逻辑回归 算法 实例

horseColicTraining.txt

2.000000 1.000000 38.500000 66.000000 28.000000 3.000000 3.000000 0.000000 2.000000 5.000000 4.000000 4.000000 0.000000 0.000000 0.000000 3.000000 5.000000 45.000000 8.400000 0.000000 0.000000 0.000000
1.000000 1.000000 39.200000 88.000000 20.000000 0.000000 0.000000 4.000000 1.000000 3.000000 4.000000 2.000000 0.000000 0.000000 0.000000 4.000000 2.000000 50.000000 85.000000 2.000000 2.000000 0.000000
2.000000 1.000000 38.300000 40.000000 24.000000 1.000000 1.000000 3.000000 1.000000 3.000000 3.000000 1.000000 0.000000 0.000000 0.000000 1.000000 1.000000 33.000000 6.700000 0.000000 0.000000 1.000000
1.000000 9.000000 39.100000 164.000000 84.000000 4.000000 1.000000 6.000000 2.000000 2.000000 4.000000 4.000000 1.000000 2.000000 5.000000 3.000000 0.000000 48.000000 7.200000 3.000000 5.300000 0.000000
2.000000 1.000000 37.300000 104.000000 35.000000 0.000000 0.000000 6.000000 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 74.000000 7.400000 0.000000 0.000000 0.000000
2.000000 1.000000 0.000000 0.000000 0.000000 2.000000 1.000000 3.000000 1.000000 2.000000 3.000000 2.000000 2.000000 1.000000 0.000000 3.000000 3.000000 0.000000 0.000000 0.000000 0.000000 1.000000
1.000000 1.000000 37.900000 48.000000 16.000000 1.000000 1.000000 1.000000 1.000000 3.000000 3.000000 3.000000 1.000000 1.000000 0.000000 3.000000 5.000000 37.000000 7.000000 0.000000 0.000000 1.000000
1.000000 1.000000 0.000000 60.000000 0.000000 3.000000 0.000000 0.000000 1.000000 0.000000 4.000000 2.000000 2.000000 1.000000 0.000000 3.000000 4.000000 44.000000 8.300000 0.000000 0.000000 0.000000
2.000000 1.000000 0.000000 80.000000 36.000000 3.000000 4.000000 3.000000 1.000000 4.000000 4.000000 4.000000 2.000000 1.000000 0.000000 3.000000 5.000000 38.000000 6.200000 0.000000 0.000000 0.000000
2.000000 9.000000 38.300000 90.000000 0.000000 1.000000 0.000000 1.000000 1.000000 5.000000 3.000000 1.000000 2.000000 1.000000 0.000000 3.000000 0.000000 40.000000 6.200000 1.000000 2.200000 1.000000
1.000000 1.000000 38.100000 66.000000 12.000000 3.000000 3.000000 5.000000 1.000000 3.000000 3.000000 1.000000 2.000000 1.000000 3.000000 2.000000 5.000000 44.000000 6.000000 2.000000 3.600000 1.000000
2.000000 1.000000 39.100000 72.000000 52.000000 2.000000 0.000000 2.000000 1.000000 2.000000 1.000000 2.000000 1.000000 1.000000 0.000000 4.000000 4.000000 50.000000 7.800000 0.000000 0.000000 1.000000
1.000000 1.000000 37.200000 42.000000 12.000000 2.000000 1.000000 1.000000 1.000000 3.000000 3.000000 3.000000 3.000000 1.000000 0.000000 4.000000 5.000000 0.000000 7.000000 0.000000 0.000000 1.000000
2.000000 9.000000 38.000000 92.000000 28.000000 1.000000 1.000000 2.000000 1.000000 1.000000 3.000000 2.000000 3.000000 0.000000 7.200000 1.000000 1.000000 37.000000 6.100000 1.000000 0.000000 0.000000
1.000000 1.000000 38.200000 76.000000 28.000000 3.000000 1.000000 1.000000 1.000000 3.000000 4.000000 1.000000 2.000000 2.000000 0.000000 4.000000 4.000000 46.000000 81.000000 1.000000 2.000000 1.000000
1.000000 1.000000 37.600000 96.000000 48.000000 3.000000 1.000000 4.000000 1.000000 5.000000 3.000000 3.000000 2.000000 3.000000 4.500000 4.000000 0.000000 45.000000 6.800000 0.000000 0.000000 0.000000
1.000000 9.000000 0.000000 128.000000 36.000000 3.000000 3.000000 4.000000 2.000000 4.000000 4.000000 3.000000 3.000000 0.000000 0.000000 4.000000 5.000000 53.000000 7.800000 3.000000 4.700000 0.000000
2.000000 1.000000 37.500000 48.000000 24.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000
1.000000 1.000000 37.600000 64.000000 21.000000 1.000000 1.000000 2.000000 1.000000 2.000000 3.000000 1.000000 1.000000 1.000000 0.000000 2.000000 5.000000 40.000000 7.000000 1.000000 0.000000 1.000000
2.000000 1.000000 39.400000 110.000000 35.000000 4.000000 3.000000 6.000000 0.000000 0.000000 3.000000 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000 55.000000 8.700000 0.000000 0.000000 1.000000

