机器学习——Python实现逻辑回归（实例：预测病马死亡率）

每个回归系数初始化为1
重复R次：
    计算整个数据集的梯度
    适用alpha x gradient 更新回归系数的向量
返回回归系数

import numpy as np

def loadDataSet():
    '''
    加载数据集
    '''
    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):
    '''
    S函数
    '''
    return 1.0 / (1 + np.exp(-inX))

def gradAscent(dataMatIn, classLabels):
    '''
    梯度上升算法
    param dataMatIn: 特征值
    param classLabels: 标签
    '''
    # 特征值矩阵
    dataMatix = np.mat(dataMatIn)

    # 标签矩阵；行向量转置为列向量
    labelMat = np.mat(classLabels).transpose()
    # 获取特征值矩阵大小
    m, n = np.shape(dataMatix)
    # 移动步长
    alpha = 0.001
    # 迭代次数
    maxCycles = 500
    # 回归系数初始化为1
    weights = np.ones((n, 1))

    for k in range(maxCycles):
        h = sigmoid(dataMatix * weights)
        error = (labelMat - h)
        weights = weights + alpha * dataMatix.transpose() * error

    return weights

dataArr, labelMat = loadDataSet()
weights = gradAscent(dataArr, labelMat)
weights
[out]
matrix([[ 4.12414349],
        [ 0.48007329],
        [-0.6168482 ]])

def plotBestFit(weights):
    '''
    画出数据集和逻辑回归最佳拟合直线
    '''
    import matplotlib.pyplot as plt
    dataMat, labelMat = loadDataSet()
    dataArr = np.array(dataMat)
    n = np.shape(dataMat)[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 = np.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()

plotBestFit(weights.getA())

所有回归系数初始化为1
对数据集中每个样本
    计算该样本的梯度
    适用 alpha x gradient 更新回归系数值
返回回归系数值

def stocGradAscent0(dataMatrix, classLabels):
    '''
    随机梯度上升算法
    '''
    m, n = np.shape(dataMatrix)
    alpha = 0.01
    weights = np.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

dataArr, labelMat = loadDataSet()
weights = stocGradAscent0(np.array(dataArr), labelMat)
plotBestFit(weights)

def classifyVector(inX, weights):
    '''
    逻辑回归分类函数
    parameter inX: 特征向量
    parameter weights: 回归系数
    '''
    prob = sigmoid(sum(inX*weights))
    if prob > 0.5:
        return 1.0
    else:
        return 0.0

def colicTest():
    '''
    打开测试集和训练集，并对数据进行格式化处理
    '''
    frTrain = open('horseColicTraining.txt')
    frTest = open('horseColicTest.txt')
    trainingSet = []
    trainingLabels = []

    # 格式化训练集
    for line in frTrain.readlines():
        currLine = line.strip().split('\t')
        lineArr = []

        # 导入特征值，有21个特征
        for i in range(21):
            lineArr.append(float(currLine[i]))

        trainingSet.append(lineArr)
        # 导入类别标签，类别标签为最后一项
        trainingLabels.append(float(currLine[21]))

    # 使用随机梯度上升算法计算回归系数向量
    trainWeights = stocGradAscent1(np.array(trainingSet), trainingLabels, 500)
    errorCount = 0
    numTestVec = 0.0

    # 格式化测试集
    for line in frTest.readlines():
        numTestVec += 1.0
        currLine = line.strip().split('\t')
        lineArr = []

        # 导入特征值
        for i in range(21):
            lineArr.append(float(currLine[i]))

        # 使用训练集计算出的回归系数对测试集进行分类，并比对测试集的类别标签，计算错误数量
        if int(classifyVector(np.array(lineArr), trainWeights)) != int(currLine[21]):
            errorCount += 1

    # 错误率
    errorRate = (float(errorCount)/numTestVec)
    print 'the error rate of this test is: %f' % errorRate

    return errorRate

def multiTest():
    '''
    调用colicTest函数10次，取错误率平均值
    '''
    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))

multiTest()
[out]
the error rate of this test is: 0.328358
the error rate of this test is: 0.358209
the error rate of this test is: 0.283582
the error rate of this test is: 0.313433
the error rate of this test is: 0.373134
the error rate of this test is: 0.373134
the error rate of this test is: 0.358209
the error rate of this test is: 0.343284
the error rate of this test is: 0.432836
the error rate of this test is: 0.388060
after 10 iterations the average error rate is: 0.355224