From 2a55c832f7b7992c84d0dfa7643767ad17890ffe Mon Sep 17 00:00:00 2001 From: ApacheCN Date: Sat, 25 Feb 2017 16:53:03 +0800 Subject: [PATCH 01/10] Initial commit --- .gitignore | 89 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ README.md | 1 + 2 files changed, 90 insertions(+) create mode 100644 .gitignore create mode 100644 README.md diff --git a/.gitignore b/.gitignore new file mode 100644 index 000000000..72364f99f --- /dev/null +++ b/.gitignore @@ -0,0 +1,89 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +env/ +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +*.egg-info/ +.installed.cfg +*.egg + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*,cover +.hypothesis/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# IPython Notebook +.ipynb_checkpoints + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# dotenv +.env + +# virtualenv +venv/ +ENV/ + +# Spyder project settings +.spyderproject + +# Rope project settings +.ropeproject diff --git a/README.md b/README.md new file mode 100644 index 000000000..00dbeff49 --- /dev/null +++ b/README.md @@ -0,0 +1 @@ +# MachineLearning \ No newline at end of file From d9d21f52583f6aa606e5ac4523844d679eef5487 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sat, 25 Feb 2017 17:15:10 +0800 Subject: [PATCH 02/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0README?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 40 +++++++++++++++++++++++++++++++++++++++- 1 file changed, 39 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 00dbeff49..711e5cedf 100644 --- a/README.md +++ b/README.md @@ -1 +1,39 @@ -# MachineLearning \ No newline at end of file +# MachineLearning + +**Mahchine Leaning in Action (python)** + +## 第一部分 分类 + +* 1) 机器学习基础 +* 2) k-紧邻算法 +* 3) 决策树 +* 4) 基于概率论的分类方法：朴素贝叶斯 +* 5) Logistic回归 +* 6) 支持向量机 +* 7) 利用AdaBoost元算法提高分类 + +## 第二部分 利用回归预测数值型数据 + +* 8) 预测数值型数据：回归 +* 9) 数回归 + +### 第三部分 无监督学习 + +* 10) 使用K-均值聚类算法对未标注数据分组 +* 11) 使用Apriori算法进行关联分析 +* 12) 使用FP-growth算法来高效发现频繁项集 + +### 第四部分 其他工具 + +* 13) 使用PCA来简化数据 +* 14) 使用SVD简化数据 +* 15) 大数据与MapReduce + +* * * + +* 附录A Python入门 +* 附录B 线性代数 +* 附录C 概率论复习 +* 附录D 资源 +* 索引 +* 版权声明 \ No newline at end of file From f69881fcc3703bb13be4f1bfe3d0d5c4edbb581c Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sat, 25 Feb 2017 19:19:30 +0800 Subject: [PATCH 03/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0readme?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .vscode/settings.json | 3 + .vscode/tasks.json | 9 ++ README.md | 22 +++ docs/README.md | 39 +++++ src/python/01.NumPy.py | 21 +++ src/python/Logistic.py | 136 ++++++++++++++++++ src/python/apriori.py | 206 +++++++++++++++++++++++++++ src/python/regression.py | 298 +++++++++++++++++++++++++++++++++++++++ 8 files changed, 734 insertions(+) create mode 100644 .vscode/settings.json create mode 100644 .vscode/tasks.json create mode 100644 docs/README.md create mode 100644 src/python/01.NumPy.py create mode 100644 src/python/Logistic.py create mode 100644 src/python/apriori.py create mode 100644 src/python/regression.py diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 000000000..fe7159848 --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,3 @@ +{ + "python.linting.pylintEnabled": false +} \ No newline at end of file diff --git a/.vscode/tasks.json b/.vscode/tasks.json new file mode 100644 index 000000000..66d0b4ec2 --- /dev/null +++ b/.vscode/tasks.json @@ -0,0 +1,9 @@ +{ + // See https://go.microsoft.com/fwlink/?LinkId=733558 + // for the documentation about the tasks.json format + "version": "0.1.0", + "command": "/usr/bin/python", + "isShellCommand": true, + "args": ["${file}"], + "showOutput": "always" +} diff --git a/README.md b/README.md index 711e5cedf..4de2019f8 100644 --- a/README.md +++ b/README.md @@ -5,6 +5,28 @@ ## 第一部分 分类 * 1) 机器学习基础 + * 机器学习是什么 + * 把无序的数据转换成有用的信息。 + * 机器学习的意义 + * 我们利用计算机来彰显数据背后的真实含义。 + * 监督学习 + * 样本集：训练数据 + 测试数据 + * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值/回归-连续值<0~100、 -999～999>) + * `知识表示`：机器已经学会如何识别鸟类的过程 + * 1.可以采用规则集的形式 + * 2.可以采用概率分布的形式 + * 3.可以使训练样本集中的一个实例 + * 非监督学习 + * 开发的步骤 + * 1.收集数据 + * 2.准备输入数据 + * 3.分析输入数据 + * 4.训练算法 + * 5.测试算法 + * 6.