Logistic 迴歸__Logistic

  迴歸: 假設現在有一些資料點，我們用一條直線對這些點進行擬合(該線稱為最佳擬合直線)，這個擬合過程就稱作 迴歸。

       Logistic 迴歸的目的 是尋找一個非線性函數Sigmoid的最佳擬合參數，求解過程可以由最佳化演算法來完成。

具體的實現代碼如下：

'''Logistic Regression Working Module'''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,labelMatdef sigmoid(inX):    return 1.0/(1+exp(-inX))def gradAscent(dataMatIn, classLabels):    dataMatrix = mat(dataMatIn)             #convert to NumPy matrix    labelMat = mat(classLabels).transpose() #convert to NumPy matrix    m,n = shape(dataMatrix)    alpha = 0.001    maxCycles = 500    weights = ones((n,1))    for k in range(maxCycles):              #heavy on matrix operations        h = sigmoid(dataMatrix*weights)     #matrix mult        error = (labelMat - h)              #vector subtraction        weights = weights + alpha * dataMatrix.transpose()* error #matrix mult    return weightsdef 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]    ax.plot(x, y)    plt.xlabel('X1'); plt.ylabel('X2');    plt.show()def stocGradAscent0(dataMatrix, classLabels):    m,n = shape(dataMatrix)    alpha = 0.01    weights = ones(n)   #initialize to all ones    for i in range(m):        h = sigmoid(sum(dataMatrix[i]*weights))        error = classLabels[i] - h        weights = weights + alpha * error * dataMatrix[i]    return weightsdef stocGradAscent1(dataMatrix, classLabels, numIter=150):    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    #apha decreases with iteration, does not             randIndex = int(random.uniform(0,len(dataIndex)))#go to 0 because of the constant            h = sigmoid(sum(dataMatrix[randIndex]*weights))            error = classLabels[randIndex] - h            weights = weights + alpha * error * dataMatrix[randIndex]            del(dataIndex[randIndex])    return weightsdef classifyVector(inX, weights):    prob = sigmoid(sum(inX*weights))    if prob > 0.5: return 1.0    else: return 0.0def 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]):            errorCount += 1    errorRate = (float(errorCount)/numTestVec)    print "the error rate of this test is: %f" % errorRate    return errorRatedef 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))