[机器学习]Logistic回归梯度上升法与改进的随机梯度上升算法

http://sbp810050504.blog.51cto.com/2799422/1608064/这个网址解释了多维空间的sigmoid函数与梯度上升算法的原理，大家可以参考一下。

from numpy import *def loadDataSet():#读数据    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(intX):#sigmoid函数    return 1.0 / (1 + exp(-intX))def gradAscent(dataMatIn, classLabels):#Logistic回归梯度上升优化算法    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 = weights + alpha * dataMatrix.transpose() * error    return weightsdef stocGradAscent0(dataMatrix,classLabels):#随机梯度上升算法    m,n =shape(dataMatrix)    alpha = 0.01    weights =ones(n)    for i in range(m):        h = sigmoid(dataMatrix[i]*weights)        error = classLabels[i] - h        weights = weights + alpha*error*dataMatrix[i]    return weightsdef stocGradAscent1(dataMatrix,classLabels,numIter=150):#改进的随机梯度上升算法    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 weightsdef plotBestFit(weights):#数据可视化    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='blue', marker='s')    ax.scatter(xcord2, ycord2, s=30, c='red')    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 main():    dataArr,labelMat = loadDataSet()    weights1 = gradAscent(dataArr,labelMat)    print(weights1)    plotBestFit(weights1.getA())    dataArr, labelMat = loadDataSet()    weights2 = stocGradAscent0(array(dataArr),labelMat)    print(weights2)    plotBestFit(weights2)        dataArr, labelMat = loadDataSet()    weight3 = stocGradAscent1(array(dataArr),labelMat)    print(weight3)    plotBestFit(weight3)if __name__ == '__main__':    main()

结果：

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