使用算法 + * Python相关的库 + * 科学函数库：SciPy、`NumPy`(底层语言：C和Fortran) + * 绘图工具库：`Matplotlib` * 2) k-紧邻算法 * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 diff --git a/docs/README.md b/docs/README.md new file mode 100644 index 000000000..711e5cedf --- /dev/null +++ b/docs/README.md @@ -0,0 +1,39 @@ +# MachineLearning + +**Mahchine Leaning in Action (python)** + +## 第一部分 分类 + +* 1) 机器学习基础 +* 2) k-紧邻算法 +* 3) 决策树 +* 4) 基于概率论的分类方法：朴素贝叶斯 +* 5) Logistic回归 +* 6) 支持向量机 +* 7) 利用AdaBoost元算法提高分类 + +## 第二部分 利用回归预测数值型数据 + +* 8) 预测数值型数据：回归 +* 9) 数回归 + +### 第三部分 无监督学习 + +* 10) 使用K-均值聚类算法对未标注数据分组 +* 11) 使用Apriori算法进行关联分析 +* 12) 使用FP-growth算法来高效发现频繁项集 + +### 第四部分 其他工具 + +* 13) 使用PCA来简化数据 +* 14) 使用SVD简化数据 +* 15) 大数据与MapReduce + +* * * + +* 附录A Python入门 +* 附录B 线性代数 +* 附录C 概率论复习 +* 附录D 资源 +* 索引 +* 版权声明 \ No newline at end of file diff --git a/src/python/01.NumPy.py b/src/python/01.NumPy.py new file mode 100644 index 000000000..8425a6cee --- /dev/null +++ b/src/python/01.NumPy.py @@ -0,0 +1,21 @@ +#!/usr/bin/python +# coding:utf8 + +from numpy import random + +''' +# NumPy 矩阵和数字的区别 +NumPy存在2中不同的数据类型: + 1. 矩阵 matrix + 2. 数组 array +相似点： + 都可以处理行列表示的数字元素 +不同点： + 1. 2个数据类型上执行相同的数据运算可能得到不同的结果。 + 2. NumPy函数库中的 matrix 与 MATLAB中 matrices 等价。 +''' + +# 生成一个 4*4 的随机数组 +print random.rand(4, 4) + + diff --git a/src/python/Logistic.py b/src/python/Logistic.py new file mode 100644 index 000000000..82ca465cd --- /dev/null +++ b/src/python/Logistic.py @@ -0,0 +1,136 @@ +#!/usr/bin/python +# coding: utf8 + +''' +Created on Oct 27, 2010 +Logistic Regression Working Module +@author: Peter +''' + +import os +from numpy import * +import matplotlib.pyplot as plt +# 解析数据 +def loadDataSet(file_name): + # dataMat为原始数据， labelMat为原始数据的标签 + dataMat = []; labelMat = [] + fr = open(file_name) + for line in fr.readlines(): + lineArr = line.strip().split() + dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) + labelMat.append(int(lineArr[2])) + return dataMat,labelMat + +# sigmoid跳跃函数 +def sigmoid(inX): + return 1.0/(1+exp(-inX)) + +# 正常的处理方案 +def gradAscent(dataMatIn, classLabels): + dataMatrix = mat(dataMatIn) #convert to NumPy matrix + # transpose() 行列转制函数 + # 将行矩阵转化为列矩阵 => 矩阵的转置 + labelMat = mat(classLabels).transpose() #convert to NumPy matrix + m,n = shape(dataMatrix) + # print m, n, '__'*10, shape(dataMatrix.transpose()), '__'*100 + alpha = 0.001 + maxCycles = 500 + # 权重 + weights = ones((n,1)) + for k in range(maxCycles): #heavy on matrix operations + # m*3的矩阵 * 3*1的单位矩阵 ＝ m*1的矩阵 + # 那么乘上单位矩阵的意义，就代表：通过公式得到的理论值 + # 参考地址： 矩阵乘法的本质是什么？ https://www.zhihu.com/question/21351965/answer/31050145 + # n*3 * 3*1 = n*1 + h = sigmoid(dataMatrix*weights) #matrix mult + # labelMat是实际值 + error = (labelMat - h) #vector subtraction + # 0.001* (3*m)*(m*1) 表示在每一个列上的一个误差情况，最后得出 x1,x2,xn的系数的偏移量 + weights = weights + alpha * dataMatrix.transpose() * error #matrix mult + return array(weights) + +# 梯度上升算法 +def stocGradAscent0(dataMatrix, classLabels): + m,n = shape(dataMatrix) + alpha = 0.01 + # n*1的矩阵 + # 函数ones创建一个全1的数组 + weights = ones(n) #initialize to all ones + for i in range(m): + # sum(dataMatrix[i]*weights)为了求 f(x)的值， f(x)=a1*x1+b2*x2+..+nn*xn + h = sigmoid(sum(dataMatrix[i]*weights)) + error = classLabels[i] - h + # 0.01*(1*1)*(1*n) + print weights, "*"*10 , dataMatrix[i], "*"*10 , error + weights = weights + alpha * error * dataMatrix[i] + return weights + +# 随机梯度上升算法（随机化） +def stocGradAscent1(dataMatrix, classLabels, numIter=150): + m,n = shape(dataMatrix) + weights = ones(n) #initialize to all ones + # 随机剃度, 循环150,观察是否收敛 + for j in range(numIter): + # [0, 1, 2 .. m-1] + dataIndex = range(m) + for i in range(m): + # i和j的不断增大，导致alpha的值不断减少，但是不为0 + alpha = 4/(1.0+j+i)+0.0001 #apha decreases with iteration, does not + # 随机产生一个 0～len()之间的一个值 + randIndex = int(random.uniform(0,len(dataIndex)))#go to 0 because of the constant + # sum(dataMatrix[i]*weights)为了求 f(x)的值， f(x)=a1*x1+b2*x2+..