Naive Bayes怎么使用

這篇文章主要講解了“Naive Bayes怎么使用”，文中的講解內容簡單清晰，易于學習與理解，下面請大家跟著小編的思路慢慢深入，一起來研究和學習“Naive Bayes怎么使用”吧！

一、概述

優點：在數據少的情況下仍然有效，可以處理多類別問題

缺點：對于輸入數據的準備方式較為敏感

適用數據類型：標稱型數據

二、原理

三、文檔分類

A,B,C,D..為文檔中單詞。假設總詞匯只有A,B,C,D四種。訓練樣本為5個

類別：C0,C1

測試文檔：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個0類型的文檔，3個1類型的文檔

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在類別0文檔中出現的次數/ 類別0文檔中的總詞匯量

P(B|C0)=(0 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=1/5 ==> B在類別0文檔中出現的次數/ 類別0文檔中的總詞匯量

P(C|C0)=(1 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=2/5 ==> C在類別0文檔中出現的次數/ 類別0文檔中的總詞匯量

P(D|C0)=(1 + 1)/(0 + 0 + 1 + 1 + 0 + 1 + 1 + 1)=2/5 ==> D在類別0文檔中出現的次數/ 類別0文檔中的總詞匯量

因為相乘為存在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)]

同理計算log[P(W|C1) * P(C1)]

測試樣本：

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==>不考慮詞在文檔中出現的次數，只考慮出不出現。假定詞是等權重中的
2.多項式模型
'''

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]  標簽集合的向量
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個文檔
numWords = 4 => 4個特征
pAbusive = (0 + 0 + 0 + 1 + 1) / 5 = 2/5 ==> 先驗概率
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) ==> 無需再計算了
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


測試樣本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，我們設置
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、過濾垃圾郵件

def textParse(bigString):
    import re
    listOfTokens = re.split(r'\W*', bigString)   #簡單空格分詞
    return [tok.lower() for tok in listOfTokens if len(tok) > 2]  #簡單過濾詞長<=2的詞

def spamTest():
    docList = []
    classList = []
    #fullText = []
    
    for i in range(1,26):
        #讀取所有的單詞
        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)

感謝各位的閱讀，以上就是“Naive Bayes怎么使用”的內容了，經過本文的學習后，相信大家對Naive Bayes怎么使用這一問題有了更深刻的體會，具體使用情況還需要大家實踐驗證。這里是億速云，小編將為大家推送更多相關知識點的文章，歡迎關注！