《Machine Learning in Action》

為防止連續乘法時每個乘數過小，而導致的下溢出（太多很小的數相乘結果為0，或者不能正確分類）

訓練：

def trainNB0(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory)/float(numTrainDocs)
    p0Num = ones(numWords);p1Num = ones(numWords)#計算頻數初始化為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)#註意
    p0Vect = log(p0Num/p0Denom)#註意
    return p0Vect,p1Vect,pAbusive#返回各類對應特征的條件概率向量
                                 #和各類的先驗概率

分類：

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

def testingNB():#流程展示
    listOPosts,listClasses = loadDataSet()#加載數據
    myVocabList = createVocabList(listOPosts)#建立詞匯表
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(bagOfWord2VecMN(myVocabList,postinDoc))
    p0V,p1V,pAb = trainNB0(trainMat,listClasses)#訓練
    #測試
    testEntry = [‘love‘,‘my‘,‘dalmation‘]
    thisDoc = bagOfWord2VecMN(myVocabList,testEntry)
    print testEntry,‘classified as: ‘,classifyNB(thisDoc,p0V,p1V,pAb)

註意：上述代碼中標有註意的地方，是公式中概率連乘變成了對數概率相加。此舉可以在數學上證明不會影響分類結果，且在實際計算中，避免了因概率因子遠小於1而連乘造成的下溢出。　　

樸素貝葉斯-Numpy-對數似然