的差异
+
+3.  [Li et. al. 2022. Competition-Level Code Generation with AlphaCode](https://arxiv.org/abs/2203.07814)
+
+- 在 715GB 的 GitHub 代码上预训练一个 41B 模型，然后在包含 13k 问题的 CodeContest 数据集上进行微调
+- 在测试期间，使用采样并根据是否通过示例测试来过滤解决方案。从某种意义上说，这种做法类似于推理问题中的 [self-consistency](https://arxiv.org/abs/2203.11171) 方法。
+
+
+目前关于指令微调的理解是：
 
+- 通过使用对话格式的数据，将基本模型调优为聊天机器人相对容易（参见像 Alpaca 和 MOSS 这样的优秀示例）。然而，闲聊的能力并不能转化为执行复杂任务的能力。从这个角度来看，模型就像人类一样：说得多不如干得好，代码见真章。
+- 实际上，指令调优问题是一个数据混合问题：如何最好地混合来自不同来源的指令数据，以便从所有角度均匀地提高模型性能（而不是像在 [CoT specialization](https://arxiv.org/abs/2301.12726) 和 [the flan collection](https://arxiv.org/abs/2301.13688) 中讨论的那样，增加一个维度但降低另一个维度）。
+- 数据混合的简单起点是：使用 10-20 个非思维链的数据点（以平衡不同维度的能力），但尽可能多地使用链式思维数据（以最大化推理能力）。
\ No newline at end of file

From f6463dfe07cebe524291ad8ce8a40be16b8ca141 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 14 Mar 2024 09:09:05 +0800
Subject: [PATCH 1372/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index b951217a..64d31e06 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -98,4 +98,15 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 - 通过使用对话格式的数据，将基本模型调优为聊天机器人相对容易（参见像 Alpaca 和 MOSS 这样的优秀示例）。然而，闲聊的能力并不能转化为执行复杂任务的能力。从这个角度来看，模型就像人类一样：说得多不如干得好，代码见真章。
 - 实际上，指令调优问题是一个数据混合问题：如何最好地混合来自不同来源的指令数据，以便从所有角度均匀地提高模型性能（而不是像在 [CoT specialization](https://arxiv.org/abs/2301.12726) 和 [the flan collection](https://arxiv.org/abs/2301.13688) 中讨论的那样，增加一个维度但降低另一个维度）。
-- 数据混合的简单起点是：使用 10-20 个非思维链的数据点（以平衡不同维度的能力），但尽可能多地使用链式思维数据（以最大化推理能力）。
\ No newline at end of file
+- 数据混合的简单起点是：使用 10-20 个非思维链的数据点（以平衡不同维度的能力），但尽可能多地使用链式思维数据（以最大化推理能力）。
+
+#### 强化学习 
+
+我们分析：
+
+- Uesato. et. al. 2022. [Solving math word problems with process- and outcome-based feedback](https://arxiv.org/abs/2211.14275)
+    - 基于中间推理和最终推理结果构建奖励模型。
+- Le et. al. 2022. [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://arxiv.org/abs/2207.01780)
+    - 根据诸如编译错误、运行时错误或是否通过测试等信号训练奖励模型。
+
+这两项工作都使用中间信号（对于推理，看中间步骤是否正确；对于编码，看代码是否编译）和最终信号（对于推理，最终答案是否正确；对于编码，代码是否通过测试）作为奖励。需要注意的是，这种类型的强化学习与基于人类反馈的强化学习（RLHF）有所不同，因为它不需要人类反馈。
\ No newline at end of file

From d0b463229654d26e89c70db370f393f1f9d409d7 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 15 Mar 2024 09:06:32 +0800
Subject: [PATCH 1373/1406] feat:update llm

---
 assets/src/LLM/llm01.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 64d31e06..75d9d68d 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -109,4 +109,4 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Le et. al. 2022. [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://arxiv.org/abs/2207.01780)
     - 根据诸如编译错误、运行时错误或是否通过测试等信号训练奖励模型。
 
-这两项工作都使用中间信号（对于推理，看中间步骤是否正确；对于编码，看代码是否编译）和最终信号（对于推理，最终答案是否正确；对于编码，代码是否通过测试）作为奖励。需要注意的是，这种类型的强化学习与基于人类反馈的强化学习（RLHF）有所不同，因为它不需要人类反馈。
\ No newline at end of file
+这两项工作都使用中间信号（对于推理，看中间步骤是否正确；对于编码，看代码是否编译）和最终信号作为奖励。 需要注意的是，这种类型的强化学习与基于人类反馈的强化学习（RLHF）有所不同，因为它不需要人类反馈。
\ No newline at end of file

From 324b19bcc7fdd96f27d380e9ea5b0f04dd883a8a Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 16 Mar 2024 15:36:21 +0800
Subject: [PATCH 1374/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 19 ++++++++++++++++++-
 1 file changed, 18 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 75d9d68d..9cfb21fb 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -109,4 +109,21 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Le et. al. 2022. [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://arxiv.org/abs/2207.01780)
     - 根据诸如编译错误、运行时错误或是否通过测试等信号训练奖励模型。
 
-这两项工作都使用中间信号（对于推理，看中间步骤是否正确；对于编码，看代码是否编译）和最终信号作为奖励。 需要注意的是，这种类型的强化学习与基于人类反馈的强化学习（RLHF）有所不同，因为它不需要人类反馈。
\ No newline at end of file
+这两项工作都使用中间信号（对于推理，看中间步骤是否正确；对于编码，看代码是否编译）和最终信号作为奖励。 需要注意的是，这种类型的强化学习与基于人类反馈的强化学习（RLHF）有所不同，因为它不需要人类反馈。
+
+#### 推理能力和代码能力的耦合
+
+我们提出了一个假设，即在代码上进行训练可能会提高推理能力，原因如下:
+
+｜-----------------｜-----------｜-----------|
+｜                 ｜   推理     ｜ 代码      ｜
+｜数据格式           ｜  思维链    ｜逐行注释    ｜
+｜简单和中等难度的任务 ｜ 一步一步推理｜面向过程编程 ｜
+｜困难任务           ｜ 问题分解   ｜面向对象编程  ｜
+
+
+- 代码注释是自然存在的链式思维数据
+- 面向过程编程类似于逐步解决任务。这适用于简单和中等复杂度的任务
+- 面向对象编程类似于将任务分解为较小的任务，然后分别解决它们。这适用于较高复杂度的任务。
+
+从这个显著的一致性中，我们看到提高推理能力与提高编程能力非常相似。在此，我们通过强调训练大型语言模型进行推理或编码的配方相似性，深化了这个假设：
\ No newline at end of file

From dc937ba4d3e9fff31c71b1d6063d738fb7cd1eb1 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 18 Mar 2024 09:05:05 +0800
Subject: [PATCH 1375/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 16 +++++++++++++++-
 1 file changed, 15 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 9cfb21fb..57295fb1 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -126,4 +126,18 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - 面向过程编程类似于逐步解决任务。这适用于简单和中等复杂度的任务
 - 面向对象编程类似于将任务分解为较小的任务，然后分别解决它们。这适用于较高复杂度的任务。
 
