一、概述
优点：在数据少的情况下仍然有效，可以处理多类别问题
缺点：对于输入数据的准备方式较为敏感
适用数据类型：标称型数据
二、原理
三、文档分类
A,B,C,D..为文档中单词。假设总词汇只有A,B,C,D四种。训练样本为5个
A    B    C    D    类别
文档1    0    0    1    1    0
文档2    0    1    1    1    0
文档3    1    0    0    1    1
文档4    1    1    0    0    1
文档5    1    1    1    0    1
测试文档    1    0    1    0    ?
类别：C0,C1
测试文档：W
求：max{P(C0|W),P(C1|W)} ===> max{log[P(C0|W)],log[P(C1|W)]}
P(C0|W) = P(W|C0) * P(C0) / P(W)
P(C0) = 2 / 5 ==> 2个0类型的文档，3个1类型的文档
P(W|C0) = P(A*B*C*D|C0) ==> Navie Bayes ==> P(A|C0) * P(B|C0) * P(C|C0) * P(D|C0)
P(A|C0)=(0 + 0)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=0 ==> A在类别0文档中出现的次数/ 类别0文档中的总词汇量
P(B|C0)=(0 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=1/5 ==> B在类别0文档中出现的次数/ 类别0文档中的总词汇量
P(C|C0)=(1 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=2/5 ==> C在类别0文档中出现的次数/ 类别0文档中的总词汇量
P(D|C0)=(1 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=2/5 ==> D在类别0文档中出现的次数/ 类别0文档中的总词汇量
因为相乘为存在0* ==>0 取log
log[P(W|C0) * P(C0)] = log[P(A|C0) * P(B|C0) * P(C|C0) * P(D|C0) * P(C0)]
=log[P(A|C0)] + log[P(B|C0)] + log[P(C|C0)] + log[P(D|C0) ] + log[P(C0)]

同理计算log[P(W|C1) * P(C1)]

测试样本：
log[P(C0|W)] = 0 * log(1/5) + 1 * log(2/5) + 0 * log(2/5) + log(2/5) =
log[P(C1|W)] = 1 * log(3/7) + 0 * log(2/7) + 1 * log(1/7) + 0 * log(1/7) + log(1  - 2/5) =
# -*- coding:UTF-8
from numpy import *
 
'''
1.伯努利模型==>不考虑词在文档中出现的次数，只考虑出不出现。假定词是等权重中的
2.多项式模型
'''
 
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]
    return postingList,classVec
 
def createVocabList(dataSet):
    vocaSet = set([])
    for document in dataSet:
        vocaSet = vocaSet | set(document)
    return list(vocaSet)
 
 
'''
vocabList = ['','',.....]
inputSet = ['my', 'dog', 'has', 'flea', 'problems', 'help', 'please']
'''
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
 
'''
P(c|w) = P(w|c) * P(c) / P(w)
1.P(c)
2.P(w|c)
 
trainMatrix
 
trainCategory===>[0,0,1,1,0]  标签集合的向量
pAbusive = (0  + 0 +  1 + 1 + 0) / 5
 
A    B    C    D    category
0    0    1    1    0
0    1    1    1    0
1    0    0    1    1
1    1    0    0    1
1    1    1    0    1
1    0    1    0    ?
 
numTrainDocs = 5 => 5个文档
numWords = 4 => 4个特征
pAbusive = (0 + 0 + 0 + 1 + 1) / 5 = 2/5 ==> 先验概率
p0Num = [0,0,0,0]
p1Num = [0,0,0,0]
p0Denom = 0.0
p1Denom = 0.0
    0    0    1    1    0 ===> p0Num=[0,0,1,1]  p0Denom=1
    0    1    1    1    0 ===> p0Num=[0,1,2,2]  p0Denom=2
    1    0    0    1    1 ===> p1Num=[1,0,0,1]  p1Denom=1
    1    1    0    0    1 ===> p1Num=[2,1,0,1]  p1Denom=2
    1    1    1    0    1 ===> p1Num=[3,2,1,1]  p1Denom=3
     
P(C0|W) = P(W|C0) * P(C0) / P(W) = P(A*B*C*D|C0) * P(C0) / P(W) = P(A|C0) * P(B|C0) * P(C|C0) * P(D|C0) * P(C0) / P(W)
P(C1|W) = P(W|C1) * P(C1) / P(W) = P(A*B*C*D|C1) * P(C1) / P(W) = P(A|C1) * P(B|C1) * P(C|C1) * P(D|C1) * P(C1) / P(W)
 
