朴素贝叶斯原理及Python实现

朴素贝叶斯分类器优缺点

优点：在数据较少的情况下依然有效，可以处理多分类问题

缺点：对输入数据的准备方式较为敏感

使用数据类型：标称型数据

算法原理

朴素贝叶斯分类器是基于贝叶斯概率理论构建的，即我们希望通过一个已知事务的先验概率（条件概率）去推测该事物的后验概率。

首先我们来回顾一下贝叶斯概率理论原理：



贝叶斯公式说明：

1，事件A在事件B发生的条件下的概率，与事件B在事件A发生的条件下的概率是不一样的。但是这两者是有确定关系的。

2，我们可以通过已知的三个概率去推测第四个概率，即从结果上溯到源头（也即逆向概率）。

对于一个有多维的特征的样本而言，其贝叶斯公式是：

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

我们之所以称之为朴素（naive）贝叶斯分类器是因为它有两点假设前提：

1，假设样本特征之间是相互独立的，即p(AB)=p(A)p(B)

2，假设每个特征同等重要

Python实现

#-*- 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代表侮辱性言论 0 代表正常言论
return postingList,classVec

#创建一个包含所有文档中不重复词的列表
def createVocabList(dataSet):
vocabSet = set([]) #set 集合类中不包含重复的元素
for document in dataSet:
vocabSet = vocabSet | set(document)  #操作符  | 用于求两个合集的并集，这也是一个按位或（OR）操作符，
# 在数学符号表示上，按位或操作与集合求并操作使用相同的符号
return list(vocabSet)
#词集模型
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
#词袋模型
def bagOfWords2VecMN(vocabList,inputSet):
returnVec = [0] * len(vocabList)
for word in inputSet:
if word in vocabList:
returnVec[vocabList.index(word)] += 1
return  returnVec
#朴素贝叶斯分类器的训练函数
def trainNB0(trainMatrix,trainCategory):
numTrainDocs = len(trainMatrix)
numWords = len(trainMatrix[0])
pAbusive = sum(trainCategory)/float(numTrainDocs) #计算侮辱性言论的概率
#p0Num = zeros(numWords);p1Num = zeros(numWords) #生成长度为所有词汇量个数的向量
#p0Denom = 0.0; p1Denom = 0.0 #初始化分母项
#在后续计算多个概率的成绩时，为了避免某一个概率为0导致整个成绩的结果为0，将上述两行代码做一下修改
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
#为了避免许多数值过小的概率相乘造成下溢出的问题，对概率成绩取自然对数，上述两行改为
p1Vect = log(p1Num/p1Denom)
p0Vect = log(p0Num/p0Denom)
return p0Vect,p1Vect,pAbusive
#朴素贝叶斯的分类函数
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邮件测试函数
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]