-从这个显著的一致性中，我们看到提高推理能力与提高编程能力非常相似。在此，我们通过强调训练大型语言模型进行推理或编码的配方相似性，深化了这个假设：
\ No newline at end of file
+从这个显著的一致性中，我们看到提高推理能力与提高编程能力非常相似。在此，我们通过强调训练大型语言模型进行推理或编码的配方相似性，深化了这个假设：
+
+｜------------------｜-----------------------------------------------------------------------------------｜----------------------------------------------------------------|
+｜       持续训练   ｜  在科学文献上持续训练,数据格式 = 文本 + latex ,例子: Minerva / Galactica                  ｜ 在代码上持续训练,数据格式 = 文本 + 编程语言 ,例子: Codex             ｜
+｜       监督微调   ｜  使用思维链指令做监督微调,数据格式 = 思维链,例子: CoT specialization                       ｜ 使用代码指令做监督微调, 数据格式 = 代码 例子: AlphaCode              ｜
+｜       强化学习   ｜  使用思维链指令做监督微调,数据格式 = 思维链,例子: CoT specialization                       ｜ 使用代码指令做监督微调, 数据格式 = 代码 例子: AlphaCode              ｜
+｜       监督微调   ｜  使用中间过程和推理结果作为反馈,格式：是否推理正确,例子: process and outcome based reward    ｜ 使用编译率和通过率作为反馈,格式 = 代码是否正确执行 例子: CodeRL        ｜
+｜       采样和解码 ｜  Self-consistency：采样多个解决方案，然后进行多数投票                                      ｜ Sampling and filtering: ,采样多个解决方案，然后过滤并聚类这些解决方案 ｜
+
+看到推理和代码都经历了：
+
+- 在连续训练阶段，可以在基础模型上增加代码和科学文献数据。
+- 在有监督的微调阶段，可以根据要求完成复杂任务的指令或编写代码对模型进行微调
+- 在强化学习阶段，将中间推理步骤 / 编译率和最终推理结果 / 代码通过率作为奖励
+- 在解码过程中，推理和编码都会采样多个解决方案，然后从解码空间中选择最佳方案。
\ No newline at end of file

From 8d45fdaf0deb0fadfe02edcbb208ecd955fb7d62 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 19 Mar 2024 09:05:56 +0800
Subject: [PATCH 1376/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 57295fb1..8d8c6252 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -140,4 +140,29 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - 在连续训练阶段，可以在基础模型上增加代码和科学文献数据。
 - 在有监督的微调阶段，可以根据要求完成复杂任务的指令或编写代码对模型进行微调
 - 在强化学习阶段，将中间推理步骤 / 编译率和最终推理结果 / 代码通过率作为奖励
-- 在解码过程中，推理和编码都会采样多个解决方案，然后从解码空间中选择最佳方案。
\ No newline at end of file
+- 在解码过程中，推理和编码都会采样多个解决方案，然后从解码空间中选择最佳方案。
+
+#### 复杂推理的提示工程
+
+* 基础思维链提示工程
+
+推荐给初学者：
+
+- Wei et. al. 2022. [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://arxiv.org/abs/2201.11903).
+  - 本文是第一篇发现当使用链式思维进行提示时，存在一个相变现象，表明大型模型在很大程度上优于较小的模型，这进一步导致了[涌现能力](https://arxiv.org/abs/2206.07682)的发现。
+- Wang et. al. 2022. [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://arxiv.org/abs/2203.11171)
+  - 对采样的 CoT 推理路径进行多数投票，显著提高了推理性能。
+- Suzgun et. al. 2022. [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://arxiv.org/abs/2210.09261)
+  - 使用 CoT 处理 big-bench 中困难的任务。这篇论文的一个有意义的副产品是 BigBench Hard 数据集，它在测试模型推理能力方面非常有效。
+
+
+* 进阶技巧及分析
+
+高级 CoT 提示实践：
+
+- Fu et. al. 2023. [Complexity-Based Prompting for Multi-Step Reasoning](https://arxiv.org/abs/2210.00720)
+  - 使用复杂链代替简单链作为上下文示例
+- Khot et. al. 2023. [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://arxiv.org/abs/2210.02406)
+  - 将复杂任务分解为更简单的任务，然后逐个解决
+
+通常，对于复杂任务，首先将其分解为更简单的任务，然后逐步解决更简单的任务。
\ No newline at end of file

From 93ea3968006f38026f6cd3e7930b8b9e24d25409 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 20 Mar 2024 08:58:56 +0800
Subject: [PATCH 1377/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 22 +++++++++++++++-------
 1 file changed, 15 insertions(+), 7 deletions(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 8d8c6252..0e52f018 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -122,8 +122,8 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 ｜困难任务           ｜ 问题分解   ｜面向对象编程  ｜
 
 
-- 代码注释是自然存在的链式思维数据
-- 面向过程编程类似于逐步解决任务。这适用于简单和中等复杂度的任务
+- 代码注释是自然存在的链式思维数据。
+- 面向过程编程类似于逐步解决任务。这适用于简单和中等复杂度的任务。
 - 面向对象编程类似于将任务分解为较小的任务，然后分别解决它们。这适用于较高复杂度的任务。
 
 从这个显著的一致性中，我们看到提高推理能力与提高编程能力非常相似。在此，我们通过强调训练大型语言模型进行推理或编码的配方相似性，深化了这个假设：
@@ -138,8 +138,8 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 看到推理和代码都经历了：
 
 - 在连续训练阶段，可以在基础模型上增加代码和科学文献数据。
-- 在有监督的微调阶段，可以根据要求完成复杂任务的指令或编写代码对模型进行微调
-- 在强化学习阶段，将中间推理步骤 / 编译率和最终推理结果 / 代码通过率作为奖励
+- 在有监督的微调阶段，可以根据要求完成复杂任务的指令或编写代码对模型进行微调。
+- 在强化学习阶段，将中间推理步骤 / 编译率和最终推理结果 / 代码通过率作为奖励。
 - 在解码过程中，推理和编码都会采样多个解决方案，然后从解码空间中选择最佳方案。
 
 #### 复杂推理的提示工程
@@ -161,8 +161,16 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 高级 CoT 提示实践：
 
 - Fu et. al. 2023. [Complexity-Based Prompting for Multi-Step Reasoning](https://arxiv.org/abs/2210.00720)
-  - 使用复杂链代替简单链作为上下文示例
+  - 使用复杂链代替简单链作为上下文示例。
 - Khot et. al. 2023. [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://arxiv.org/abs/2210.02406)
-  - 将复杂任务分解为更简单的任务，然后逐个解决
+  - 将复杂任务分解为更简单的任务，然后逐个解决。
+
+通常，对于复杂任务，首先将其分解为更简单的任务，然后逐步解决更简单的任务。
+
+
+
+
+
+
+
 
-通常，对于复杂任务，首先将其分解为更简单的任务，然后逐步解决更简单的任务。
\ No newline at end of file

From 635da4bac0d277a112024dcc7d318e4fb06b1876 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 21 Mar 2024 09:07:22 +0800
Subject: [PATCH 1378/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 0e52f018..b838d872 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -167,7 +167,14 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 通常，对于复杂任务，首先将其分解为更简单的任务，然后逐步解决更简单的任务。
 
+以下论文讨论了**上下文学习为什么起作用**：
 
+- Xie et. al. 2021. [An Explanation of In-context Learning as Implicit Bayesian Inference](https://arxiv.org/abs/2111.02080)
+  - 语言模型在提示中的示例之间推断出一个潜在概念，并进入相应的任务模式
+- Wei et. al. 2023. [Larger language models do in-context learning differently](https://arxiv.org/abs/2303.03846)
+  - 当出现与先验知识相矛盾的上下文示例时，尽管大型模型可能具有更强的语义先验，大型模型可以根据提示词来覆盖语义先验。
+
+简而言之，上下文学习的要点是提示中的示例使模型进入相应的任务模式，然后执行任务。
 
 
 

From 777d2f9b8555669598d196a68491eaa1ce00ac62 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 22 Mar 2024 08:58:00 +0800
Subject: [PATCH 1379/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index b838d872..f46e0332 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -167,7 +167,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 通常，对于复杂任务，首先将其分解为更简单的任务，然后逐步解决更简单的任务。
 
