机器学习：朴素贝叶斯分类
贝叶斯定理:
已知两个独立事件A和B，事件B发生的前提下，事件A发生的概率可 以表示为P(A|B)，即上图中橙色部分占红色部分的比例
在机器学习中的2个视角：
一：判别式模型
二：生成式模型
朴素贝叶斯分类器(Naïve Bayes Classifier)采用了“属性条件独立性 假设” ，即每个属性独立地对分类结果发生影响
为方便公式标记，不妨记P(C=c|X=x)为P(c|x)，基于属性条件独立 性假设，贝叶斯公式可重写为
– 其中d为属性数目，xi为 x 在第i个属性上的取值。
我们这里使用垃圾邮件分类进行交叉验证贝叶斯的交叉验证
textParse()该函数用于接受一个字符串并解析为一个字符串列表
该函数去掉少于2个字符的字符串，并将所有字符串转换为小写
def textParse(bigString): #input is big string, #output is word list
import re
listOfTokens = re.split(r'\W*', bigString)
return [tok.lower() for tok in listOfTokens if len(tok) > 2] spamTest()
该函数用于对贝叶斯垃圾邮件分类器进行自动化处理
导入2个文件夹的文本文件并解析为词列表
随机选择十个文件
用setOfWords2Vec()和traindNB0()函数进行分类，最后给出总的错误百分比
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)
#return vocabList,fullTextsetOfWords2Vec()
对每封邮件基于词汇表并使用该函数 构建词向量
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这些词在traindNB0()函数中用于计算分类所需概率
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
输出结果：
