Logistic.py

#!/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()