机器学习：朴素贝叶斯分类

贝叶斯定理: 

已知两个独立事件A和B，事件B发生的前提下，事件A发生的概率可 以表示为P(A|B)，即上图中橙色部分占红色部分的比例

在机器学习中的2个视角：

一：判别式模型

二：生成式模型

朴素贝叶斯分类器(Naïve Bayes Classifier)采用了“属性条件独立性 假设” ，即每个属性独立地对分类结果发生影响

为方便公式标记，不妨记P(C=c|X=x)为P(c|x)，基于属性条件独立 性假设，贝叶斯公式可重写为

– 其中d为属性数目，xi为 x 在第i个属性上的取值。

我们这里使用垃圾邮件分类进行交叉验证贝叶斯的交叉验证

textParse()该函数用于接受一个字符串并解析为一个字符串列表

该函数去掉少于2个字符的字符串，并将所有字符串转换为小写

def textParse(bigString):    #input is big string, #output is word list
    import re
    listOfTokens = re.split(r'\W*', bigString)
    return [tok.lower() for tok in listOfTokens if len(tok) > 2] 

spamTest()
该函数用于对贝叶斯垃圾邮件分类器进行自动化处理

导入2个文件夹的文本文件并解析为词列表

随机选择十个文件

用setOfWords2Vec()和traindNB0()函数进行分类，最后给出总的错误百分比

def spamTest():
    docList=[]; classList = []; fullText =[]
    for i in range(1,26):
        wordList = textParse(open('email/spam/%d.txt' % i).read())
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(1)
        wordList = textParse(open('email/ham/%d.txt' % i).read())
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(0)
    vocabList = createVocabList(docList)#create vocabulary
    trainingSet = range(50); testSet=[]           #create test set
    for i in range(10):
        randIndex = int(random.uniform(0,len(trainingSet)))
        testSet.append(trainingSet[randIndex])
        del(trainingSet[randIndex])  
    trainMat=[]; trainClasses = []
    for docIndex in trainingSet:#train the classifier (get probs) trainNB0
        trainMat.append(bagOfWords2VecMN(vocabList, docList[docIndex]))
        trainClasses.append(classList[docIndex])
    p0V,p1V,pSpam = trainNB0(array(trainMat),array(trainClasses))
    errorCount = 0
    for docIndex in testSet:        #classify the remaining items
        wordVector = bagOfWords2VecMN(vocabList, docList[docIndex])
        if classifyNB(array(wordVector),p0V,p1V,pSpam) != classList[docIndex]:
            errorCount += 1
            print "classification error",docList[docIndex]
    print 'the error rate is: ',float(errorCount)/len(testSet)
    #return vocabList,fullText

setOfWords2Vec()

对每封邮件基于词汇表并使用该函数 构建词向量

def setOfWords2Vec(vocabList, inputSet):
    returnVec = [0]*len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] = 1
        else: print "the word: %s is not in my Vocabulary!" % word
    return returnVec

这些词在traindNB0()函数中用于计算分类所需概率

def trainNB0(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory)/float(numTrainDocs)
    p0Num = ones(numWords); p1Num = ones(numWords)      #change to ones() 
    p0Denom = 2.0; p1Denom = 2.0                        #change to 2.0
    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)          #change to log()
    p0Vect = log(p0Num/p0Denom)          #change to log()
    return p0Vect,p1Vect,pAbusive

输出结果：