MLiA笔记_Logistic回归

#-*-coding:utf-8-*-
from numpy import *

# 5.1 logistic回归梯度上升优化算法

# 便利函数loadDataSet()，打开文本文件并逐行读取。每行前两值分别是X1和X2，第三个值是数据对应的类别标签。
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))

# gradAscent()函数有两个参数，第一个是dataMathIn，是一个2维NumPy数组（每列代表每个不同的特征，每行则代表每个训练样本。）
# 我们使用的是100ge样本的简单数据集，加上第0维特征，是一个100*3的矩阵
def gradAscent(dataMatIn, classLabels):
    # 获得输入数据，并转换为NumPy矩阵数据类型
    dataMatrix = mat(dataMatIn)
    # 第二个参数是类别标签，它是一个1*00的行向量。为了便于矩阵运算，转置为列向量，再将其赋值给labelMat
    labelMat = mat(classLabels).transpose()
    # 得到矩阵大小
    m,n = shape(dataMatrix)
    # 设置梯度上升算法所需的参数
    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) # h是一个列向量，元素个数等于样本个数
        error = (labelMat - h)
        weights = weights+alpha*dataMatrix.transpose()*error # 矩阵相乘
    return weights

# 5.2 画出数据集和Logistic回归最佳拟合直线的函数
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] #最佳拟合直线
    ax.plot(x,y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()


# 5.3 随机梯度上升算法
# stocGradAscent0()的变量h和误差error都是向量，而不是数值
def stocGradAscent0(dataMatrix, classLabels):
    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

# 5.4 改进的随机梯度上升算法
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m,n = shape(dataMatrix)
    weights = ones(n)
    for j in range(numIter):
        dataIndex = range(m)
        for i in range(m):
            # alpha每次迭代时需要调整。虽然alpha会随着迭代次数不断减小，但永远不会减小到0.（存在一个常数项）
            alpha = 4/(1.0+j+i)+0.01 # j是迭代次数，i是样本点的下标
            # 随机选取更新
            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



# 5.5 Logistic回归分类函数
# classifyVector()函数以回归系数和特征向量作为输入来计算对应的sigmoid值。如果sigmoid值大于0.5，函数返回1，否则返回0
def classifyVector(inX, weights):
    prob = sigmoid(sum(inX*weights))
    if prob>0.5: return 1.0
    else: return 0.0

# colicTest()函数，用于打开测试集和村练级，并对数据进行格式化处理道德函数。
def 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]))
    # 数据导入后便可使用stocGradAscent1()函数来计算回归系数向量。可自由设置迭代的次数，例如在训练集上使用500次迭代，结果表明比默认150要好。
    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 500)
    errorCount = 0; numTestVec = 0.0
    # 导入测试集并计算分类错误率
    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

# 最后一个函数是miltiTest()函数，其功能是调用函数coliTest()10次并求结果的平均值。
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))