+nn*xn + h = sigmoid(sum(dataMatrix[randIndex]*weights)) + error = classLabels[randIndex] - h + # print weights, '__h=%s' % h, '__'*20, alpha, '__'*20, error, '__'*20, dataMatrix[randIndex] + weights = weights + alpha * error * dataMatrix[randIndex] + del(dataIndex[randIndex]) + return weights + +# 可视化展示 +def plotBestFit(dataArr, labelMat, weights): + n = shape(dataArr)[0] + xcord1 = []; ycord1 = [] + xcord2 = []; ycord2 = [] + for i in range(n): + if int(labelMat[i])== 1: + xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2]) + else: + xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2]) + fig = plt.figure() + ax = fig.add_subplot(111) + ax.scatter(xcord1, ycord1, s=30, c='red', marker='s') + ax.scatter(xcord2, ycord2, s=30, c='green') + x = arange(-3.0, 3.0, 0.1) + """ + y的由来，卧槽，是不是没看懂？ + 首先理论上是这个样子的。 + dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) + w0*x0+w1*x1+w2*x2=f(x) + x0最开始就设置为1叻， x2就是我们画图的y值，而f(x)被我们磨合误差给算到w0,w1,w2身上去了 + 所以： w0+w1*x+w2*y=0 => y = (-w0-w1*x)/w2 + """ + y = (-weights[0]-weights[1]*x)/weights[2] + ax.plot(x, y) + plt.xlabel('X'); plt.ylabel('Y') + plt.show() + +def main(): + project_dir = os.path.dirname(os.path.dirname(os.getcwd())) + # 1.收集并准备数据 + dataMat, labelMat = loadDataSet("%s/resources/testSet.txt" % project_dir) + + # print dataMat, '---\n', labelMat + # 2.训练模型， f(x)=a1*x1+b2*x2+..+nn*xn中 (a1,b2, .., nn).T的矩阵值 + # 因为数组没有是复制n份， array的乘法就是乘法 + dataArr = array(dataMat) + # print dataArr + # weights = gradAscent(dataArr, labelMat) + # weights = stocGradAscent0(dataArr, labelMat) + weights = stocGradAscent1(dataArr, labelMat) + # print '*'*30, weights + + # 数据可视化 + plotBestFit(dataArr, labelMat, weights) + +if __name__=="__main__": + main() \ No newline at end of file diff --git a/src/python/apriori.py b/src/python/apriori.py new file mode 100644 index 000000000..ee6af908d --- /dev/null +++ b/src/python/apriori.py @@ -0,0 +1,206 @@ +#!/usr/bin/python +# coding: utf8 + +''' +Created on Mar 24, 2011 +Ch 11 code +@author: Peter +''' +from numpy import * + +def loadDataSet(): + return [[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]] + +def createC1(dataSet): + C1 = [] + for transaction in dataSet: + for item in transaction: + if not [item] 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(D, Ck, minSupport): + ssCnt = {} + for tid in D: + for can in Ck: + # s.issubset(t) 测试是否 s 中的每一个元素都在 t 中 + if can.issubset(tid): + if not ssCnt.has_key(can): ssCnt[can]=1 + else: ssCnt[can] += 1 + numItems = float(len(D)) + retList = [] + supportData = {} + for key in ssCnt: + support = ssCnt[key]/numItems + if support >= minSupport: + retList.insert(0, key) + supportData[key] = support + return retList, supportData + +def aprioriGen(Lk, k): #creates Ck + 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 + retList.append(Lk[i] | Lk[j]) #set union + return retList + +def apriori(dataSet, minSupport = 0.5): + # 冻结每一行数据 + C1 = createC1(dataSet) + D = map(set, dataSet) + + # 计算支持support + L1, supportData = scanD(D, C1, minSupport) + print("outcome: ", supportData) + + L = [L1] + k = 2 + while (len(L[k-2]) > 0): + Ck = aprioriGen(L[k-2], k) + Lk, supK = scanD(D, Ck, minSupport)#scan DB to get Lk + supportData.update(supK) + L.append(Lk) + k += 1 + return L, supportData + +def main(): + # project_dir = os.path.dirname(os.path.dirname(os.getcwd())) + # 1.收集并准备数据 + # dataMat, labelMat = loadDataSet("%s/resources/testSet.txt" % project_dir) + + + # 1. 加载数据 + dataSet = loadDataSet() + print(dataSet) + # 调用 apriori 做购物篮分析 + apriori(dataSet, minSupport = 0.7) + +if __name__=="__main__": + main() + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +def generateRules(L, supportData, minConf=0.7): #supportData is a dict coming from scanD + bigRuleList = [] + for i in range(1, len(L)):#only get the sets with two or more items + for freqSet in L[i]: + H1 = [frozenset([item]) for item in freqSet] + if (i > 1): + rulesFromConseq(freqSet, H1, supportData, bigRuleList, minConf) + else: + calcConf(freqSet, H1, supportData, bigRuleList, minConf) + return bigRuleList + +def calcConf(freqSet, H, supportData, brl, minConf=0.7): + prunedH = [] #create new list to return + for conseq in H: + conf = supportData[freqSet]/supportData[freqSet-conseq] #calc confidence + if conf >= minConf: + print freqSet-conseq,'-->',conseq,'conf:',conf + brl.append((freqSet-conseq, conseq, conf)) + prunedH.append(conseq) + return prunedH + +def rulesFromConseq(freqSet, H, supportData, brl, minConf=0.7): + m = len(H[0]) + if (len(freqSet) > (m + 1)): #try further merging + Hmp1 = aprioriGen(H, m+1)#create Hm+1 new candidates + Hmp1 = calcConf(freqSet, Hmp1, supportData, brl, minConf) + if (len(Hmp1) > 1): #need at least two sets to merge + rulesFromConseq(freqSet, Hmp1, supportData, brl, minConf) + +def pntRules(ruleList, itemMeaning): + for ruleTup in ruleList: + for item in ruleTup[0]: + print itemMeaning[item] + print " -------->" + for item in ruleTup[1]: + print itemMeaning[item] + print "confidence: %f" % ruleTup[2] + print #print a blank line + + +# from time import sleep +# from votesmart import votesmart +# votesmart.apikey = 'a7fa40adec6f4a77178799fae4441030' +# #votesmart.apikey = 'get your api key first' +# def getActionIds(): +# actionIdList = []; billTitleList = [] +# fr = open('recent20bills.txt') +# for line in fr.readlines(): +# billNum = int(line.split('\t')[0]) +# try: +# billDetail = votesmart.votes.getBill(billNum) #api call +# for action in billDetail.actions: +# if action.level == 'House' and \ +# (action.stage == 'Passage' or action.stage == 'Amendment Vote'): +# actionId = int(action.actionId) +# print 'bill: %d has actionId: %d' % (billNum, actionId) +# actionIdList.append(actionId) +# billTitleList.append(line.strip().split('\t')[1]) +# except: +# print "problem getting bill %d" % billNum +# sleep(1) #delay to be polite +# return actionIdList, billTitleList +# +# def getTransList(actionIdList, billTitleList): #this will return a list of lists containing ints +# itemMeaning = ['Republican', 'Democratic']#list of what each item stands for +# for billTitle in billTitleList:#fill up itemMeaning list +# itemMeaning.append('%s -- Nay' % billTitle) +# itemMeaning.append('%s -- Yea' % billTitle) +# transDict = {}#list of items in each transaction (politician) +# voteCount = 2 +# for actionId in actionIdList: +# sleep(3) +# print 'getting votes for actionId: %d' % actionId +# try: +# voteList = votesmart.votes.getBillActionVotes(actionId) +# for vote in voteList: +# if not transDict.has_key(vote.candidateName): +# transDict[vote.candidateName] = [] +# if vote.officeParties == 'Democratic': +# transDict[vote.candidateName].append(1) +# elif vote.officeParties == 'Republican': +# transDict[vote.candidateName].append(0) +# if vote.action == 'Nay': +# transDict[vote.candidateName].append(voteCount) +# elif vote.action == 'Yea': +# transDict[vote.candidateName].append(voteCount + 1) +# except: +# print "problem getting actionId: %d" % actionId +# voteCount += 2 +# return transDict, itemMeaning diff --git a/src/python/regression.py b/src/python/regression.py new file mode 100644 index 000000000..de3283682 --- /dev/null +++ b/src/python/regression.py @@ -0,0 +1,298 @@ +#!/usr/bin/python +# coding: utf8 + +''' +Created on Jan 8, 2011 + +@author: Peter +''' + +import os +from numpy import * +import matplotlib.pylab as plt + +def loadDataSet(fileName): #general function to parse tab -delimited floats + numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields + dataMat = []; labelMat = [] + fr = open(fileName) + for line in fr.readlines(): + lineArr =[] + curLine = line.strip().split('\t') + for i in range(numFeat): + lineArr.append(float(curLine[i])) + dataMat.append(lineArr) + labelMat.append(float(curLine[-1])) + return dataMat,labelMat + +def standRegres(xArr,yArr): + # >>> A.T # transpose, 转置 + xMat = mat(xArr); yMat = mat(yArr).T + # 转置矩阵*矩阵 + xTx = xMat.T*xMat + if linalg.det(xTx) == 0.0: + print "This matrix is singular, cannot do inverse" + return + # >>> print A.I # inverse, 逆矩阵 + # print xTx.I, "*"*10, xMat.T, "*"*10, yMat + ws = xTx.I * (xMat.T*yMat) # 最小二乘法求最优解 + return ws + +def plotBestFit(xArr, yArr, ws): + + xMat = mat(xArr) + yMat = mat(yArr) + fig = plt.figure() + ax = fig.add_subplot(111) + ax.scatter(xMat[:,1].flatten().A[0], yMat.T[:,0].flatten().A[0]) + + yHat = xMat*ws + # 再计算相关系数 + print "相关系数\n", corrcoef(yHat.T, yMat) + + xMat.sort(0) + yHat = xMat*ws + n = shape(xMat)[0] + xcord = []; ycord = [] + for i in range(n): + xcord.append(xMat[i, 1]); ycord.append(yHat[i, 0]) + + ax.plot(xcord, ycord, c='red') + plt.xlabel('X'); plt.ylabel('Y') + plt.show() + +def main1(): + # w0*x0+w1*x1+w2*x2=f(x) + project_dir = os.path.dirname(os.path.dirname(os.getcwd())) + # 1.