Logistic 回归梯度上升优化函数

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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

 

 

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def sigmoid(inX):

    return 1.0/(1+exp(-inX))

 

 

 

批量梯度下降

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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) #   h是一个矩阵

        error = (labelMat - h)

        weights = weights + alpha * dataMatrix.transpose() * error

    return weights 

 

 

 

随机梯度下降

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def stocGradAscent0(dataMatrix, classLabels):

    m,n = shape(dataMatrix)

    alpha = 0.01

    weights = ones(n)

    #weights = [0.1,0.1,0.1]

    for i in range(m):

        h = sigmoid(sum(dataMatrix[i]*weights))#  h是一个数值

        print dataMatrix[i]

        print weights

        print dataMatrix[i]*weights

        error = classLabels[i] - h

        weights = weights + alpha * error * dataMatrix[i]

    return weights

 

 

 

sum()的参数是一个list 下面是改进的随机梯度上升算法：

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def stocGradAscent1(dataMatrix, classLabels, numIter=150):

    m,n = shape(dataMatrix)

    weights = ones(n)

    #weights = [0.1,0.1,0.1]

    for j in range(numIter):

        dataIndex = 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))#  h是一个数值

            error = classLabels[randIndex] - h

            weights = weights + alpha * error * dataMatrix[randIndex]

            del(dataIndex[randIndex])

    return weights

 

 

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#import logRegres

 

 

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dataArr,labelMat = loadDataSet()

 

 

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#weights=gradAscent(dataArr,labelMat)

weights=stocGradAscent1(array(dataArr),labelMat,500)

 

 

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def plotBestFit(wei):

    import matplotlib.pyplot as plt

    weights = wei

    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()

 

 

 

h = subplot(m,n,p)/subplot(mnp) 将figure划分为m×n块，在第p块创建坐标系，并返回它的句柄。当m,n,p<10时，可以简化为subplot(mnp)或者subplot mnp （注：subplot（m,n,p）或者subplot（mnp）此函数最常用：subplot是将多个图画到一个平面上的工具。其中，m表示是图排成m行，n表示图排成n列，也就是整个figure中有n个图是排成一行的，一共m行，如果第一个数字是2就是表示2行图。p是指你现在要把曲线画到figure中哪个图上，最后一个如果是1表示是从左到右第一个位置。 ）

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from numpy import *

#reload

print weights

plotBestFit(weights)