朴素贝叶斯算法

• 给出猜测的概率估计值
• 朴素：整个过程只做最原始最简单的假设（假设特征相互独立）
• 判断样本属于各个分类的概率，选择高概率对应的类别作为预测结果

• 贝叶斯公式： image.png

典型应用示例就是区分垃圾邮件（书中代码用的歧视性邮件示例，一个意思啦）

根据文本构建词向量

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 is abusive, 0 not
    return postingList,classVec
                 
def createVocabList(dataSet):
    vocabSet = set([])  #create empty set
    for document in dataSet:
        vocabSet = vocabSet | set(document) #union of the two sets
    return list(vocabSet)

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

从词向量计算概率

• A表示词向量, B_i表示该文本被划分为i概率（1表示歧视性邮件，0表示正常邮件）

• image.png

• 朴素贝叶斯分类器训练函数

初始词数都算作1，防止一个为0，概率相乘就变成0了
使用了log处理概率，因为防止数值太小相乘会下溢，即变为0

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

• 朴素贝叶斯分类函数

def classifyNB(vec2Classify, p0Vec, p1Vec, pClass1):
    p1 = sum(vec2Classify * p1Vec) + log(pClass1)    #element-wise mult
    p0 = sum(vec2Classify * p0Vec) + log(1.0 - pClass1)
    if p1 > p0:
        return 1
    else: 
        return 0
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', 'dalmation']
    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)

文档词袋模型

• 计算文档的数字向量时，考虑词语出现次数

def bagOfWords2VecMN(vocabList, inputSet):
    returnVec = [0]*len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] += 1
    return returnVec