收集并准备数据 + xArr, yArr = loadDataSet("%s/resources/ex0.txt" % project_dir) + # print xArr, '---\n', yArr + # 2.训练模型， f(x)=a1*x1+b2*x2+..+nn*xn中 (a1,b2, .., nn).T的矩阵值 + ws = standRegres(xArr, yArr) + print '*'*30, '---\n', ws + + # 数据可视化 + plotBestFit(xArr, yArr, ws) + + +def lwlr(testPoint, xArr, yArr,k=1.0): + xMat = mat(xArr); yMat = mat(yArr).T + m = shape(xMat)[0] + weights = mat(eye((m))) + for j in range(m): #next 2 lines create weights matrix + diffMat = testPoint - xMat[j,:] + # 高斯核对应的加权 + weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2)) + xTx = xMat.T * (weights * xMat) + if linalg.det(xTx) == 0.0: + print "This matrix is singular, cannot do inverse" + return + + # 加权的回归系数求解 + ws = xTx.I * (xMat.T * (weights * yMat)) + return testPoint * ws + +def lwlrTest(testArr,xArr,yArr,k=1.0): #loops over all the data points and applies lwlr to each one + m = shape(testArr)[0] + # m*1的矩阵 + # 函数 zeros 创建一个全0的数组 + yHat = zeros(m) + print "shape(yHat)", shape(yHat) + for i in range(m): + yHat[i] = lwlr(testArr[i],xArr,yArr,k) + return yHat + +def lwlrTestPlot(xArr, yArr, yHat): + + xMat = mat(xArr) + yMat = mat(yArr) + fig = plt.figure() + ax = fig.add_subplot(111) + ax.scatter(xMat[:,1].flatten().A[0], yMat.T[:,0].flatten().A[0]) + + # 再计算相关系数 + print "相关系数\n", corrcoef(yHat.T, yMat) + + n = shape(xMat)[0] + xcord = []; ycord = [] + for i in range(n): + xcord.append(xMat[i, 1]), ycord.append(yHat[i]) + + xcord.sort(), ycord.sort() + # print xcord, "------\n", ycord + ax.plot(xcord, ycord, c='red') + plt.xlabel('X'); plt.ylabel('Y') + plt.show() + +def main2(): + # w0*x0+w1*x1+w2*x2=f(x) + project_dir = os.path.dirname(os.path.dirname(os.getcwd())) + # 1.收集并准备数据 + xArr, yArr = loadDataSet("%s/resources/ex0.txt" % project_dir) + # print xArr, '---\n', yArr + # 2.训练模型， f(x)=a1*x1+b2*x2+..+nn*xn中 (a1,b2, .., nn).T的矩阵值 + yHat = lwlrTest(xArr, xArr, yArr, 0.003) + print xArr, '---\n', yHat[1] + + # 数据可视化 + lwlrTestPlot(xArr, yArr, yHat) + +if __name__=="__main__": + # 线性回归 + # main1() + # 局部加权线性回归 + main2() + +def rssError(yArr,yHatArr): #yArr and yHatArr both need to be arrays + return ((yArr-yHatArr)**2).sum() + +def ridgeRegres(xMat,yMat,lam=0.2): + xTx = xMat.T*xMat + denom = xTx + eye(shape(xMat)[1])*lam + if linalg.det(denom) == 0.0: + print "This matrix is singular, cannot do inverse" + return + ws = denom.I * (xMat.T*yMat) + return ws + +def ridgeTest(xArr,yArr): + xMat = mat(xArr); yMat=mat(yArr).T + yMean = mean(yMat,0) + yMat = yMat - yMean #to eliminate X0 take mean off of Y + #regularize X's + xMeans = mean(xMat,0) #calc mean then subtract it off + xVar = var(xMat,0) #calc variance of Xi then divide by it + xMat = (xMat - xMeans)/xVar + numTestPts = 30 + wMat = zeros((numTestPts,shape(xMat)[1])) + for i in range(numTestPts): + ws = ridgeRegres(xMat,yMat,exp(i-10)) + wMat[i,:]=ws.T + return wMat + +def regularize(xMat):#regularize by columns + inMat = xMat.copy() + inMeans = mean(inMat,0) #calc mean then subtract it off + inVar = var(inMat,0) #calc variance of Xi then divide by it + inMat = (inMat - inMeans)/inVar + return inMat + +def stageWise(xArr,yArr,eps=0.01,numIt=100): + xMat = mat(xArr); yMat=mat(yArr).T + yMean = mean(yMat,0) + yMat = yMat - yMean #can also regularize ys but will get smaller coef + xMat = regularize(xMat) + m,n=shape(xMat) + #returnMat = zeros((numIt,n)) #testing code remove + ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy() + for i in range(numIt): + print ws.T + lowestError = inf; + for j in range(n): + for sign in [-1,1]: + wsTest = ws.copy() + wsTest[j] += eps*sign + yTest = xMat*wsTest + rssE = rssError(yMat.A,yTest.A) + if rssE < lowestError: + lowestError = rssE + wsMax = wsTest + ws = wsMax.copy() + #returnMat[i,:]=ws.T + #return returnMat + +def scrapePage(inFile,outFile,yr,numPce,origPrc): + from BeautifulSoup import BeautifulSoup + fr = open(inFile); fw=open(outFile,'a') #a is append mode writing + soup = BeautifulSoup(fr.read()) + i=1 + currentRow = soup.findAll('table', r="%d" % i) + while(len(currentRow)!