-以下论文讨论了**上下文学习为什么起作用**：
+以下论文讨论了上下文学习为什么起作用：
 
 - Xie et. al. 2021. [An Explanation of In-context Learning as Implicit Bayesian Inference](https://arxiv.org/abs/2111.02080)
   - 语言模型在提示中的示例之间推断出一个潜在概念，并进入相应的任务模式

From 15adc61bd4024de69e3641bce56a3f3da5d46d29 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 23 Mar 2024 10:00:36 +0800
Subject: [PATCH 1380/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index f46e0332..56979fa8 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -177,7 +177,16 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 简而言之，上下文学习的要点是提示中的示例使模型进入相应的任务模式，然后执行任务。
 
 
+以下论文讨论了**模型在进行思维链推理时的行为**：
 
+- Min et. al. 2022. [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work](https://arxiv.org/abs/2202.12837)
+  - 当某些标签错误时，模型仍然可以做出正确的预测。这表明模型更受提示的 [格式] 影响，而不是提示的 [意义] 。
+- Wang et. al. 2022. [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://arxiv.org/abs/2212.10001)
+  - 即使提示中的推理错误，模型仍然可以正确推理，但提示的相关性和推理步骤的顺序更为重要 —— 这再次表明，模型更受提示的 [格式] 影响，而不是提示的[意义]。
+- Madaan and Yazdanbakhsh. 2022. [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://arxiv.org/abs/2209.07686).
+  - 详细分析显示，提示的格式可以改善 CoT 推理（虽然内容的正确性可能不起到强烈作用）
+
+因此呢，模型只关注提示的格式，但可能不会受到提示正确性的显著影响。然而，模型在多大程度上会受到提示正确性的影响，或者提示可以在[多大程度上覆盖模型的先验信念](https://arxiv.org/abs/2303.03846)，还是一个尚待研究的问题。
 
 
 

From 6143c8e714d50f14e49da337cf2b3dbf67c57f8f Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 25 Mar 2024 09:08:15 +0800
Subject: [PATCH 1381/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 56979fa8..919f2bed 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -189,4 +189,11 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 因此呢，模型只关注提示的格式，但可能不会受到提示正确性的显著影响。然而，模型在多大程度上会受到提示正确性的影响，或者提示可以在[多大程度上覆盖模型的先验信念](https://arxiv.org/abs/2303.03846)，还是一个尚待研究的问题。
 
 
+以下论文讨论了如何**通过改进和反馈来提高模型性能**：
 
+- Madaan. et. al. 2023. [Self-refine: Iterative refinement with self-feedback](https://arxiv.org/abs/2303.17651)
+  - 模型可以在多个场景中（包括代码优化、数学推理、对话响应生成等）对自身的推理进行优化和改进。
+- Madaan et. al. 2023. [Learning Performance-Improving Code Edits](https://arxiv.org/abs/2302.07867)
+  - 在程序轨迹上进行训练可以改善编码。
+
+简而言之，以自然语言形式（而非强化学习中的奖励形式）对模型进行改进和反馈非常有效，可以进一步提高语言模型的性能（无论是通过上下文学习还是微调）。

From e9eba8333dffce30a7a956c232a30c6960fb019c Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 26 Mar 2024 09:07:17 +0800
Subject: [PATCH 1382/1406] feat: update llm

---
 assets/images/468.jpg   | Bin 0 -> 507093 bytes
 assets/src/LLM/llm01.md |  19 +++++++++++++++++++
 2 files changed, 19 insertions(+)
 create mode 100644 assets/images/468.jpg

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diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 919f2bed..1a9d6ba3 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -197,3 +197,22 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
   - 在程序轨迹上进行训练可以改善编码。
 
 简而言之，以自然语言形式（而非强化学习中的奖励形式）对模型进行改进和反馈非常有效，可以进一步提高语言模型的性能（无论是通过上下文学习还是微调）。
+
+#### 评价大语言模型的推理能力
+
+## 评价方法的基础知识
+
+在谈论评估时，有三个重要因素需要考虑：数据格式、能力类型和模型类型。
+
+首先，提示时有四种数据格式：
+
+<p align="center">
+<img width="700" align="center" src="../../images/468.jpg" />
+</p>
+
+其中：
+
+- In-context 指的是在测试问题之前附加一系列上下文示例。
+- Zero-shot 是指在没有上下文示例的情况下直接将测试问题输入给模型。
+- Chain-of-thought 是指在回答之前生成推理。
+- Answer-only 是指没有链式思维，直接给答案。

From b51edfe63daa6637691c11f23d1fb09b0c2c4d72 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 27 Mar 2024 09:05:35 +0800
Subject: [PATCH 1383/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 1a9d6ba3..e1b89a60 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -216,3 +216,18 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Zero-shot 是指在没有上下文示例的情况下直接将测试问题输入给模型。
 - Chain-of-thought 是指在回答之前生成推理。
 - Answer-only 是指没有链式思维，直接给答案。
+
+
+对于模型能力，有两种大致正交的能力类型：
+
+- 知识 knowledge：模型是否了解世界
+- 推理 reasoning：模型是否可以根据其知识进行推理。
+
+这两个方面并不是严格正交的，因为一些推理规则也可以被视为某种形式的知识。然而，在评估时，这两种能力有明显的差异：
+
+- 一些数据集更注重对知识的评估，如 [MMLU](https://arxiv.org/abs/2009.03300)，它测试模型是否具有高达大学水平的知识。
+- 一些数据集更注重对推理的评估，如 [BBH](https://arxiv.org/abs/2210.09261)，它测试模型是否具有逐步解决问题的能力。
+- 对于知识，链式思维与仅回答的表现相似（参见 FlanPaLM 论文）
+- 对于推理，链式思维比仅回答表现得更好（参见原始 [CoT 论文](https://arxiv.org/abs/2201.11903)，然后参见 [FlanPaLM论文](https://arxiv.org/abs/2210.11416)
+
+在实践中，因为 CoT 在达到或优于 Answer-only 的表现，而且 CoT 更加用户友好（因为它告诉用户思考过程），现代聊天机器人总是部署 CoT（无论你问 ChatGPT 什么，它都会告诉你一堆它的想法）。
\ No newline at end of file

From cd20bf2dab604346dbac7c32a4f90f56943f07b5 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 28 Mar 2024 09:13:27 +0800
Subject: [PATCH 1384/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index e1b89a60..14267136 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -230,4 +230,10 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - 对于知识，链式思维与仅回答的表现相似（参见 FlanPaLM 论文）
 - 对于推理，链式思维比仅回答表现得更好（参见原始 [CoT 论文](https://arxiv.org/abs/2201.11903)，然后参见 [FlanPaLM论文](https://arxiv.org/abs/2210.11416)
 
-在实践中，因为 CoT 在达到或优于 Answer-only 的表现，而且 CoT 更加用户友好（因为它告诉用户思考过程），现代聊天机器人总是部署 CoT（无论你问 ChatGPT 什么，它都会告诉你一堆它的想法）。
\ No newline at end of file
+在实践中，因为 CoT 在达到或优于 Answer-only 的表现，而且 CoT 更加用户友好（因为它告诉用户思考过程），现代聊天机器人总是部署 CoT（无论你问 ChatGPT 什么，它都会告诉你一堆它的想法）。
+
+
+最后，在评估方面，我们区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
+
+1. 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “[让我们逐步思考(https://arxiv.org/abs/2205.11916)” 的论文）。 
+2. 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会[稍有下降](https://arxiv.org/abs/2203.02155)。
\ No newline at end of file

