使用Logistic迴歸進行分類（代碼筆記）

基於Sigmoid函數和Logistic迴歸的分類算法。

思想：使用梯度上升找到最優迴歸係數，相當於找到決策邊界。再用數據特徵和Logistic迴歸就能算出分類。

import numpy as np
'''
用Logistic迴歸擬合決策邊界從而進行分類
'''
def sigmoid(x):
    try:
        return 1.0/(1+np.exp(-x))
    except:
        return 0.0  #overflow

# 隨機梯度上升算法
def stocGradAscent1(xMat, classLabels, numIter=150):
    m,n = np.shape(xMat)
    w = np.ones(n)
    for j in range(numIter):
        dataIdx = range(m)
        for i in range(m):
            alpha = 4/(1.0+j+i)+0.01
            randIdx = int(np.random.uniform(0,len(dataIdx)))
            h = sigmoid(sum(xMat[dataIdx[randIdx]]*w))
            err = classLabels[dataIdx[randIdx]] - h
            w = w + alpha*err*xMat[dataIdx[randIdx]]
            del(dataIdx[randIdx])
    return w

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

def colicTest():
    allData = open('horseColic.txt')
    allSet = []
    allLab = []
    for line in allData.readlines():
        currLine = line.strip().split(' ')
        lineArr = []
        for i in range(27):  # 27個特徵,第28列是類別
            lineArr.append(0 if currLine[i] is '?' else float(currLine[i]))  # 缺失數據補爲0
        allSet.append(lineArr)
        allLab.append(0.0 if int(currLine[27]) is 2 else float(currLine[27]))# 標籤1和2變成1和0
    trainSet = np.array(allSet[:300])  # 共368個樣本,前300個用作訓練,後68個用於預測
    trainLab = np.array(allLab[:300])
    testSet = np.array(allSet[300:])
    testLab = np.array(allLab[300:])

    trainW = stocGradAscent1(trainSet, trainLab, 500)  # 梯度上升迭代求迴歸係數
    
    # ----------------------------- 預測樣本集 ------------------------------
    predLab = []
    errCount = 0.0
    numTest = np.shape(testSet)[0]
    for i in range(numTest):  # 依次計算每個預測樣本
        predLab.append(classifyVector(testSet[i], trainW))
        print(classifyVector(testSet[i], trainW), testLab[i])
        if int(classifyVector(testSet[i], trainW)) is not int(testLab[i]):
            errCount += 1.0
    errRate = float(errCount)/numTest
    print('the error rate is: %f, error count:%f' % (errRate,errCount))
    return predLab, errRate