=0): + title = currentRow[0].findAll('a')[1].text + lwrTitle = title.lower() + if (lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1): + newFlag = 1.0 + else: + newFlag = 0.0 + soldUnicde = currentRow[0].findAll('td')[3].findAll('span') + if len(soldUnicde)==0: + print "item #%d did not sell" % i + else: + soldPrice = currentRow[0].findAll('td')[4] + priceStr = soldPrice.text + priceStr = priceStr.replace('$','') #strips out $ + priceStr = priceStr.replace(',','') #strips out , + if len(soldPrice)>1: + priceStr = priceStr.replace('Free shipping', '') #strips out Free Shipping + print "%s\t%d\t%s" % (priceStr,newFlag,title) + fw.write("%d\t%d\t%d\t%f\t%s\n" % (yr,numPce,newFlag,origPrc,priceStr)) + i += 1 + currentRow = soup.findAll('table', r="%d" % i) + fw.close() + +from time import sleep +import json +import urllib2 +def searchForSet(retX, retY, setNum, yr, numPce, origPrc): + sleep(10) + myAPIstr = 'AIzaSyD2cR2KFyx12hXu6PFU-wrWot3NXvko8vY' + searchURL = 'https://www.googleapis.com/shopping/search/v1/public/products?key=%s&country=US&q=lego+%d&alt=json' % (myAPIstr, setNum) + pg = urllib2.urlopen(searchURL) + retDict = json.loads(pg.read()) + for i in range(len(retDict['items'])): + try: + currItem = retDict['items'][i] + if currItem['product']['condition'] == 'new': + newFlag = 1 + else: newFlag = 0 + listOfInv = currItem['product']['inventories'] + for item in listOfInv: + sellingPrice = item['price'] + if sellingPrice > origPrc * 0.5: + print "%d\t%d\t%d\t%f\t%f" % (yr,numPce,newFlag,origPrc, sellingPrice) + retX.append([yr, numPce, newFlag, origPrc]) + retY.append(sellingPrice) + except: print 'problem with item %d' % i + +def setDataCollect(retX, retY): + searchForSet(retX, retY, 8288, 2006, 800, 49.99) + searchForSet(retX, retY, 10030, 2002, 3096, 269.99) + searchForSet(retX, retY, 10179, 2007, 5195, 499.99) + searchForSet(retX, retY, 10181, 2007, 3428, 199.99) + searchForSet(retX, retY, 10189, 2008, 5922, 299.99) + searchForSet(retX, retY, 10196, 2009, 3263, 249.99) + +def crossValidation(xArr,yArr,numVal=10): + m = len(yArr) + indexList = range(m) + errorMat = zeros((numVal,30))#create error mat 30columns numVal rows + for i in range(numVal): + trainX=[]; trainY=[] + testX = []; testY = [] + random.shuffle(indexList) + for j in range(m):#create training set based on first 90% of values in indexList + if j < m*0.9: + trainX.append(xArr[indexList[j]]) + trainY.append(yArr[indexList[j]]) + else: + testX.append(xArr[indexList[j]]) + testY.append(yArr[indexList[j]]) + wMat = ridgeTest(trainX,trainY) #get 30 weight vectors from ridge + for k in range(30):#loop over all of the ridge estimates + matTestX = mat(testX); matTrainX=mat(trainX) + meanTrain = mean(matTrainX,0) + varTrain = var(matTrainX,0) + matTestX = (matTestX-meanTrain)/varTrain #regularize test with training params + yEst = matTestX * mat(wMat[k,:]).T + mean(trainY)#test ridge results and store + errorMat[i,k]=rssError(yEst.T.A,array(testY)) + #print errorMat[i,k] + meanErrors = mean(errorMat,0)#calc avg performance of the different ridge weight vectors + minMean = float(min(meanErrors)) + bestWeights = wMat[nonzero(meanErrors==minMean)] + #can unregularize to get model + #when we regularized we wrote Xreg = (x-meanX)/var(x) + #we can now write in terms of x not Xreg: x*w/var(x) - meanX/var(x) +meanY + xMat = mat(xArr); yMat=mat(yArr).T + meanX = mean(xMat,0); varX = var(xMat,0) + unReg = bestWeights/varX + print "the best model from Ridge Regression is:\n",unReg + print "with constant term: ",-1*sum(multiply(meanX,unReg)) + mean(yMat) \ No newline at end of file From d1676db7e8ee54d3780c0590a7d84c7779ed4c4f Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:10:46 +0800 Subject: [PATCH 04/10] Update README.md --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 711e5cedf..ffc5dae13 100644 --- a/README.md +++ b/README.md @@ -17,13 +17,13 @@ * 8) 预测数值型数据：回归 * 9) 数回归 -### 第三部分 无监督学习 +## 第三部分 无监督学习 * 10) 使用K-均值聚类算法对未标注数据分组 * 11) 使用Apriori算法进行关联分析 * 12) 使用FP-growth算法来高效发现频繁项集 -### 第四部分 其他工具 +## 第四部分 其他工具 * 13) 使用PCA来简化数据 * 14) 使用SVD简化数据 @@ -36,4 +36,4 @@ * 附录C 概率论复习 * 附录D 资源 * 索引 -* 版权声明 \ No newline at end of file +* 版权声明 From 73bb7076d6c8958aeb6a5914053fce8ba95cca00 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:20:44 +0800 Subject: [PATCH 05/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E7=89=88=E6=9C=AC?