From 741aa62baa09ce83e29952b580a14b2a1b0c7dba Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 29 Mar 2024 08:59:43 +0800
Subject: [PATCH 1385/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 14267136..a98c8fd5 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -188,7 +188,6 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 因此呢，模型只关注提示的格式，但可能不会受到提示正确性的显著影响。然而，模型在多大程度上会受到提示正确性的影响，或者提示可以在[多大程度上覆盖模型的先验信念](https://arxiv.org/abs/2303.03846)，还是一个尚待研究的问题。
 
-
 以下论文讨论了如何**通过改进和反馈来提高模型性能**：
 
 - Madaan. et. al. 2023. [Self-refine: Iterative refinement with self-feedback](https://arxiv.org/abs/2303.17651)
@@ -196,7 +195,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Madaan et. al. 2023. [Learning Performance-Improving Code Edits](https://arxiv.org/abs/2302.07867)
   - 在程序轨迹上进行训练可以改善编码。
 
-简而言之，以自然语言形式（而非强化学习中的奖励形式）对模型进行改进和反馈非常有效，可以进一步提高语言模型的性能（无论是通过上下文学习还是微调）。
+因此，以自然语言形式（而非强化学习中的奖励形式）对模型进行改进和反馈非常有效，可以进一步提高语言模型的性能（无论是通过上下文学习还是微调）。
 
 #### 评价大语言模型的推理能力
 
@@ -217,7 +216,6 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Chain-of-thought 是指在回答之前生成推理。
 - Answer-only 是指没有链式思维，直接给答案。
 
-
 对于模型能力，有两种大致正交的能力类型：
 
 - 知识 knowledge：模型是否了解世界
@@ -227,12 +225,11 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 - 一些数据集更注重对知识的评估，如 [MMLU](https://arxiv.org/abs/2009.03300)，它测试模型是否具有高达大学水平的知识。
 - 一些数据集更注重对推理的评估，如 [BBH](https://arxiv.org/abs/2210.09261)，它测试模型是否具有逐步解决问题的能力。
-- 对于知识，链式思维与仅回答的表现相似（参见 FlanPaLM 论文）
+- 对于知识，链式思维与仅回答的表现相似（参见 FlanPaLM 论文）。
 - 对于推理，链式思维比仅回答表现得更好（参见原始 [CoT 论文](https://arxiv.org/abs/2201.11903)，然后参见 [FlanPaLM论文](https://arxiv.org/abs/2210.11416)
 
 在实践中，因为 CoT 在达到或优于 Answer-only 的表现，而且 CoT 更加用户友好（因为它告诉用户思考过程），现代聊天机器人总是部署 CoT（无论你问 ChatGPT 什么，它都会告诉你一堆它的想法）。
 
-
 最后，在评估方面，我们区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
 
 1. 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “[让我们逐步思考(https://arxiv.org/abs/2205.11916)” 的论文）。 

From f5967e91b721d94dc5ae3cb5aac3e2b88c25062b Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sun, 31 Mar 2024 17:14:45 +0800
Subject: [PATCH 1386/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index a98c8fd5..d482b8cd 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -233,4 +233,14 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 最后，在评估方面，我们区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
 
 1. 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “[让我们逐步思考(https://arxiv.org/abs/2205.11916)” 的论文）。 
-2. 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会[稍有下降](https://arxiv.org/abs/2203.02155)。
\ No newline at end of file
+2. 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会[稍有下降](https://arxiv.org/abs/2203.02155)。
+
+最后，在评估方面，我们区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
+
+- 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “让我们逐步思考” 的论文）。
+- 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会稍有下降。
+
+综上所述，我们建议使用 in-context chain-of-thought 进行评估：
+
+- In-context 是评估 pretrained checkpoint 的更好方法，因为它更好地揭示了模型潜力。Zero-shot 可能低估模型性能，尤其是对于不支持 Zero-shot chain-of-thought 的（“让我们逐步思考”）的模型。
+- Chain-of-thought prompting 是评估推理能力的更好方法，因为它比 answer-only prompting 更充分地发挥了模型的推理性能。
\ No newline at end of file

From caf11a0ccef8881c843d5d26684e63aea04167a7 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 1 Apr 2024 09:07:53 +0800
Subject: [PATCH 1387/1406] feat: update llm

---
 assets/images/469.jpg   | Bin 0 -> 81453 bytes
 assets/src/LLM/llm01.md |  42 +++++++++++++++++++++++++++++++++++++++-
 2 files changed, 41 insertions(+), 1 deletion(-)
 create mode 100644 assets/images/469.jpg

diff --git a/assets/images/469.jpg b/assets/images/469.jpg
new file mode 100644
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diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index d482b8cd..83fcd454 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -243,4 +243,44 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 综上所述，我们建议使用 in-context chain-of-thought 进行评估：
 
 - In-context 是评估 pretrained checkpoint 的更好方法，因为它更好地揭示了模型潜力。Zero-shot 可能低估模型性能，尤其是对于不支持 Zero-shot chain-of-thought 的（“让我们逐步思考”）的模型。
-- Chain-of-thought prompting 是评估推理能力的更好方法，因为它比 answer-only prompting 更充分地发挥了模型的推理性能。
\ No newline at end of file
+- Chain-of-thought prompting 是评估推理能力的更好方法，因为它比 answer-only prompting 更充分地发挥了模型的推理性能。
+
+#### Chain-of-thought Hub 简介
+
+在讨论了所有评估基础知识之后，这里在介绍 Chain-of-thought Hub，这是一个正在进行的工作，希望成为评估语言模型推理能力的统一平台。他们汇编了一个包括数学（GSM8K）、科学（MATH）、符号（BBH）、知识（MMLU）等复杂推理任务的列表，以衡量哪些模型确实更好。
+
+下面是当前的排行榜。尽管许多数字还没跑出来，但当前的内容仍然能给一个大概的模型排名：
+
+<p align="center">
+<img width="700" align="center" src="../../images/469.jpg" />
+</p>
+
+
+总的来说：
+
+- 我们根据 GSM8K 对模型性能进行排名，这是一个经典的基准测试，用于衡量链式思维数学推理性能。这不是唯一的度量标准，但一个很好的解释是 “在保持其他通用能力的同时，模型在数学方面的表现如何” —— 这也非常困难。
+- GPT-4 在 GSM8K 和 MMLU 上明显优于所有其他模型。
+- 65B LLaMA 与 text/code-davinci-002 非常接近，这意味着基于它，如果 SFT 和 RLHF 操作正确，我们很有可能基于 65B LLaMA 复现 ChatGPT。
+- Claude 是唯一可以与 GPT 系列相媲美的模型家族。
+- 较小的模型，如 FlanT5 11B 和 LLaMA 7B，明显落后于排行榜，这意味着复杂推理可能只是大型模型的能力。
+
+进一步地，在 github 仓库中，我们包括了：
+
+- 详细的实验设置和结果分析
+- 用于重现 GPT 和 Claude 所有结果的脚本
+
+因此，在上面我们讨论了大型语言模型的推理能力。复杂推理不仅仅是因为它是更强模型与更弱模型之间的核心区分点，而且它还是模型成为下一代计算平台或者操作系统的基础能力，从而有可能在大模型上建立一个新的生态系统。
+
+我们讨论了构建具有强大推理能力的模型的方法：预训练、有监督的微调和强化学习。我们发现提高推理能力的方法与提高代码能力的方法密切相关，这加深了我们先前关于推理与代码之间密切关系的假设。我们进一步讨论了高级提示工程技巧和在执行复杂推理时模型行为的分析。
+
+最后，我们讨论了如何评估模型的推理能力，并介绍了 chain-of-thought hub，这是一个正在进行的项目，旨在统一评估语言模型的推理性能。
+
+希望这篇文章能成为构建具有强大推理能力的开源模型的路线图。
+
+
+#### 更多大语言模型推理的相关资源
+
+* [Prompt Engineering](https://lilianweng.github.io/posts/2023-03-15-prompt-engineering/)
+* [Microsoft Semantic Kernel ](https://github.com/microsoft/semantic-kernel)
+* [Prompt Engineering Guide](https://github.com/dair-ai/Prompt-Engineering-Guide)
+* [Towards Reasoning in Large Language Models: A Survey](https://arxiv.org/abs/2212.10403)
\ No newline at end of file

