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这篇文章主要讲解了“Naive Bayes怎么使用”,文中的讲解内容简单清晰,易于学习与理解,下面请大家跟着小编的思路慢慢深入,一起来研究和学习“Naive Bayes怎么使用”吧!
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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)
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