horseColicTest.txt

2 1 38.50 54 20 0 1 2 2 3 4 1 2 2 5.90 0 2 42.00 6.30 0 0 1
2 1 37.60 48 36 0 0 1 1 0 3 0 0 0 0 0 0 44.00 6.30 1 5.00 1
1 1 37.7 44 28 0 4 3 2 5 4 4 1 1 0 3 5 45 70 3 2 1
1 1 37 56 24 3 1 4 2 4 4 3 1 1 0 0 0 35 61 3 2 0
2 1 38.00 42 12 3 0 3 1 1 0 1 0 0 0 0 2 37.00 5.80 0 0 1
1 1 0 60 40 3 0 1 1 0 4 0 3 2 0 0 5 42 72 0 0 1
2 1 38.40 80 60 3 2 2 1 3 2 1 2 2 0 1 1 54.00 6.90 0 0 1
2 1 37.80 48 12 2 1 2 1 3 0 1 2 0 0 2 0 48.00 7.30 1 0 1
2 1 37.90 45 36 3 3 3 2 2 3 1 2 1 0 3 0 33.00 5.70 3 0 1
2 1 39.00 84 12 3 1 5 1 2 4 2 1 2 7.00 0 4 62.00 5.90 2 2.20 0
2 1 38.20 60 24 3 1 3 2 3 3 2 3 3 0 4 4 53.00 7.50 2 1.40 1
1 1 0 140 0 0 0 4 2 5 4 4 1 1 0 0 5 30 69 0 0 0
1 1 37.90 120 60 3 3 3 1 5 4 4 2 2 7.50 4 5 52.00 6.60 3 1.80 0
2 1 38.00 72 36 1 1 3 1 3 0 2 2 1 0 3 5 38.00 6.80 2 2.00 1
2 9 38.00 92 28 1 1 2 1 1 3 2 3 0 7.20 0 0 37.00 6.10 1 1.10 1
1 1 38.30 66 30 2 3 1 1 2 4 3 3 2 8.50 4 5 37.00 6.00 0 0 1
2 1 37.50 48 24 3 1 1 1 2 1 0 1 1 0 3 2 43.00 6.00 1 2.80 1
1 1 37.50 88 20 2 3 3 1 4 3 3 0 0 0 0 0 35.00 6.40 1 0 0
2 9 0 150 60 4 4 4 2 5 4 4 0 0 0 0 0 0 0 0 0 0

#-*- coding:utf-8 -*-
'''
Created on Oct 27, 2010
Logistic Regression Working Module
@author: Peter
'''
from numpy import *

#***读取数据
#前两列为特征，最后一列为类别
def loadDataSet():
    #训练数据
    dataMat = []; 
    #类别标签
    labelMat = []
    fr = open('testSet.txt')#读文件
    #按行读取文件内容
    for line in fr.readlines(): 
        lineArr = line.strip().split()#每一行数据
        #为计算方便，增加一列特征x0=1,其系数为w0
        #线性回归h(x)=w0*1+w1*x1+w2*x2=(w0,w1,w2)*(1,x1,x2)
        #(w0,w1,w2)为所求回归系数
        #将(1,x1,x2)写入到dataMat[]中
        dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
        #类别标签
        labelMat.append(int(lineArr[2]))
    return dataMat,labelMat

#sigmoid函数(logistic函数)
def sigmoid(inX):
    return 1.0/(1+exp(-inX))

#***梯度上升
#输入：训练数据，类别标签
def gradAscent(dataMatIn, classLabels):
    #列表转成矩阵
    dataMatrix = mat(dataMatIn)   
    #转成列向量矩阵
    labelMat = mat(classLabels).transpose() 
    #训练数据个数m，特征维数n
    m,n = shape(dataMatrix) 
    #迭代步长
    alpha = 0.001
    #循环次数，认为设定
    maxCycles = 500
    #回归系数列向量，每个特征对应一个回归系数
    weights = ones((n,1))
    #循环最大次数maxCycles
    for k in range(maxCycles):               
        #预测值(乘法次数m*n次),列向量
        h = sigmoid(dataMatrix*weights)      
        #预测误差，列向量
        error = (labelMat - h)      
        #回归系数更新        
        weights = weights + alpha * dataMatrix.transpose()* error  
    return weights

