朴素贝叶斯-Numpy-对数似然

《Machine Learning in Action》

为防止连续乘法时每个乘数过小，而导致的下溢出（太多很小的数相乘结果为0，或者不能正确分类）

训练：

def trainNB0(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory)/float(numTrainDocs)
    p0Num = ones(numWords);p1Num = ones(numWords)#计算频数初始化为1
    p0Denom = 2.0;p1Denom = 2.0                  #即拉普拉斯平滑
    for i in range(numTrainDocs):
        if trainCategory[i]==1:
            p1Num += trainMatrix[i]
            p1Denom += sum(trainMatrix[i])
        else:
            p0Num += trainMatrix[i]
            p0Denom += sum(trainMatrix[i])
    p1Vect = log(p1Num/p1Denom)#注意
    p0Vect = log(p0Num/p0Denom)#注意
    return p0Vect,p1Vect,pAbusive#返回各类对应特征的条件概率向量
                                 #和各类的先验概率

分类：

def classifyNB(vec2Classify,p0Vec,p1Vec,pClass1):
    p1 = sum(vec2Classify * p1Vec) + log(pClass1)#注意
    p0 = sum(vec2Classify * p0Vec) + log(1-pClass1)#注意
    if p1 > p0:
        return 1
    else:
        return 0

def testingNB():#流程展示
    listOPosts,listClasses = loadDataSet()#加载数据
    myVocabList = createVocabList(listOPosts)#建立词汇表
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(bagOfWord2VecMN(myVocabList,postinDoc))
    p0V,p1V,pAb = trainNB0(trainMat,listClasses)#训练
    #测试
    testEntry = [‘love‘,‘my‘,‘dalmation‘]
    thisDoc = bagOfWord2VecMN(myVocabList,testEntry)
    print testEntry,‘classified as: ‘,classifyNB(thisDoc,p0V,p1V,pAb)

注意：上述代码中标有注意的地方，是公式中概率连乘变成了对数概率相加。此举可以在数学上证明不会影响分类结果，且在实际计算中，避免了因概率因子远小于1而连乘造成的下溢出。