From cfdc706ea5069935a6446dbb2eacd8274a99218f Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 2 Apr 2024 09:10:28 +0800
Subject: [PATCH 1388/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 83fcd454..59b0057c 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -264,10 +264,10 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - Claude 是唯一可以与 GPT 系列相媲美的模型家族。
 - 较小的模型，如 FlanT5 11B 和 LLaMA 7B，明显落后于排行榜，这意味着复杂推理可能只是大型模型的能力。
 
-进一步地，在 github 仓库中，我们包括了：
+在 github 中，进一步地分析和了解：
 
-- 详细的实验设置和结果分析
-- 用于重现 GPT 和 Claude 所有结果的脚本
+- 详细的实验设置和结果分析。
+- 用于重现 GPT 和 Claude 所有结果的脚本。
 
 因此，在上面我们讨论了大型语言模型的推理能力。复杂推理不仅仅是因为它是更强模型与更弱模型之间的核心区分点，而且它还是模型成为下一代计算平台或者操作系统的基础能力，从而有可能在大模型上建立一个新的生态系统。
 

From 1b9c1f9bf1b904d7c559bddb5c849adf5758cb05 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 4 Apr 2024 16:26:28 +0800
Subject: [PATCH 1389/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 59b0057c..c7031565 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -235,7 +235,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 1. 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “[让我们逐步思考(https://arxiv.org/abs/2205.11916)” 的论文）。 
 2. 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会[稍有下降](https://arxiv.org/abs/2203.02155)。
 
-最后，在评估方面，我们区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
+最后，在评估方面，这里区分了两种类型的模型：预训练之后的 checkpoint 和指令微调之后的 checkpoint。
 
 - 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “让我们逐步思考” 的论文）。
 - 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会稍有下降。
@@ -258,7 +258,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 总的来说：
 
-- 我们根据 GSM8K 对模型性能进行排名，这是一个经典的基准测试，用于衡量链式思维数学推理性能。这不是唯一的度量标准，但一个很好的解释是 “在保持其他通用能力的同时，模型在数学方面的表现如何” —— 这也非常困难。
+- 根据 GSM8K 对模型性能进行排名，这是一个经典的基准测试，用于衡量链式思维数学推理性能。这不是唯一的度量标准，但一个很好的解释是 “在保持其他通用能力的同时，模型在数学方面的表现如何” —— 这也非常困难。
 - GPT-4 在 GSM8K 和 MMLU 上明显优于所有其他模型。
 - 65B LLaMA 与 text/code-davinci-002 非常接近，这意味着基于它，如果 SFT 和 RLHF 操作正确，我们很有可能基于 65B LLaMA 复现 ChatGPT。
 - Claude 是唯一可以与 GPT 系列相媲美的模型家族。

From 04630675117bc79601fdaca7ebb4a3db516e0650 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 6 Apr 2024 18:41:41 +0800
Subject: [PATCH 1390/1406] =?UTF-8?q?feat=EF=BC=9A=20update=20llm?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 assets/src/LLM/llm01.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index c7031565..b0aff186 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -240,7 +240,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 - 预训练 checkpoint 具有 in-context learning 的能力。大多数预训练模型可以进行 in-context answer-only，一些更好的模型可以进行 in-context chain-of-thought（但目前尚不清楚为什么某些预训练模型可以进行 CoT 而其他模型却不能）。然而，预训练 checkpoint 可能无法进行 zero-shot，因为它们没有经过这方面的训练（但某些预训练检查点仍然可以进行 zero-shot CoT，请参阅 “让我们逐步思考” 的论文）。
 - 指令微调过后的 checkpoint 既具有 zero-shot 又有 in-context 的能力。这里需要注意的是，如果没调好，指令微调之后 in-context 性能可能会稍有下降。
 
-综上所述，我们建议使用 in-context chain-of-thought 进行评估：
+综上所述，我们建议使用 in-context 和 chain-of-thought 进行评估：
 
 - In-context 是评估 pretrained checkpoint 的更好方法，因为它更好地揭示了模型潜力。Zero-shot 可能低估模型性能，尤其是对于不支持 Zero-shot chain-of-thought 的（“让我们逐步思考”）的模型。
 - Chain-of-thought prompting 是评估推理能力的更好方法，因为它比 answer-only prompting 更充分地发挥了模型的推理性能。

From 751afa530e5cc1930f0ad77a73c3078639413cba Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sun, 7 Apr 2024 09:11:17 +0800
Subject: [PATCH 1391/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index b0aff186..1920759c 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -121,7 +121,6 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 ｜简单和中等难度的任务 ｜ 一步一步推理｜面向过程编程 ｜
 ｜困难任务           ｜ 问题分解   ｜面向对象编程  ｜
 
-
 - 代码注释是自然存在的链式思维数据。
 - 面向过程编程类似于逐步解决任务。这适用于简单和中等复杂度的任务。
 - 面向对象编程类似于将任务分解为较小的任务，然后分别解决它们。这适用于较高复杂度的任务。
@@ -199,7 +198,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 #### 评价大语言模型的推理能力
 
-## 评价方法的基础知识
+#### 评价方法的基础知识
 
 在谈论评估时，有三个重要因素需要考虑：数据格式、能力类型和模型类型。
 

From ae94bf1eab48739d5dc62547febc21cd91c55adf Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 8 Apr 2024 09:08:36 +0800
Subject: [PATCH 1392/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index 1920759c..d8df185e 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -113,7 +113,7 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 
 #### 推理能力和代码能力的耦合
 
-我们提出了一个假设，即在代码上进行训练可能会提高推理能力，原因如下:
+这里我们提出了一个假设，即在代码上进行训练可能会提高推理能力，原因如下:
 
 ｜-----------------｜-----------｜-----------|
 ｜                 ｜   推理     ｜ 代码      ｜

From 773c54503b734ad6957d7e2b13bb6279987643a0 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 10 Apr 2024 08:51:07 +0800
Subject: [PATCH 1393/1406] feat: update llm

---
 assets/src/LLM/llm01.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/assets/src/LLM/llm01.md b/assets/src/LLM/llm01.md
index d8df185e..8bdfcd04 100644
--- a/assets/src/LLM/llm01.md
+++ b/assets/src/LLM/llm01.md
@@ -277,6 +277,9 @@ LLM 将通过实现客户自助服务自动化、加快对越来越多任务的
 希望这篇文章能成为构建具有强大推理能力的开源模型的路线图。
 
 
+人世间数百万个闲暇的小时流逝过去，方始出现一个真正的历史性时刻，人类星光闪耀的时刻  ——  《人类群星闪耀时》斯蒂芬·茨威格
+
+
 #### 更多大语言模型推理的相关资源
 
 * [Prompt Engineering](https://lilianweng.github.io/posts/2023-03-15-prompt-engineering/)

From 7bc1161af49766ee8de56206de7581bb53b22a60 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 12 Apr 2024 09:21:18 +0800
Subject: [PATCH 1394/1406] feat: update llm02

---
 assets/src/LLM/llm02.md | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 assets/src/LLM/llm02.md

