代碼註釋：機器學習實戰第5章 Logistic迴歸

寫在開頭的話：在學習《機器學習實戰》的過程中發現書中很多代碼並沒有註釋，這對新入門的同學是一個挑戰，特此貼出我對代碼做出的註釋，僅供參考，歡迎指正。

1、隨機梯度上升

#coding:gbk
from numpy import *

#功能：導入數據集
#輸入：無
#輸出：數據矩陣，標籤向量
def loadDataSet():
    dataMat = []#數據矩陣
    labelMat = []#標籤向量
    fr = open('testSet.txt')
    for line in fr.readlines():
        lineArr = line.strip().split()#strip()表示刪除空白符，split()表示分割
        dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])#1.0表示x0
        labelMat.append(int(lineArr[2]))
    return dataMat, labelMat

#功能：計算x的Sigmoid函數
#輸入：x
#輸出：x的Sigmoid函數
def sigmoid(inX):
    return 1.0 / (1 + exp(-inX))

#功能：Logistic迴歸梯度上升優化算法
#輸入：無
#輸出：優化後的權重向量
def gradAscent():
    dataMatIn, classLabels = loadDataSet()#得數據矩陣，標籤向量
    dataMatrix = mat(dataMatIn)#將列表轉換成m*n矩陣
    labelMat = mat(classLabels).transpose()#將1*m標籤向量轉換成m*1矩陣
    m, n = shape(dataMatrix)#得dataMatrix的行數、列數
    alpha = 0.001#步長
    maxCycles = 500#最大迭代數量
    weights = ones((n,1))#n*1權重矩陣
    for k in range(maxCycles):
        h = sigmoid(dataMatrix * weights)
        error = (labelMat - h)
        weights = weights + alpha * dataMatrix.transpose() * error#數學推導，f = x * w so w = xT * f
    return weights

#功能：畫出決策邊界
#輸入：無
#輸出：無
def plotBestFit():
    weights = stocGradAscent1()#得優化後的權重向量
    #weights = weights.getA()#主窗口輸入help(numpy.matrix.getA)，將matrix轉換爲array
    import matplotlib.pyplot as plt
    dataMat, labelMat = loadDataSet()#得數據矩陣，標籤向量
    dataArr = array(dataMat)#將dataMat轉換爲array
    n = shape(dataArr)[0]#得dataArr行數
    xcord1 = []
    ycord1 = []
    xcord2 = []
    ycord2 = []
    for i in range(n):
        if int(labelMat[i]) == 1:#標籤爲1
            xcord1.append(dataArr[i, 1])
            ycord1.append(dataArr[i, 2])
        else:#標籤爲0
            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')#red square紅方塊
    ax.scatter(xcord2, ycord2, s = 30, c='green')#綠圓點
    x = arange(-3.0, 3.0, 0.1)#在[-3.0,3.0]區間裏以0.1的步長取數，得列表
    y = (-weights[0] - weights[1] * x) / weights[2]#直線方程：weights[0] + weights[1] * x + weights[2] * 2 = 0
    ax.plot(x, y)
    plt.xlabel('X1')
    plt.ylabel('X2')
    plt.show()

#功能：隨機梯度上升
#輸入：無
#輸出：優化後的權重向量
def stocGradAscent0():
    dataArr, classLabels = loadDataSet()  # 得數據矩陣，標籤向量
    dataMatrix = array(dataArr)  # 將列表轉換成m*n矩陣
    m, n = shape(dataMatrix)#得dataMatrix的行數、列數
    alpha = 0.01#步長
    weights = ones(n)#n階權重向量
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i] * weights))
        error = classLabels[i] - h
        weights = weights + alpha * error *dataMatrix[i]
    return weights

2、改進的隨機梯度上升

#功能：改進的隨機梯度上升
#輸入：無
#輸出：優化後的權重向量
def stocGradAscent1(dataMatrix, classLabels, numIter = 150):
    m, n = shape(dataMatrix)  # 得dataMatrix的行數、列數
    weights = ones(n)  # n階權重向量
    for j in range(numIter):#n次迭代
        dataIndex = range(m)
        for i in range(m):
            alpha = 4 / (1.0 + j + i) + 0.01#使得步長隨着迭代的進行而逐漸減小
            randIndex = int(random.uniform(0, len(dataIndex)))#隨機取第randIndex行的dataMatrix
            h = sigmoid(sum(dataMatrix[randIndex] * weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del(dataIndex[randIndex])#刪除第randIndex行，不參與迭代
    return weights

3、從疝氣病症預測病馬的死亡率

#功能：預測類別標籤
#輸入：特徵向量，迴歸係數
#輸出：預測的類別標籤
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')#strip()表示刪除空白符，split()表示分割
        lineArr = []
        for i in range(21):
            lineArr.append(float(currLine[i]))#將這個屬性放入lineArr
        trainingSet.append(lineArr)#屬性集
        trainingLabels.append(float(currLine[21]))#標籤集
    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 500)
    errorCount = 0
    numTestVec = 0.0
    for line in frTest.readlines():
        numTestVec += 1.0
        currLine = line.strip().split('\t')#strip()表示刪除空白符，split()表示分割
        lineArr = []
        for i in range(21):
            lineArr.append(float(currLine[i]))#將這個屬性放入lineArr
        if int(classifyVector(array(lineArr), trainWeights)) != int(currLine[21]):#預測標籤和驗證標籤不一致
            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 "the %d test: " % k
    print "after %d iterations the average error rate is: %f" % (numTests, errorSum / float(numTests))