第5章 Logistic回归

越来越体会到了数学的重要性，最近在不断的学习丢掉的数学知识。。

这篇写的很好 优快云-logistic回归    把公式的推导过程都展示出来了（略有瑕疵，在公式13及相关的求导过程中，少了个负号）

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 1.0/(1+exp(-inX))
    
def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)
    labelMat = mat(classLabels).transpose() #向量转置，将行向量转换为列向量
    m,n = shape(dataMatrix) #矩阵大小，几行几列
    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):  
        h = sigmoid(dataMatrix*weights) #定性的说，下面这几行的作用是：计算真实类别和预测类别的差值，按照差值的方向调整回归系数  （这里省去了一个简单的数学推导）
        error = (labelMat-h)
        weights = weights + alpha*dataMatrix.transpose()*error
    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')
    x= arange(-3.0, 3.0, 0.1)
    y=(-weights[0]-weights[1]*x)/weights[2] #这里设置了sigmoid函数为0.   没有懂。。。
    ax.plot(x,y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()
    
def stocGradAscent0(dataMatrix, classLabels): #随机梯度上升法
    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): #改进的随机梯度上升法
    m,n = shape(dataMatrix)
    weights = 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
    
def classifyVector(inX, weights):  #(我的理解来区分) inX 是 特征向量，代表那些x1,x2,x3...等等的；  weights是回归系数
    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')  #\t水平制表符，相当于按下TAB键
        lineArr=[]
        for i in range(21): # there are 21 features in total
            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)))