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
new file mode 100644
index 00000000..c5e901d9
--- /dev/null
+++ b/assets/src/LLM/llm02.md
@@ -0,0 +1,27 @@
+#### 什么是大型语言模型？
+
+大型语言模型（LLM）是基于大量数据进行预训练的超大型深度学习模型。底层转换器是一组神经网络，这些神经网络由具有自注意力功能的编码器和解码器组成。编码器和解码器从一系列文本中提取含义，并理解其中的单词和短语之间的关系。
+
+转换器 LLM 能够进行无监督的训练，但更精确的解释是转换器可以执行自主学习。通过此过程，转换器可学会理解基本的语法、语言和知识。
+
+与早期按顺序处理输入的循环神经网络（RNN）不同，转换器并行处理整个序列。这可让数据科学家使用 GPU 训练基于转换器的 LLM，从而大幅度缩短训练时间。
+
+借助转换器神经网络架构，您可使用非常大规模的模型，其中通常具有数千亿个参数。这种大规模模型可以摄取通常来自互联网的大量数据，但也可以从包含 500 多亿个网页的 Common Crawl 和拥有约 5700 万个页面的 Wikipedia 等来源摄取数据。
+
+#### 大语言模型综述
+
+语言是人类表达和交流的突出能力，它在儿童早期发展 并在一生中不断演变。然而，机器不能自然地掌握以人类语言形式理解和交流的能力，除非配备了强大的人工智能算法。实现这一目标，让机器像人类一样阅读、写作和交流一直是一个长期的研究挑战。
+
+从技术上讲，语言建模是提高机器语言智能的主要方法之一。一般来说，语言建模旨在对词序列的生成概率进行建模，以预测未来(或缺失)单词的概率。语言建模的研究在文献中受到了广泛关注，可以分为四个主要发展阶段:
+
+
+1. 统计语言模型 (SLM)
+
+SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基本思想是基于马尔可夫 假设建立词预测模型，例如根据最近的上下文预测下一个词。
+具有固定上下文长度 n 的 SLM 也称为 n-gram 语言模型，例 如 bigram 和 trigram 语言模型。SLM 已被广泛应用于提高信 息检索和自然语言处理的任务性能。然而，它们通常受到维数灾难的困扰：由于需要估计指数级数量的转 换概率，因此很难准确估计高阶语言模型。因此，专门设计的平滑策略，如回退估计和 Good–Turing 估计已被引入以缓解数据稀疏问题。
+
+
+
+
+
+

From 410a1ecde1aa63f628e8dc6a7e398fe57781d548 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 15 Apr 2024 09:18:21 +0800
Subject: [PATCH 1395/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index c5e901d9..b12bae01 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -21,6 +21,11 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 具有固定上下文长度 n 的 SLM 也称为 n-gram 语言模型，例 如 bigram 和 trigram 语言模型。SLM 已被广泛应用于提高信 息检索和自然语言处理的任务性能。然而，它们通常受到维数灾难的困扰：由于需要估计指数级数量的转 换概率，因此很难准确估计高阶语言模型。因此，专门设计的平滑策略，如回退估计和 Good–Turing 估计已被引入以缓解数据稀疏问题。
 
 
+2. 神经语言模型(NLM)
+
+使用神经网络（例 如循环神经网络）来刻画词序列的概率。作为一个显著贡献，的工作引入了词的分布式表示概念，并在聚合上下文特征（即分布式词向量）的条件下构建词预测函数。通过扩展学习词或句子有效特征的想法，已有研究开发了一种通用神经
+
+此外，word2vec被提出来构建一个简化的浅层神经网用于学习分布式词表示，这些表示在各种自然语言处理任务中被证明非常有效。这些研究开创了将语言模型用于表示学习（超越词序列建模），对自然语言处理领域产生了重要影响。
 
 
 

From d35a0397417f88eadc8033c70ad59758dd4a95fe Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Mon, 15 Apr 2024 09:21:26 +0800
Subject: [PATCH 1396/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index b12bae01..6a81f697 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -14,13 +14,11 @@
 
 从技术上讲，语言建模是提高机器语言智能的主要方法之一。一般来说，语言建模旨在对词序列的生成概率进行建模，以预测未来(或缺失)单词的概率。语言建模的研究在文献中受到了广泛关注，可以分为四个主要发展阶段:
 
-
 1. 统计语言模型 (SLM)
 
 SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基本思想是基于马尔可夫 假设建立词预测模型，例如根据最近的上下文预测下一个词。
 具有固定上下文长度 n 的 SLM 也称为 n-gram 语言模型，例 如 bigram 和 trigram 语言模型。SLM 已被广泛应用于提高信 息检索和自然语言处理的任务性能。然而，它们通常受到维数灾难的困扰：由于需要估计指数级数量的转 换概率，因此很难准确估计高阶语言模型。因此，专门设计的平滑策略，如回退估计和 Good–Turing 估计已被引入以缓解数据稀疏问题。
 
-
 2. 神经语言模型(NLM)
 
 使用神经网络（例 如循环神经网络）来刻画词序列的概率。作为一个显著贡献，的工作引入了词的分布式表示概念，并在聚合上下文特征（即分布式词向量）的条件下构建词预测函数。通过扩展学习词或句子有效特征的想法，已有研究开发了一种通用神经

From 0b303489c6b7866aa19f74181be295db3f908ada Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 16 Apr 2024 09:19:49 +0800
Subject: [PATCH 1397/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 6a81f697..1fee758c 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -25,6 +25,10 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 
 此外，word2vec被提出来构建一个简化的浅层神经网用于学习分布式词表示，这些表示在各种自然语言处理任务中被证明非常有效。这些研究开创了将语言模型用于表示学习（超越词序列建模），对自然语言处理领域产生了重要影响。
 
+3. 预训练语言模型 (PLM)
 
+作为早期尝试，ELMo被提出来通过预训练一个双向 LSTM（biLSTM）网络（而不是 学习固定的词表示）来捕捉上下文感知的词表示，然后根据特定的下游任务微调 biLSTM 网络。进一步，基于自注意力机制的高度并行化 Transformer 架构，BERT作为双向语言模型，在大规模无标签语料库上使用专门设计的预训练任务。
 
+这些预训练的上下文感知词表示作为通用语义特征非常有效，极大地提高了自然语言处理任务的性能。这项研究激发了大量后续工作，确立了“预训练和微调”学习范式。
+遵循这一范式，已经建立了大量关于预训练语言模型的研究引入了不同的架构（例如 GPT-2和 BART），或者改进的预训练策略。在这个范式中，通常需要对预训练语言模型进行微调以适应不同的下游任务。
 

From aba91426103af724db89d6a2f633adb2577b6e07 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 17 Apr 2024 20:45:43 +0800
Subject: [PATCH 1398/1406] feat: update llm02

---
 assets/src/LLM/llm02.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 1fee758c..d98d228f 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -32,3 +32,9 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 这些预训练的上下文感知词表示作为通用语义特征非常有效，极大地提高了自然语言处理任务的性能。这项研究激发了大量后续工作，确立了“预训练和微调”学习范式。
 遵循这一范式，已经建立了大量关于预训练语言模型的研究引入了不同的架构（例如 GPT-2和 BART），或者改进的预训练策略。在这个范式中，通常需要对预训练语言模型进行微调以适应不同的下游任务。
 
+
+4. 大语言模型 (LLM)
+
+研究人员发现，扩展预训练语言模型（例如扩展模型大小或数据大小）通常会提高下游任务的模型容量（即遵循扩展定律）。许多研究通过训练越来越大的 PLM（例如 175B 参数的 GPT-3 和 540B 参数的 PaLM）来探索性能极限。尽管扩展主要在模型大小方面进行（具有类似的架构和预训练任务），但这些大尺寸的预训练语言模型表现出与较小的预训练语言模型（如 330M 参数的 BERT和 1.5B 参数的 GPT-2）不同的行为，
+并在解决一系列复杂任务中展示了惊人的能力（称为涌现能力）。例如，GPT-3 可以通过上下文学习解决少样本任务，而 GPT-2 则表现不佳。因此，研究界为这些大型预训练语言模型命名为“大语言模型 (LLM)”1。LLM 的一个显著应用是 ChatGPT2，它将 GPT 系列的 LLM 应用于对话，展现了惊人的与人类对话的能力。 
+

