机器学习实战精读--------朴素贝叶斯（NBC）

朴素贝叶斯法是基于贝叶斯定理与特征条件独立假设的分类方法
贝叶斯决策理论核心思想：选择具有最高概率的决策

贝叶斯分类器的基本方法：在统计资料的基础上，依据某些特征，计算各个类别的概率，从而实现分类
朴素：朴素贝叶斯假设特征之间是独立，互不影响。

拉普拉斯平滑：为了解决零概率的问题，法国数学家拉普拉斯最早提出用加1的方法估计没有出现过的现象的概率，所以加法平滑也叫做拉普拉斯平滑。
贝努利模型：假设词是等权重的，只考虑出现不出现，不考虑出现的次数
多项式模型：考虑词在文档中的出现次数

#coding:utf-8
from numpy import *

#创建实验样本
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 是侮辱性的, 0 不是
return postingList,classVec

#创建词汇表，表中数据不重复
def createVocabList(dataSet):
vocabSet = set([])  #创建一个空的集合
for document in dataSet:
vocabSet = vocabSet | set(document) #求两个集合的并集
return list(vocabSet)       #返回一个包含一个在所有文档中出现的不重复词的列表

#输出文档向量   给一篇文档,返回一个词向量
def setOfWords2Vec(vocabList, inputSet):
returnVec = [0]*len(vocabList) #创建一个和词汇表等长的向量,讲它的元素都设置为0
for word in inputSet:                    #遍历文档中所有单词
if word in vocabList:                #如果出现词汇表中的单词
returnVec[vocabList.index(word)] = 1    #将输出文档向量的对应值设为1
else: print "the word: %s is not in my Vocabulary!" % word
return returnVec

#朴素贝叶斯分类器训练函数
def trainNB0(trainMatrix,trainCategory):  #trainMatrix :文档矩阵;trainCategory;词向量
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])
p1Vect = log(p1Num/p1Denom)          #log() 方法返回x的自然对数。
p0Vect = log(p0Num/p0Denom)
return p0Vect,p1Vect,pAbusive

#朴素贝叶斯分类函数
def classifyNB(vec2Classify, p0Vec, p1Vec, pClass1):  #vec2Classify:要分类的向量; p0Vec p1Vec pClass1 : trainNB0 的输出的三个概率值
p1 = sum(vec2Classify * p1Vec) + log(pClass1)    #计算两个向量相乘的结果
p0 = sum(vec2Classify * p0Vec) + log(1.0 - pClass1)
if p1 > p0:
return 1
else:
return 0

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

#便利函数,封装所有的操作
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)

#接收一个大写字符串并将其解析为字符串列表.
def textParse(bigString):    #输入一个大字符串, #输出一个词列表
import re
listOfTokens = re.split(r'\W*', bigString)
return [tok.lower() for tok in listOfTokens if len(tok) > 2] #使用列表推导式 把所有的字符串转换为小写

#对贝叶斯垃圾邮件分类器进行自动化处理
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)

def calcMostFreq(vocabList,fullText):
import operator
freqDict = {}
for token in vocabList:     #遍历词汇表
freqDict[token]=fullText.count(token) #统计词在文本中出现的次数，写入字典freqDict中
sortedFreq = sorted(freqDict.iteritems(), key=operator.itemgetter(1), reverse=True) #根据出现次数从高到低对词典进行排序
return sortedFreq[:30]       #返回排序最高的30个单词

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

#显示最具表征性的词汇
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]

小结：
所有特征彼此独立"这个假设，在现实中不太可能成立，但是它可以大大简化计算，而且有研究表明对分类结果的准确性影响不大。
词袋模型：每个词可以出现多次
词集模型：每个词只能出现一次
下溢出：通过求对数可以避免下溢出或者浮点数摄入导致的错误。
停用词：是指在信息检索中，为节省存储空间和提高搜索效率，在处理自然语言数据（或文本）之前或之后会自动过滤掉某些字或词，这些字或词即被称为Stop Words（停用词）。
演绎推理：就是从一般性的前提出发，通过推导即“演绎”，得出具体陈述或个别结论的过程。