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 4de2019f8..c530c70e1 100644 --- a/README.md +++ b/README.md @@ -39,13 +39,13 @@ * 8) 预测数值型数据：回归 * 9) 数回归 -### 第三部分 无监督学习 +## 第三部分 无监督学习 * 10) 使用K-均值聚类算法对未标注数据分组 * 11) 使用Apriori算法进行关联分析 * 12) 使用FP-growth算法来高效发现频繁项集 -### 第四部分 其他工具 +## 第四部分 其他工具 * 13) 使用PCA来简化数据 * 14) 使用SVD简化数据 From 315df1fef6519f10aa325b2a4bc306dd97605833 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:28:48 +0800 Subject: [PATCH 06/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index c530c70e1..60de4d2b9 100644 --- a/README.md +++ b/README.md @@ -58,4 +58,4 @@ * 附录C 概率论复习 * 附录D 资源 * 索引 -* 版权声明 \ No newline at end of file +* 版权声明 From 59940b7532ad180fdc07239bafed30b371f09a94 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:39:49 +0800 Subject: [PATCH 07/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0docs?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 22 ---------------------- docs/README.md | 28 +++++++++++++++++++++++++--- 2 files changed, 25 insertions(+), 25 deletions(-) diff --git a/README.md b/README.md index 60de4d2b9..ffc5dae13 100644 --- a/README.md +++ b/README.md @@ -5,28 +5,6 @@ ## 第一部分 分类 * 1) 机器学习基础 - * 机器学习是什么 - * 把无序的数据转换成有用的信息。 - * 机器学习的意义 - * 我们利用计算机来彰显数据背后的真实含义。 - * 监督学习 - * 样本集：训练数据 + 测试数据 - * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值/回归-连续值<0~100、 -999～999>) - * `知识表示`：机器已经学会如何识别鸟类的过程 - * 1.可以采用规则集的形式 - * 2.可以采用概率分布的形式 - * 3.可以使训练样本集中的一个实例 - * 非监督学习 - * 开发的步骤 - * 1.收集数据 - * 2.准备输入数据 - * 3.分析输入数据 - * 4.训练算法 - * 5.测试算法 - * 6.使用算法 - * Python相关的库 - * 科学函数库：SciPy、`NumPy`(底层语言：C和Fortran) - * 绘图工具库：`Matplotlib` * 2) k-紧邻算法 * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 diff --git a/docs/README.md b/docs/README.md index 711e5cedf..60de4d2b9 100644 --- a/docs/README.md +++ b/docs/README.md @@ -5,6 +5,28 @@ ## 第一部分 分类 * 1) 机器学习基础 + * 机器学习是什么 + * 把无序的数据转换成有用的信息。 + * 机器学习的意义 + * 我们利用计算机来彰显数据背后的真实含义。 + * 监督学习 + * 样本集：训练数据 + 测试数据 + * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值/回归-连续值<0~100、 -999～999>) + * `知识表示`：机器已经学会如何识别鸟类的过程 + * 1.可以采用规则集的形式 + * 2.可以采用概率分布的形式 + * 3.可以使训练样本集中的一个实例 + * 非监督学习 + * 开发的步骤 + * 1.收集数据 + * 2.准备输入数据 + * 3.分析输入数据 + * 4.训练算法 + * 5.测试算法 + * 6.使用算法 + * Python相关的库 + * 科学函数库：SciPy、`NumPy`(底层语言：C和Fortran) + * 绘图工具库：`Matplotlib` * 2) k-紧邻算法 * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 @@ -17,13 +39,13 @@ * 8) 预测数值型数据：回归 * 9) 数回归 -### 第三部分 无监督学习 +## 第三部分 无监督学习 * 10) 使用K-均值聚类算法对未标注数据分组 * 11) 使用Apriori算法进行关联分析 * 12) 使用FP-growth算法来高效发现频繁项集 -### 第四部分 其他工具 +## 第四部分 其他工具 * 13) 使用PCA来简化数据 * 14) 使用SVD简化数据 @@ -36,4 +58,4 @@ * 附录C 概率论复习 * 附录D 资源 * 索引 -* 版权声明 \ No newline at end of file +* 版权声明 From 3d9905cafaabf575d7f2ea4afdd2b63ad4fe42f8 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:50:02 +0800 Subject: [PATCH 08/10] =?UTF-8?q?=E7=BC=96=E5=86=99=E6=96=87=E6=A1=A3?= =?UTF-8?q?=E8=A7=84=E8=8C=83demo?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 1 + ...46\344\271\240\345\237\272\347\241\200.md" | 25 ++++++++ docs/README.md | 61 ------------------- 3 files changed, 26 insertions(+), 61 deletions(-) create mode 100644 "docs/1.\346\234\272\345\231\250\345\255\246\344\271\240\345\237\272\347\241\200.md" delete mode 100644 docs/README.md diff --git a/README.md b/README.md index ffc5dae13..1de515299 100644 --- a/README.md +++ b/README.md @@ -5,6 +5,7 @@ ## 第一部分 分类 * 1) 机器学习基础 + * [1.机器学习基础](./docs/1.机器学习基础.md) * 2) k-紧邻算法 * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 diff --git "a/docs/1.\346\234\272\345\231\250\345\255\246\344\271\240\345\237\272\347\241\200.md" "b/docs/1.\346\234\272\345\231\250\345\255\246\344\271\240\345\237\272\347\241\200.md" new file mode 100644 index 000000000..b7ca10063 --- /dev/null +++ "b/docs/1.\346\234\272\345\231\250\345\255\246\344\271\240\345\237\272\347\241\200.md" @@ -0,0 +1,25 @@ + +# 1) 机器学习基础 + +* 机器学习是什么 + * 把无序的数据转换成有用的信息。 +* 机器学习的意义 + * 我们利用计算机来彰显数据背后的真实含义。 +* 监督学习 + * 样本集：训练数据 + 测试数据 + * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值/回归-连续值<0~100、 -999～999>) + * `知识表示`：机器已经学会如何识别鸟类的过程 + * 1.可以采用规则集的形式 + * 2.可以采用概率分布的形式 + * 3.可以使训练样本集中的一个实例 +* 非监督学习 +* 开发的步骤 + * 1.收集数据 + * 2.准备输入数据 + * 3.分析输入数据 + * 4.训练算法 + * 5.测试算法 + * 6.