From 496e7cbc758e8c964316011332c909d6ef1995d1 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 18 Apr 2024 09:18:10 +0800
Subject: [PATCH 1399/1406] feat: update llm02

---
 assets/src/LLM/llm02.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index d98d228f..71c2bcf1 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -38,3 +38,5 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 研究人员发现，扩展预训练语言模型（例如扩展模型大小或数据大小）通常会提高下游任务的模型容量（即遵循扩展定律）。许多研究通过训练越来越大的 PLM（例如 175B 参数的 GPT-3 和 540B 参数的 PaLM）来探索性能极限。尽管扩展主要在模型大小方面进行（具有类似的架构和预训练任务），但这些大尺寸的预训练语言模型表现出与较小的预训练语言模型（如 330M 参数的 BERT和 1.5B 参数的 GPT-2）不同的行为，
 并在解决一系列复杂任务中展示了惊人的能力（称为涌现能力）。例如，GPT-3 可以通过上下文学习解决少样本任务，而 GPT-2 则表现不佳。因此，研究界为这些大型预训练语言模型命名为“大语言模型 (LLM)”1。LLM 的一个显著应用是 ChatGPT2，它将 GPT 系列的 LLM 应用于对话，展现了惊人的与人类对话的能力。 
 
+在现有文献中，PLM 已经得到了广泛的讨论和调研，而很少有研究对 LLM 以系统的方式进行回顾。为了激发我们的调研，我们首先强调 LLM 和 PLM 之间的三个主要区别。首先，LLM 表现出一些令人惊讶的涌现能力，这些能力可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 的强大和有效性。其次，LLM 将彻底改变人类开发和使用人 工智能算法的方式。与小型 PLM 不同，访问 LLM 的主要方法是通过提示接口(例如 GPT-4 API)。
+人们必须了解 LLM的工作原理，并以 LLM 能够遵循的方式形式化他们的任务。第三，LLM 的发展不再明确区分研究和工程。训练 LLM 需要在大规模数据处理和分布式并行训练方面具有丰富的实践经验。为了开发出有能力的 LLM，研究人员必须解决复杂的工程问题，与工程师合作或成为工程师。 
\ No newline at end of file

From 300b290d499946b4a54cccfc70e9f0324b301b31 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Fri, 19 Apr 2024 09:27:16 +0800
Subject: [PATCH 1400/1406] feat: update llm02

---
 assets/src/LLM/llm02.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 71c2bcf1..3611750a 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -39,4 +39,6 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 并在解决一系列复杂任务中展示了惊人的能力（称为涌现能力）。例如，GPT-3 可以通过上下文学习解决少样本任务，而 GPT-2 则表现不佳。因此，研究界为这些大型预训练语言模型命名为“大语言模型 (LLM)”1。LLM 的一个显著应用是 ChatGPT2，它将 GPT 系列的 LLM 应用于对话，展现了惊人的与人类对话的能力。 
 
 在现有文献中，PLM 已经得到了广泛的讨论和调研，而很少有研究对 LLM 以系统的方式进行回顾。为了激发我们的调研，我们首先强调 LLM 和 PLM 之间的三个主要区别。首先，LLM 表现出一些令人惊讶的涌现能力，这些能力可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 的强大和有效性。其次，LLM 将彻底改变人类开发和使用人 工智能算法的方式。与小型 PLM 不同，访问 LLM 的主要方法是通过提示接口(例如 GPT-4 API)。
-人们必须了解 LLM的工作原理，并以 LLM 能够遵循的方式形式化他们的任务。第三，LLM 的发展不再明确区分研究和工程。训练 LLM 需要在大规模数据处理和分布式并行训练方面具有丰富的实践经验。为了开发出有能力的 LLM，研究人员必须解决复杂的工程问题，与工程师合作或成为工程师。 
\ No newline at end of file
+人们必须了解 LLM的工作原理，并以 LLM 能够遵循的方式形式化他们的任务。第三，LLM 的发展不再明确区分研究和工程。训练 LLM 需要在大规模数据处理和分布式并行训练方面具有丰富的实践经验。为了开发出有能力的 LLM，研究人员必须解决复杂的工程问题，与工程师合作或成为工程师。 
+
+如今，LLM 对 AI 社区产生了重大影响，ChatGPT 和GPT-4 的出现促使人们重新思考通用人工智能(AGI)的可能性。

From 6a5d349f7af2ee080caa3895a750a33b8cda9ea2 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sat, 20 Apr 2024 11:10:47 +0800
Subject: [PATCH 1401/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 3611750a..9e0484b2 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -41,4 +41,8 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 在现有文献中，PLM 已经得到了广泛的讨论和调研，而很少有研究对 LLM 以系统的方式进行回顾。为了激发我们的调研，我们首先强调 LLM 和 PLM 之间的三个主要区别。首先，LLM 表现出一些令人惊讶的涌现能力，这些能力可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 可能在以前较小的 PLM 中没有观察到。这些能力是语言模型 的强大和有效性。其次，LLM 将彻底改变人类开发和使用人 工智能算法的方式。与小型 PLM 不同，访问 LLM 的主要方法是通过提示接口(例如 GPT-4 API)。
 人们必须了解 LLM的工作原理，并以 LLM 能够遵循的方式形式化他们的任务。第三，LLM 的发展不再明确区分研究和工程。训练 LLM 需要在大规模数据处理和分布式并行训练方面具有丰富的实践经验。为了开发出有能力的 LLM，研究人员必须解决复杂的工程问题，与工程师合作或成为工程师。 
 
-如今，LLM 对 AI 社区产生了重大影响，ChatGPT 和GPT-4 的出现促使人们重新思考通用人工智能(AGI)的可能性。
+
+如今，LLM 对 AI 社区产生了重大影响，ChatGPT 和GPT-4 的出现促使人们重新思考通用人工智能(AGI)的可能性。OpenAI 已经发布了一篇名为“Planning for AGI and beyond”的技术文章，讨论了实现 AGI 的短期和长期计划而一篇更近期的论文认为 GPT-4 可能被视为 AGI 系统的早期版本。AI 研究领域正因 LLM 的迅速发展而发生革命性变革。在自然语言处理领域，LLM 可以在一定程度上作为通用语言任务解决器，其研究范式已经转向使用 LLM。
+在信 息检索领域，传统搜索引擎正受到通过 AI 聊天机器人(即ChatGPT)搜索新信息的挑战，而 New Bing3展示了一个初步的基于 LLM 增强搜索结果的研究尝试。在计算机视觉领域，研究人员试图开发类似 ChatGPT 的视觉-语言模型，以更好地为多模态对话提供服务GPT-4已经通过整合视觉信息支持多模态输入。这一新技术浪潮可能会带来 例如GPT-3、PaLM、Galactica和LLaMA。
+
+

From 64347776d07b47c197c65748f4a76ca4dcabf805 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sun, 21 Apr 2024 20:16:22 +0800
Subject: [PATCH 1402/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 9e0484b2..c24ea193 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -46,3 +46,4 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 在信 息检索领域，传统搜索引擎正受到通过 AI 聊天机器人(即ChatGPT)搜索新信息的挑战，而 New Bing3展示了一个初步的基于 LLM 增强搜索结果的研究尝试。在计算机视觉领域，研究人员试图开发类似 ChatGPT 的视觉-语言模型，以更好地为多模态对话提供服务GPT-4已经通过整合视觉信息支持多模态输入。这一新技术浪潮可能会带来 例如GPT-3、PaLM、Galactica和LLaMA。
 
