使用Python实现Logistic回归,代码思路来源于机器学习实战,改正了原代码中的一些在Python3.5上运行存在的bug。对随机梯度上升法进行了简单的修改。

from math import exp
from numpy import *

def loadDataSet():
    dataMat = []; labelMat = []
    fr = open('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]))
    return dataMat, labelMat

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

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

def stocGradAscent0(dataMatrix, classLabels):
    m, n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i]*weights))
        error = classLabels[i] - h
        weights = weights + alpha * error * dataMatrix[i]
    return weights

def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m, n = shape(dataMatrix)
    weights = ones(n)
    for i in range(numIter):
        dataIndex = len(list(range(m)))
        for j in range(m):
            alpha = 4/(1.0+i+j)+0.01
            randIndex = int(random.uniform(0, dataIndex))
            h = sigmoid(sum(dataMatrix[randIndex]*weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            dataIndex -= 1
    return weights

def plotBestFit(weights):
    import matplotlib.pyplot as plt
    dataMat,labelMat=loadDataSet()
    dataArr = array(dataMat)
    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')
    if weights is not None:
        x = arange(-3.0, 3.0, 0.1)
        y = (-weights[0]-weights[1]*x)/weights[2]   #令w0*x0 + w1*x1 + w2*x2 = 0,其中x0=1,解出x1和x2的关系
        ax.plot(x, y)                               #一个作为X一个作为Y,画出直线
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()

def classifyVector(inX, weights):
    prob = sigmoid(sum(inX*weights))
    if prob > 0.5: return 1.0
    else: return 0.0

def colicTest():
    frTrain = open('horseColicTraining.txt')
    frTest = open('horseColicTest.txt')
    trainingSet = []; trainingLabels = []
    for line in frTrain.readlines():
        currLine = line.strip().split('\t')
        lineArr = []
        for i in range(21):
            lineArr.append(float(currLine[i]))
        trainingSet.append(lineArr)
        trainingLabels.append(float(currLine[21]))
    trainWeights = stocGradAscent1(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(21):
            lineArr.append(float(currLine[i]))
        if int(classifyVector(array(lineArr), trainWeights)) != int(currLine[21]):
            errorCount += 1
    errorRate = float(errorCount)/numTestVec
    print("the error rate of this test is: %f" % errorRate)
    return errorRate

def multiTest():
    numTests = 10; errorSum = 0.0
    for k in range(numTests):
        errorSum += colicTest()
    print("after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests)))

dataArr, labelMat = loadDataSet()
weights = stocGradAscent1(array(dataArr), labelMat)
multiTest()