使用算法 +* Python相关的库 + * 科学函数库：SciPy、`NumPy`(底层语言：C和Fortran) + * 绘图工具库：`Matplotlib` \ No newline at end of file diff --git a/docs/README.md b/docs/README.md deleted file mode 100644 index 60de4d2b9..000000000 --- a/docs/README.md +++ /dev/null @@ -1,61 +0,0 @@ -# MachineLearning - -**Mahchine Leaning in Action (python)** - -## 第一部分 分类 - -* 1) 机器学习基础 - * 机器学习是什么 - * 把无序的数据转换成有用的信息。 - * 机器学习的意义 - * 我们利用计算机来彰显数据背后的真实含义。 - * 监督学习 - * 样本集：训练数据 + 测试数据 - * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值/回归-连续值<0~100、 -999～999>) - * `知识表示`：机器已经学会如何识别鸟类的过程 - * 1.可以采用规则集的形式 - * 2.可以采用概率分布的形式 - * 3.可以使训练样本集中的一个实例 - * 非监督学习 - * 开发的步骤 - * 1.收集数据 - * 2.准备输入数据 - * 3.分析输入数据 - * 4.训练算法 - * 5.测试算法 - * 6.使用算法 - * Python相关的库 - * 科学函数库：SciPy、`NumPy`(底层语言：C和Fortran) - * 绘图工具库：`Matplotlib` -* 2) k-紧邻算法 -* 3) 决策树 -* 4) 基于概率论的分类方法：朴素贝叶斯 -* 5) Logistic回归 -* 6) 支持向量机 -* 7) 利用AdaBoost元算法提高分类 - -## 第二部分 利用回归预测数值型数据 - -* 8) 预测数值型数据：回归 -* 9) 数回归 - -## 第三部分 无监督学习 - -* 10) 使用K-均值聚类算法对未标注数据分组 -* 11) 使用Apriori算法进行关联分析 -* 12) 使用FP-growth算法来高效发现频繁项集 - -## 第四部分 其他工具 - -* 13) 使用PCA来简化数据 -* 14) 使用SVD简化数据 -* 15) 大数据与MapReduce - -* * * - -* 附录A Python入门 -* 附录B 线性代数 -* 附录C 概率论复习 -* 附录D 资源 -* 索引 -* 版权声明 From 9ab1f9af91983ee650cc7e4b230c2476921bce60 Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Sun, 26 Feb 2017 01:52:26 +0800 Subject: [PATCH 09/10] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E6=A0=BC=E5=BC=8F?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 1de515299..c11aceb21 100644 --- a/README.md +++ b/README.md @@ -5,7 +5,7 @@ ## 第一部分 分类 * 1) 机器学习基础 - * [1.机器学习基础](./docs/1.机器学习基础.md) + * [机器学习基础](./docs/1.机器学习基础.md) * 2) k-紧邻算法 * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 From 91955840b1187cc2a00ffd5592dcd7b5a3ef0b19 Mon Sep 17 00:00:00 2001 From: sheepmen Date: Sun, 26 Feb 2017 11:59:08 +0800 Subject: [PATCH 10/10] DEV: ADD CHATPER-2 NOTE --- .gitignore | 1 + .vscode/settings.json | 3 --- .vscode/tasks.json | 9 -------- README.md | 3 ++- ...21\351\202\273\347\256\227\346\263\225.md" | 21 +++++++++++++++++++ 5 files changed, 24 insertions(+), 13 deletions(-) delete mode 100644 .vscode/settings.json delete mode 100644 .vscode/tasks.json create mode 100644 "docs/2.k-\350\277\221\351\202\273\347\256\227\346\263\225.md" diff --git a/.gitignore b/.gitignore index 72364f99f..6564ff4af 100644 --- a/.gitignore +++ b/.gitignore @@ -87,3 +87,4 @@ ENV/ # Rope project settings .ropeproject +.vscode diff --git a/.vscode/settings.json b/.vscode/settings.json deleted file mode 100644 index fe7159848..000000000 --- a/.vscode/settings.json +++ /dev/null @@ -1,3 +0,0 @@ -{ - "python.linting.pylintEnabled": false -} \ No newline at end of file diff --git a/.vscode/tasks.json b/.vscode/tasks.json deleted file mode 100644 index 66d0b4ec2..000000000 --- a/.vscode/tasks.json +++ /dev/null @@ -1,9 +0,0 @@ -{ - // See https://go.microsoft.com/fwlink/?LinkId=733558 - // for the documentation about the tasks.json format - "version": "0.1.0", - "command": "/usr/bin/python", - "isShellCommand": true, - "args": ["${file}"], - "showOutput": "always" -} diff --git a/README.md b/README.md index c11aceb21..c75441596 100644 --- a/README.md +++ b/README.md @@ -6,7 +6,8 @@ * 1) 机器学习基础 * [机器学习基础](./docs/1.机器学习基础.md) -* 2) k-紧邻算法 +* 2) k-近邻算法 + * [k-近邻算法](./docs/2.k-近邻算法.md) * 3) 决策树 * 4) 基于概率论的分类方法：朴素贝叶斯 * 5) Logistic回归 diff --git "a/docs/2.k-\350\277\221\351\202\273\347\256\227\346\263\225.md" "b/docs/2.k-\350\277\221\351\202\273\347\256\227\346\263\225.md" new file mode 100644 index 000000000..87640c0d4 --- /dev/null +++ "b/docs/2.k-\350\277\221\351\202\273\347\256\227\346\263\225.md" @@ -0,0 +1,21 @@ + +# 2) k-近邻算法 + +* k-近邻算法的特点 + * 优点：精度高、对异常值不敏感、无数据输入假定 + * 缺点：计算复杂度高、空间复杂度高 + * 适用数据范围：数值型和标称型 +* 工作原理 + * 已知样本数据集的每一个数据的特征和所属分类，将新数据的特征与样本数据进行比较，找到最相似(最近邻)的k(通常k <= 20)个数据。选择k个数据中出现次数最多的分类，作为新数据的分类。 +* k-近邻算法的一般流程 + * 收集数据：任何方法 + * 准备数据：距离计算所需要的数值，最好是结构化的数据格式 + * 分析数据：任何方法 + * 测试数据：计算错误率 + * 使用算法：输入样本数据和结构化的输出结果，然后运行k-近邻算法判断输入数据分类属于哪个分类，最后对计算出的分类执行后续处理 +* 总结 + * k-近邻算法其实就是根据空间两个向量距离来判断类别性，关键的是引入k值，保证了一定的稳定性，很明显的缺点就是每次都要与所有样本数据进行对比。 + * 文中处理约会数据时，归一化的方法是对于消除影响很十分重要的 + * 阅读本章之前建议阅读一下numpy的文档 + * [numpy英文文档](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html) + * [numpy中文文档](http://old.sebug.net/paper/books/scipydoc/numpy_intro.html)