 
+具体而言，LLM 基于 Transformer 架构构建，其中多头注意力层堆叠在非常深的神经网络中。
\ No newline at end of file

From f17433e78f3367f8e0b0114cc0a9a4cd6ddd0381 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Tue, 23 Apr 2024 09:30:29 +0800
Subject: [PATCH 1403/1406] feat: update llm

---
 assets/src/LLM/img.png   | Bin 0 -> 243166 bytes
 assets/src/LLM/img_1.png | Bin 0 -> 243166 bytes
 assets/src/LLM/llm02.md  |   4 +++-
 3 files changed, 3 insertions(+), 1 deletion(-)
 create mode 100644 assets/src/LLM/img.png
 create mode 100644 assets/src/LLM/img_1.png

diff --git a/assets/src/LLM/img.png b/assets/src/LLM/img.png
new file mode 100644
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diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index c24ea193..20d6cb40 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -46,4 +46,6 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 在信 息检索领域，传统搜索引擎正受到通过 AI 聊天机器人(即ChatGPT)搜索新信息的挑战，而 New Bing3展示了一个初步的基于 LLM 增强搜索结果的研究尝试。在计算机视觉领域，研究人员试图开发类似 ChatGPT 的视觉-语言模型，以更好地为多模态对话提供服务GPT-4已经通过整合视觉信息支持多模态输入。这一新技术浪潮可能会带来 例如GPT-3、PaLM、Galactica和LLaMA。
 
 
-具体而言，LLM 基于 Transformer 架构构建，其中多头注意力层堆叠在非常深的神经网络中。
\ No newline at end of file
+具体而言，LLM 基于 Transformer 架构构建，其中多头注意力层堆叠在非常深的神经网络中。现有的 LLM 主要采用与小语言模型类似的模型架构（即 Transformer)和预训练目标(即语言建模)。作为主要区别，LLM 大幅扩展了模型大小、预训练数据和总计算量(若干数量级)，可以更好地根据上下文(即提示)理解自然语言并生成高质量的文本。这一能力提升可以部分通过扩展定律来描述，即任务性能大致随着模型大小的增加而显著提高然而，一些能力(例如上下文学习)是不可预测的，只有当模型大小超过一定水平时才能观察到。
+
+

From f7e0167a19c377060b0102bfd2bb0ea6597f9944 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Wed, 24 Apr 2024 09:32:00 +0800
Subject: [PATCH 1404/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 20d6cb40..45ed3c37 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -48,4 +48,5 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 
 具体而言，LLM 基于 Transformer 架构构建，其中多头注意力层堆叠在非常深的神经网络中。现有的 LLM 主要采用与小语言模型类似的模型架构（即 Transformer)和预训练目标(即语言建模)。作为主要区别，LLM 大幅扩展了模型大小、预训练数据和总计算量(若干数量级)，可以更好地根据上下文(即提示)理解自然语言并生成高质量的文本。这一能力提升可以部分通过扩展定律来描述，即任务性能大致随着模型大小的增加而显著提高然而，一些能力(例如上下文学习)是不可预测的，只有当模型大小超过一定水平时才能观察到。
 
+大语言模型的涌现能力: 在文献中，LLM 的“涌现能力”被正式定义为“在小模型中不存在但在大模型中出现的能力”，这是区分 LLM 与以前的 PLM 最突出的特征之一。它进一步介绍了一个显著的特征，即当规模达到一定水平时，性能显著提高超过随机水平。类比地，这种涌现模式与物理学中的相变”现象有着密切的联系。原则上，涌现能力可以定义为与某些复杂任务相关的能力，而我们更关注能够应用于解决各种任务的通用能力。这里，我们简要介绍三个代表性的 LLM 涌现能力。
 

From 25091fbd43b0e374e36098ae5918330b41dda232 Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Thu, 25 Apr 2024 09:11:28 +0800
Subject: [PATCH 1405/1406] feat: update llm

---
 assets/src/LLM/llm02.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 45ed3c37..98bc47d4 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -50,3 +50,5 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 
 大语言模型的涌现能力: 在文献中，LLM 的“涌现能力”被正式定义为“在小模型中不存在但在大模型中出现的能力”，这是区分 LLM 与以前的 PLM 最突出的特征之一。它进一步介绍了一个显著的特征，即当规模达到一定水平时，性能显著提高超过随机水平。类比地，这种涌现模式与物理学中的相变”现象有着密切的联系。原则上，涌现能力可以定义为与某些复杂任务相关的能力，而我们更关注能够应用于解决各种任务的通用能力。这里，我们简要介绍三个代表性的 LLM 涌现能力。
 
+* 上下文学习:上下文学习能力由 GPT-3 正式引入,假设提供给语言模型自然语言指令和/或多个任务演示，它可以通过完成输入文本的单词序列来为测试实例生成期望的输出，而无需额外的训练或梯度更新。
+* 指令遵循:通过使用自然语言描述的多任务数据集进行微调(称为指令微调)，LLM 可以在同样使用指令形式化描述的未见任务上表现良好。通过指令微调，LLM 能够在没有使用显式示例的情况下遵循任务指令,从而具有更好的泛化能力。
\ No newline at end of file

From 112d410f685ba83fa8b4ae804baf3bf93bf6751a Mon Sep 17 00:00:00 2001
From: keke <keke>
Date: Sun, 28 Apr 2024 15:14:47 +0800
Subject: [PATCH 1406/1406] feat: update llm02

---
 assets/src/LLM/llm02.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/assets/src/LLM/llm02.md b/assets/src/LLM/llm02.md
index 98bc47d4..ea675909 100644
--- a/assets/src/LLM/llm02.md
+++ b/assets/src/LLM/llm02.md
@@ -51,4 +51,5 @@ SLMs 基于统计学习方法 开发，并在 20 世纪 90 年代兴起。其基
 大语言模型的涌现能力: 在文献中，LLM 的“涌现能力”被正式定义为“在小模型中不存在但在大模型中出现的能力”，这是区分 LLM 与以前的 PLM 最突出的特征之一。它进一步介绍了一个显著的特征，即当规模达到一定水平时，性能显著提高超过随机水平。类比地，这种涌现模式与物理学中的相变”现象有着密切的联系。原则上，涌现能力可以定义为与某些复杂任务相关的能力，而我们更关注能够应用于解决各种任务的通用能力。这里，我们简要介绍三个代表性的 LLM 涌现能力。
 
 * 上下文学习:上下文学习能力由 GPT-3 正式引入,假设提供给语言模型自然语言指令和/或多个任务演示，它可以通过完成输入文本的单词序列来为测试实例生成期望的输出，而无需额外的训练或梯度更新。
-* 指令遵循:通过使用自然语言描述的多任务数据集进行微调(称为指令微调)，LLM 可以在同样使用指令形式化描述的未见任务上表现良好。通过指令微调，LLM 能够在没有使用显式示例的情况下遵循任务指令,从而具有更好的泛化能力。
\ No newline at end of file
+* 指令遵循:通过使用自然语言描述的多任务数据集进行微调(称为指令微调)，LLM 可以在同样使用指令形式化描述的未见任务上表现良好。通过指令微调，LLM 能够在没有使用显式示例的情况下遵循任务指令,从而具有更好的泛化能力。
+* 逐步推理:对于小语言模型来说，通常难以解决涉及多个推理步骤的复杂任务，例如数学问题。然而，通过采用“思维链”推理策略，LLM 可以利用包含中间推理步骤的提示机制来解决这些任务，得出最终答案。这种能力被认为可能通过在代码上进行训练来获得。
\ No newline at end of file