#***绘图决策边界
#weights:求得的参数向量
#weights[0]对应着一个数值
def plotBestFit(weights):
    import matplotlib.pyplot as plt
    #读取数据
    dataMat,labelMat=loadDataSet()
        #list类型转成array类型
    dataArr = array(dataMat)
    #样本数
    n = shape(dataArr)[0] 
    #坐标绘图坐标
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(n):
        #类别为1样本，x轴对应第一列特征，y轴对应第二列特征
        if int(labelMat[i])== 1: 
            xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])
        #类别为0样本，x轴对应第一列特征，y轴对应第二列特征
        else:   
            xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])
    fig = plt.figure()
    ax = fig.add_subplot(111)
    #类别为1样本，红色菱形
    ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
    #类别为0样本，绿色圆形
    ax.scatter(xcord2, ycord2, s=30, c='green')
    #x坐标轴的取值范围
    x = arange(-3.0, 3.0, 0.1)
    #决策边界0=w0*x0+w1*x1+w2*x2，即x2=(-w0-w1*x1)/w2
    #在绘图坐标系中，即为y=(-w0-w1*x)/w2
    y = (-weights[0]-weights[1]*x)/weights[2]
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()

#***随机梯度上升法
#输入：训练数据，类别标签
def stocGradAscent0(dataMatrix, classLabels):
    #样本数m,特征维数n
    m,n = shape(dataMatrix)
    #迭代步长
    alpha = 0.01
    #回归系数有n个，初始化全为1
    weights = ones(n)#1 x n 的行向量
    #遍历每一条数据
    for i in range(m):
        #h为当前样本的预测值，只用一个样本更新（一个数值类型）
        h = sigmoid(sum(dataMatrix[i]*weights))
        #预测误差（数值类型）
        error = classLabels[i] - h
        #只选择当前样本进行回归系数的更新
        weights = weights + alpha * error * dataMatrix[i]
    return weights

#***改进的随机梯度上升法
#输入：训练数据，类别标签，默认迭代次数150
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    #训练样本个数m,特征维数n
    m,n = shape(dataMatrix)
    #回归系数，1 x n行向量，n个特征对应n个回归系数
    #初始化为1
    weights = ones(n)    
    #迭代numIter次
    for j in range(numIter):
        #产生0~m-1共m个整数值
        dataIndex = range(m)
        #遍历每个样本
        for i in range(m):
            #更新步长
            alpha = 4/(1.0+j+i)+0.0001
            #随机抽取一个样本      
            randIndex = int(random.uniform(0,len(dataIndex)))
            #模型预测值(数值)
            h = sigmoid(sum(dataMatrix[randIndex]*weights))
            #预测误差
            error = classLabels[randIndex] - h
            #更新回归系数
            weights = weights + alpha * error * dataMatrix[randIndex]
            #被抽取的样本用于更新回归系数后，被剔除
            del(dataIndex[randIndex])
    return weights

#***分类函数
#输入：待分类的数据inX,更新好的回归系数
def classifyVector(inX, weights):
    #使用sigmoid函数预测
    prob1=inX*weights
    print'prob1=',prob1
    prob2=sum(inX*weights)
    print'prob2=',prob2

    prob = sigmoid(sum(inX*weights))
    #概率大于0.5判为第1类，概率小于0.5判为第0类
    if prob > 0.5: return 1.0
    else: return 0.0

#测试
def colicTest():
    #读训练数据
    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]))
    #利用改进的梯度下降法获取回归系数
    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 1000)
    #测试样本的预测错误数
    errorCount = 0; 
    #存测试样本个数
    numTestVec = 0.0
    #读取每个测试数据，预测类别，并判断是否正确
    for line in frTest.readlines():
        #统计测试数据个数
        numTestVec += 1.0
        currLine = line.strip().split('\t')
        #每次存一个测试样本
        lineArr =[]
        #待测试的一个样本（不含标签）
        for i in range(21):
            lineArr.append(float(currLine[i]))
        #预测标签，判断是否预测正确
        if int(classifyVector(array(lineArr), trainWeights))!= int(currLine[21]):
            #统计预测错误的个数
            errorCount += 1
    #计算错误率
    errorRate = (float(errorCount)/numTestVec)
    print "the error rate of this test is: %f" % errorRate
    return errorRate

#多次运行取平均
def multiTest():
    numTests = 10; errorSum=0.0
    #统计10次测试， 取平均错误率
    for k in range(numTests):
        errorSum += colicTest()
    print "after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests))

#运行main()函数
if __name__ == "__main__":
#   批处理梯度上升法
    #获取数据
    dataArr,labelMat=loadDataSet()
#    #求参数
    weights=gradAscent(dataArr,labelMat)
    print'weights='
    print weights
#    #画图前需要把weights的matrix类型转换成array类型用matrix.getA()
#   plotBestFit(weights.getA())

##  #***随机梯度上升法
##  #获取数据list类型
    # dataArr,labelMat=loadDataSet()
##  #求参数,把dataArr先由list类型转换成array类型
    # weights=stocGradAscent0(array(dataArr),labelMat)
#   print'weights='
#   print weights
#   plotBestFit(weights)

#   multiTest()