P(W) ==> 无需再计算了
max{P(C0|W),P(C1|W)} ===> max{Log[P(C0|W)],Log[P(C1|W)]}
 
Log[P(C0|W)] = Log[P(A|C0)] + Log[P(B|C0)] + Log[P(C|C0)] + Log[P(D|C0)] + Log[P(C0)]
P(A|C0) = 0/(0+1+2+2) = 0/5
P(B|C0) = 1/(0+1+2+2) = 1/5
P(C|C0) = 2/(0+1+2+2) = 2/5
P(D|C0) = 2/(0+1+2+2) = 2/5
 
 
Log[P(C1|W)] = Log[P(A|C1)] + Log[P(B|C1)] + Log[P(B|C1)] + Log[P(B|C1)] + Log[P(C1)]
P(A|C1) = 3/(3+2+1+1) = 3/7
P(B|C1) = 2/(3+2+1+1) = 2/7
P(C|C1) = 1/(3+2+1+1) = 1/7
P(D|C1) = 1/(3+2+1+1) = 1/7
 
 
测试样本1    0    1    0    ?
Log[P(C0|W)] = 1 * Log[0/5]  + 0 * Log[1/5] + 1 * Log[2/5] + 0 * Log[2/5] + Log[2/5]
Log[P(C1|W)] = 1 * Log[3/7]  + 0 * Log[2/7] + 1 * Log[1/7]+ 0 * Log[1/7] + Log[1 - 2/5]
 
注意存在Log[0] ==> 所有初始化，我们设置
p0Num = [1,1,1,1]
p1Num = [1,1,1,1]
p0Denom = 2.0
p1Denom = 2.0
'''
def trainNB0(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory) / float(numTrainDocs)
    p0Num = zeros(numWords)
    p1Num = zeros(numWords)
    p0Denom = 0.0
    p1Denom = 0.0
     
    for i in range(numTrainDocs):
        if trainCategory[i] == 1:
            p1Num += trainMatrix[i]
            p1Denom += sum(trainMatrix[i])
        else:
            p0Num += trainMatrix[i]
            p0Denom += sum(trainMatrix[i])
    p1Vec = log(p1Num/p1Denom)
    p0Vec = log(p0Num/p0Denom)
     
    return p0Vec,p1Vec,pAbusive
 
def trainNB1(trainMatrix,trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory) / float(numTrainDocs)
    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])
    p1Vec = log(p1Num/p1Denom)
    p0Vec = log(p0Num/p0Denom)
     
    return p0Vec,p1Vec,pAbusive
 
 
def classifyNB(vec2Classify, p0Vec, p1Vec, pClass1):
    p1 = sum(vec2Classify * p1Vec) + log(pClass1)
    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 postingDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVocabList, postingDoc))
         
    p0V,p1V,pAb = trainNB0(trainMat, listClasses)
     
    testEntry = ['love','my','dalmation']
     
    thisDoc = array(setOfWords2Vec(myVocabList, testEntry))
     
    print(testEntry,' classified as: ',classifyNB(thisDoc,p0V,p1V,pAb))

四、过滤垃圾邮件
def textParse(bigString):
    import re
    listOfTokens = re.split(r'\W*', bigString)   #简单空格分词
    return [tok.lower() for tok in listOfTokens if len(tok) > 2]  #简单过滤词长<=2的词
 
def spamTest():
    docList = []
    classList = []
    #fullText = []
     
    for i in range(1,26):
        #读取所有的单词
        wordList = textParse(open('emial/spam/%d.txt' % i).read())
        docList.append(wordList)
        #fullText.extend(wordList)
        classList.append(1)
         
        wordList = textParse(open('emial/ham/%d.txt' % i).read())
        docList.append(wordList)
        #fullText.extend(wordList)
        classList.append(0)
         
    vocabList = createVocabList(docList)
    trainSet = range(50)
    testSet = []
     
    for i in range(10):
        randIndex = int(random.uniform(0,len(trainSet)))
        testSet.append(trainSet[randIndex])
        del(trainSet[randIndex])
         
    trainMat = []
    trainClasses = []
     
    for docIndex in trainSet:
        trainMat.append(setOfWords2Vec(vocabList,docList[docIndex]))
        trainClasses.append(classList[docIndex])
         
    p0V,p1V,pSpam = trainNB0(trainMat, trainClasses)
    errorCount = 0
     
    for docIndex in testSet:
        wordVector = setOfWords2Vec(vocabList, docList[docIndex])
         
        if classifyNB(wordVector, p0V, p1V, pSpam) != classList[docIndex]:
            errorCount += 1
            print 'classification error',docList[docIndex]
         
    print 'the error rate is: ',float(errorCount) / len(testSet)