机器学习实战笔记---Logistic回归

本文转自https://blog.csdn.net/u010454729/article/details/48274955和http://cuijiahua.com/blog/2017/11/ml_6_logistic_1.html

实现Logistic回归分类器：在每个特征上都乘以一个回归系数，然后把所有的结果值相加，总和带入Sigmoid函数，其结果大于0.5分为正样本类，结果小于0.5分为负样本类。

sigmoid函数：

Sigmoid的输入z：

其可以写成z=wT*x，向量x为分类器的输入数据， w为训练器寻找的最佳参数。

参数迭代公式：

使用梯度上升找到最佳参数w：

伪代码：

 

假设Sigmoid的输入为z，求得的最佳回归系数（最优参数）为 ，那么：

即可将数据分割开

令z=0，则    （ ）

这样就求出来决策边界。

import numpy as np
import matplotlib.pyplot as plt

#加载函数
def loadDataSet():
    dataMat=[]
    labelMat=[]
    fr=open("D:/anicode/spyderworkspace/examtest/testSet.txt")
    for line in fr.readlines():
        lineArr=line.strip().split()
        dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
        labelMat.append(int(lineArr[2]))
    fr.close()
    return dataMat,labelMat

#可视化
def plotBestFit(weights):
    dataMat,labelMat=loadDataSet()
    dataArr=np.array(dataMat)
    n=np.shape(dataMat)[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=20,c='red',marker='s',alpha=.5)
    ax.scatter(xcord2,ycord2,s=20,c='green',alpha=.5)
    x=np.arange(-3.0,3.0,0.1)
    y=(-weights[0]-weights[1]*x)/weights[2]#令z=0，则x_2=(-w_0-w_1 *x_1)/w_2 
    ax.plot(x,y)
    plt.title('BestFit')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.show()

def sigmoid(inX):
    return 1.0/(1+np.exp(-inX))

#梯度上升函数
def gradAscent(dataMatIn,classLabels):
    dataMatrix=np.mat(dataMatIn)
    labelMat=np.mat(classLabels).transpose()
    m,n=np.shape(dataMatrix)
    alpha=0.001
    maxCycles=500
    weights=np.ones((n,1))
    for k in range(maxCycles):
        h=sigmoid(dataMatrix*weights)
        error=labelMat-h
        weights=weights+alpha*dataMatrix.transpose()*error
    return weights.getA()

if __name__=='__main__':
    dataMat,labelMat=loadDataSet()
    weights=gradAscent(dataMat,labelMat)
    plotBestFit(weights)

 改进

#随机梯度上升函数
def stocGradAscent(dataMatrix,classLabels,numIter=150):
    m,n=np.shape(dataMatrix)
    weights=np.ones(n)
    for j in range(numIter):
        dataIndex=list(range(m))
        for i in range(m):
            alpha=4/(1.0+j+i)+0.01
            randIndex=int(random.uniform(0,len(dataIndex)))
            h=sigmoid(sum(dataMatrix[randIndex]*weights))
            error=classLabels[randIndex]-h
            weights=weights+alpha*error*dataMatrix[randIndex]
            del(dataIndex[randIndex])
    return weights

if __name__=='__main__':
    dataMat,labelMat=loadDataSet()
    weights=stocGradAscent(np.array(dataMat),labelMat)
    plotBestFit(weights)
            

 预测病马死亡率

import numpy as np
import random

def sigmoid(inX):
    return 1.0/(1+np.exp(-inX))

def stocGradAscent(dataMatrix,classLabels,numIter=150):
    m,n=np.shape(dataMatrix)
    weights=np.ones(n)
    for j in range(numIter):
        dataIndex=list(range(m))
        for i in range(m):
            alpha=4/(1.0+j+i)+0.01
            randIndex=int(random.uniform(0,len(dataIndex)))
            h=sigmoid(sum(dataMatrix[randIndex]*weights))
            error=classLabels[randIndex]-h
            weights=weights+alpha*dataMatrix[randIndex]*error
            del(dataIndex[randIndex])
    return weights

def colicTest():
    frTrain=open("D:/anicode/spyderworkspace/examtest/horseColicTraining.txt")
    frTest=open("D:/anicode/spyderworkspace/examtest/horseColicTest.txt")
    trainingSet=[]
    trainingLabels=[]
    for line in frTrain.readlines():
        currLine=line.strip().split('\t')
        lineArr=[]
        for i in range(len(currLine)-1):
            lineArr.append(float(currLine[i]))
        trainingSet.append(lineArr)
        trainingLabels.append(float(currLine[-1]))
    trainWeights=stocGradAscent(np.array(trainingSet),trainingLabels,500)
    errorCount=0
    numTestVec=0.0
    for line in frTest.readlines():
        numTestVec+=1.0
        currLine=line.strip().split('\t')
        lineArr=[]
        for i in range(len(currLine)-1):
            lineArr.append(float(currLine[i]))
        if int(classifyVector(np.array(lineArr),trainWeights))!=int(currLine[-1]):
            errorCount+=1
    errorRate=(float(errorCount)/numTestVec)*100
    print("测试集错误率：%.2f%%"% errorRate)
        
def classifyVector(inX,weights):
    prob=sigmoid(sum(inX*weights))
    if prob>0.5:
        return 1.0
    else:  
        return 0.0

if __name__=='__main__':
    colicTest()