机器学习实战-逻辑回归

逻辑回归：1.非线性函数sigmoid最佳拟合参数     1/(1+e（-z）)

                    2.梯度上升、梯度下降、随机梯度上升、改进的逻辑梯度上升

#encoding:utf-8
from numpy import *
import math
#数据下载与处理~打开文本，逐行读取，前两行对应值x1,x2，第三行对应类别标签。并且将x0都设为1.0
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])])#将x0设为1.0
        labelMat.append(int(lineArr[2]))
    return dataMat,labelMat
#sigmoid函数-阶跃函数-将值代入此函数，得到0~1之间的数值
def sigmoid(inX):
    return 1.0/(1+math.exp(-inX))
#梯度上升算法~
#输入：dataMatIn~2维数组~每列分别表示不同的特征（x0,x1,x2）~每行表示每个训练样本
def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)             #转换为numpy矩阵类型
    labelMat = mat(classLabels).transpose() #转换为numpy矩阵类型
    m,n = shape(dataMatrix)
    alpha = 0.001#向目标移动的步长
    maxCycles = 500#迭代次数
    weights = ones((n,1))
    for k in range(maxCycles):              #heavy on matrix operations
        h = sigmoid(dataMatrix*weights)     #matrix mult
        error = (labelMat - h)              #计算真实类别与预测类别的差值，接下来按照差值方向来调整回归系数
        weights = weights + alpha * dataMatrix.transpose()* error #回归系数计算
    return weights#返回训练好的回归系数
#画出决策边界
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')
    x = arange(-3.0, 3.0, 0.1)
    y = (-weights[0]-weights[1]*x)/weights[2]#最佳拟合直线
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()
#随机梯度上升~~在梯度上升上略加修改
def stocGradAscent0(dataMatrix, classLabels):
    m,n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)   #初始化为1
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i]*weights))
        error = classLabels[i] - h#h和error都是向量
        weights = weights + alpha * error * dataMatrix[i]
    return weights
#改进的随机梯度上升
def stocGradAscent1(dataMatrix, classLabels, numIter=150):#默认迭代次数50次
    m,n = shape(dataMatrix)
    weights = ones(n)   #initialize to all ones
    for j in range(numIter):
        dataIndex = range(m)
        for i in range(m):
            alpha = 4/(1.0+j+i)+0.0001    #每次迭代都调整alpha值
            randIndex = int(random.uniform(0,len(dataIndex)))#随机选取样本更新回归系数
            h = sigmoid(sum(dataMatrix[randIndex]*weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del(dataIndex[randIndex])
    return weights

#病马预测
#逻辑回归分类函数
#输入：特征向量、回归系数    返回：1,0
def classifyVector(inX, weights):
    prob = sigmoid(sum(inX*weights))
    if prob > 0.5: return 1.0
    else: return 0.0
#打开测试集、训练集，进行格式化预处理
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, 1000)
    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]):#分类结果与测试集比较
            errorCount += 1
    errorRate = (float(errorCount)/numTestVec)
    print "the error rate of this test is: %f" % errorRate
    return errorRate
#调用colictTest() 10次~并求结果平均值
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))