ailearning/src/python/05.Logistic/logRegres.py

#!/usr/bin/env python
# -*- coding:utf-8 -*-
from numpy import *


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))


def gradAscent(dataMatIn, classLabels):
    # 转化为矩阵[[1,1,2],[1,1,2]....]
    dataMatrix = mat(dataMatIn)  # convert to NumPy matrix
    # 转化为矩阵[[0,1,0,1,0,1.....]]，并转制[[0],[1],[0].....]
    x = mat(classLabels)
    labelMat = x.transpose()  # convert to NumPy matrix
    # m->数据量 n->特征数
    m, n = shape(dataMatrix)
    # 步长
    alpha = 0.001
    # 迭代次数
    maxCycles = 500
    # 生成一个长度和特征数相同的矩阵，此处n为3 -> [[1],[1],[1]]
    weights = ones((n, 1))
    for k in range(maxCycles):  # heavy on matrix operations
        # 1. dataMatrix * weights 矩阵乘法: [[1,1,2],[1,1,2]....] * [[1],[1],[1]] -> [[]]
        s = dataMatrix * weights
        # 把每个特征与系数的乘积只和带入Sigmoid函数
        h = sigmoid(dataMatrix * weights)  # matrix mult
        # [[x,x,x,x,x,......一共一百个误差]]
        error = (labelMat - h)  # vector subtraction
        # dataMatrix.transpose() * error 推理略去
        # [[x,x,x,x....一共一百个数],[],[]]
        data_tran = dataMatrix.transpose()
        # [[a,b,c]]
        data_tran_error = data_tran * error

        # weights = weights + alpha * dataMatrix.transpose() * error  # matrix mult
        weights = weights + alpha * data_tran_error
    return weights


# 随机梯度上升
# 梯度上升优化算法在每次更新数据集时都需要遍历整个数据集，计算复杂都较高
# 随机梯度上升一次只用一个样本点来更新回归系数
def stocGradAscent0(dataMatrix, classLabels):
    m, n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)  # initialize to all ones
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i] * weights))
        error = classLabels[i] - h
        weights = weights + alpha * error * dataMatrix[i]
    return weights


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]
    ax.plot(x, y)
    plt.xlabel('X1');
    plt.ylabel('X2');
    plt.show()


def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m, n = shape(dataMatrix)
    weights = ones(n)  # initialize to all ones
    for j in range(numIter):
        dataIndex = range(m)
        for i in range(m):
            # 步长在不断减小
            alpha = 4 / (1.0 + j + i) + 0.0001  # apha decreases with iteration, does not
            # 随机选取样本减少周期波动
            randIndex = int(random.uniform(0, len(dataIndex)))  # go to 0 because of the constant
            h = sigmoid(sum(dataMatrix[randIndex] * weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del (dataIndex[randIndex])
    return weights


# a, b = loadDataSet()
# weights = gradAscent(a, b)
# plotBestFit(weights)
#

######################################################################################################################

def classifyVector(inX, weights):
    prob = sigmoid(sum(inX * weights))
    if prob > 0.5:
        return 1.0
    else:
        return 0.0


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]))
    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 1000)
    errorCount = 0;
    numTestVec = 0.0
    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


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))

    # multiTest()

colicTest()