樸素貝葉斯原理及Python實現

樸素貝葉斯分類器優缺點

優點：在數據較少的情況下依然有效，可以處理多分類問題
缺點：對輸入數據的準備方式較爲敏感
使用數據類型：標稱型數據

算法原理

樸素貝葉斯分類器是基於貝葉斯概率理論構建的，即我們希望通過一個已知事務的先驗概率（條件概率）去推測該事物的後驗概率。
首先我們來回顧一下貝葉斯概率理論原理：

貝葉斯公式說明：
1，事件A在事件B發生的條件下的概率，與事件B在事件A發生的條件下的概率是不一樣的。但是這兩者是有確定關係的。
2，我們可以通過已知的三個概率去推測第四個概率，即從結果上溯到源頭（也即逆向概率）。

對於一個有多維的特徵的樣本而言，其貝葉斯公式是：

p(ci|w)=p(w|ci)p(ci)p(w)

我們之所以稱之爲樸素（naive）貝葉斯分類器是因爲它有兩點假設前提：
1，假設樣本特徵之間是相互獨立的，即p(AB)=p(A)p(B)
2，假設每個特徵同等重要

Python實現

#-*- coding:utf-8 -*-
from numpy import *
def loadDataSet():
    postingList = [['my', 'dog', 'has', 'flea', 'problems', 'help', 'please'],
                   ['maybe', 'not', 'take', 'him', 'to', 'dog', 'park', 'stupid'],
                   ['my', 'dalmation', 'is', 'so', 'cute', 'I', 'love', 'him'],
                   ['stop', 'posting', 'stupid', 'worthless', 'garbage'],
                   ['mr', 'licks', 'ate', 'my', 'steak', 'how', 'to', 'stop', 'him'],
                   ['quit', 'buying', 'worthless', 'dog', 'food', 'stupid']]
    classVec = [0,1,0,1,0,1] #1代表侮辱性言論 0 代表正常言論
    return postingList,classVec

#創建一個包含所有文檔中不重複詞的列表
def createVocabList(dataSet):
    vocabSet = set([]) #set 集合類中不包含重複的元素
    for document in dataSet:
        vocabSet = vocabSet | set(document)  #操作符  | 用於求兩個合集的並集，這也是一個按位或（OR）操作符，
        # 在數學符號表示上，按位或操作與集合求並操作使用相同的符號
    return list(vocabSet)
#詞集模型
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
#詞袋模型
def bagOfWords2VecMN(vocabList,inputSet):
    returnVec = [0] * len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] += 1
    return  returnVec
#樸素貝葉斯分類器的訓練函數
def trainNB0(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory)/float(numTrainDocs) #計算侮辱性言論的概率
    #p0Num = zeros(numWords);p1Num = zeros(numWords) #生成長度爲所有詞彙量個數的向量
    #p0Denom = 0.0; p1Denom = 0.0 #初始化分母項
    #在後續計算多個概率的成績時，爲了避免某一個概率爲0導致整個成績的結果爲0，將上述兩行代碼做一下修改
    p0Num = ones(numWords);p1Num = ones(numWords)
    p0Denom = 2.0; p1Denom = 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 = p1Num/p1Denom
    #p0Vect = p0Num/p0Denom
    #爲了避免許多數值過小的概率相乘造成下溢出的問題，對概率成績取自然對數，上述兩行改爲
    p1Vect = log(p1Num/p1Denom)
    p0Vect = log(p0Num/p0Denom)
    return p0Vect,p1Vect,pAbusive
#樸素貝葉斯的分類函數
def classifyNB(vec2Classify,p0Vec,p1Vec,pClass1):
    p1 = sum(vec2Classify * p1Vec) + log(pClass1)
    p0 = sum(vec2Classify * p0Vec) + log(1-pClass1)
    if p1>p0:
        return 1
    else :
        return 0
#convenience function
def testingNB():
    listOPosts,listClasses = loadDataSet()
    myVocabList = createVocabList(listOPosts)
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVocabList,postinDoc))
    p0V,p1V,pAb = trainNB0(array(trainMat),array(listClasses))
    testEntry = ['love','my','damation']
    thisDoc = array(setOfWords2Vec(myVocabList,testEntry))
    print testEntry ,'classified as:',classifyNB(thisDoc,p0V,p1V,pAb)
    testEntry = ['stupid','garbage']
    thisDoc = array(setOfWords2Vec(myVocabList,testEntry))
    print testEntry ,'classified as:',classifyNB(thisDoc,p0V,p1V,pAb)


#文件解析及完整的垃圾郵件測試函數
def textParse(bigString):
    import re
    listOfTokens = re.split('\\W*',bigString)
    return [tok.lower() for tok in listOfTokens if len(tok) > 2]
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)
    trainingSet = range(50); testSet=[]
    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:
        trainMat.append(setOfWords2Vec(vocabList, docList[docIndex]))
        trainClasses.append(classList[docIndex])
    p0V,p1V,pSpam = trainNB0(array(trainMat),array(trainClasses))
    errorCount = 0
    for docIndex in testSet:
        wordVector = setOfWords2Vec(vocabList, docList[docIndex])
        if classifyNB(array(wordVector),p0V,p1V,pSpam) != classList[docIndex]:
            errorCount +=1
            print docList[docIndex]
    print 'the error rate is: ', float(errorCount)/len(testSet)

def calcMostFreq(vocabList,fullText):
    import operator
    freqDict = {}
    for token in vocabList:
        freqDict[token]=fullText.count(token)
    sortedFreq = sorted(freqDict.iteritems(), key=operator.itemgetter(1), reverse=True) 
    return sortedFreq[:30]       

def localWords(feed1,feed0):
    import feedparser
    docList=[]; classList = []; fullText =[]
    minLen = min(len(feed1['entries']),len(feed0['entries']))
    for i in range(minLen):
        wordList = textParse(feed1['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(1) #NY is class 1
        wordList = textParse(feed0['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(0)
    vocabList = createVocabList(docList)#create vocabulary
    top30Words = calcMostFreq(vocabList,fullText)   #remove top 30 words
    for pairW in top30Words:
        if pairW[0] in vocabList: vocabList.remove(pairW[0])
    trainingSet = range(2*minLen); testSet=[]           #create test set
    for i in range(20):
        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 'the error rate is: ',float(errorCount)/len(testSet)
    return vocabList,p0V,p1V

def getTopWords(ny,sf):
    import operator
    vocabList,p0V,p1V=localWords(ny,sf)
    topNY=[]; topSF=[]
    for i in range(len(p0V)):
        if p0V[i] > -6.0 : topSF.append((vocabList[i],p0V[i]))
        if p1V[i] > -6.0 : topNY.append((vocabList[i],p1V[i]))
    sortedSF = sorted(topSF, key=lambda pair: pair[1], reverse=True)
    print "SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**SF**"
    for item in sortedSF:
        print item[0]
    sortedNY = sorted(topNY, key=lambda pair: pair[1], reverse=True)
    print "NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**NY**"
    for item in sortedNY:
        print item[0]