机器学习-python编写朴素贝叶斯用于文本分类

代码及数据集下载：贝叶斯

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朴素贝叶斯估计

朴素贝叶斯是基于贝叶斯定理与特征条件独立分布假设的分类方法。首先根据特征条件独立的假设学习输入/输出的联合概率分布，然后基于此模型，对给定的输入x，利用贝叶斯定理求出后验概率最大的输出y。
具体的，根据训练数据集，学习先验概率的极大似然估计分布

P(Y=ck)=∑i=1NI(yi=ck)N    k=1,2,...,K

以及条件概率为

P(X=x|Y=ck)=P(X1=x1,X2=x2,...,Xn=xn|Y=ck)

Xl表示第l个特征，由于特征条件独立的假设，可得

P(X=x|Y=ck)=∏j=1nP(Xl=xl|Y=ck)

条件概率的极大似然估计为

P(Xl=xl|Y=ck)=∑i=1NI(yi=ck,Xl=xl)∑i=1NI(yi=ck)

根据贝叶斯定理

P(Y=ck|X=x)=P(X=x|Y=ck)P(Y=ck)∑k=1KP(X=x|Y=ck)P(Y=ck)

则由上式可以得到条件概率P(Y=ck|X=x)。

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贝叶斯估计

用极大似然估计可能会出现所估计的概率为0的情况。后影响到后验概率结果的计算，使分类产生偏差。采用如下方法解决。
条件概率的贝叶斯改为

P(Xl=xl|Y=ck)=∑i=1NI(yi=ck,Xl=xl)+λ∑i=1NI(yi=ck)+Slλ

其中Sl表示第l个特征可能取值的个数。
同样，先验概率的贝叶斯估计改为
$$
P(Y=c_k) = \frac{\sum\limits_{i=1}^NI(y_i=c_k)+\lambda}{N+K\lambda}
$K$
表示Y的所有可能取值的个数，即类型的个数。
具体意义是，给每种可能初始化出现次数为1，保证每种可能都出现过一次，来解决估计为0的情况。

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文本分类

朴素贝叶斯分类器可以给出一个最有结果的猜测值，并给出估计概率。通常用于文本分类。
分类核心思想为选择概率最大的类别。贝叶斯公式如下：

p(c|x)=p(x|c)p(c)p(x)

词条：将每个词出现的次数作为特征。
假设每个特征相互独立，即每个词相互独立，不相关。则

p(x|c)=p(x1|c)p(x2|c)...p(xn|c)

完整代码如下;

import numpy as npimport reimport feedparserimport operatordef 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 is abusive, 0 not    return postingList,classVecdef createVocabList(data):    #创建词向量    returnList = set([])    for subdata in data:        returnList = returnList | set(subdata)    return list(returnList)def setofWords2Vec(vocabList,data):      #将文本转化为词条    returnList = [0]*len(vocabList)    for vocab in data:        if vocab in vocabList:            returnList[vocabList.index(vocab)] += 1    return returnListdef trainNB0(trainMatrix,trainCategory):        #训练，得到分类概率    pAbusive = sum(trainCategory)/len(trainCategory)    p1num = np.ones(len(trainMatrix[0]))    p0num = np.ones(len(trainMatrix[0]))    p1Denom = 2    p0Denom = 2    for i in range(len(trainCategory)):        if trainCategory[i] == 1:            p1num = p1num + trainMatrix[i]            p1Denom = p1Denom + sum(trainMatrix[i])        else:            p0num = p0num + trainMatrix[i]            p0Denom = p0Denom + sum(trainMatrix[i])    p1Vect = np.log(p1num/p1Denom)    p0Vect = np.log(p0num/p0Denom)    return p0Vect,p1Vect,pAbusivedef  classifyNB(vec2Classify,p0Vec,p1Vec,pClass1):    #分类    p0 = sum(vec2Classify*p0Vec)+np.log(1-pClass1)    p1 = sum(vec2Classify*p1Vec)+np.log(pClass1)    if p1 > p0:        return 1    else:        return 0def textParse(bigString):          #文本解析    splitdata = re.split(r'\W+',bigString)    splitdata = [token.lower() for token in splitdata if len(token) > 2]    return splitdatadef spamTest():    docList = []    classList = []    for i in range(1,26):        with open('spam/%d.txt'%i) as f:            doc = f.read()        docList.append(doc)        classList.append(1)        with open('ham/%d.txt'%i) as f:            doc = f.read()        docList.append(doc)        classList.append(0)    vocalList = createVocabList(docList)    trainList = list(range(50))    testList = []    for i in range(13):        num = int(np.random.uniform(0,len(docList))-10)        testList.append(trainList[num])        del(trainList[num])    docMatrix = []    docClass = []    for i in trainList:        subVec = setofWords2Vec(vocalList,docList[i])        docMatrix.append(subVec)        docClass.append(classList[i])    p0v,p1v,pAb = trainNB0(docMatrix,docClass)    errorCount = 0    for i in testList:        subVec = setofWords2Vec(vocalList,docList[i])        if classList[i] != classifyNB(subVec,p0v,p1v,pAb):            errorCount += 1    return errorCount/len(testList)def calcMostFreq(vocabList,fullText):    count = {}    for vocab in vocabList:        count[vocab] = fullText.count(vocab)    sortedFreq = sorted(count.items(),key=operator.itemgetter(1),reverse=True)    return sortedFreq[:30]def localWords(feed1,feed0):    docList = []    classList = []    fullText = []    numList = min(len(feed1['entries']),len(feed0['entries']))    for i in range(numList):        doc1 = feed1['entries'][i]['summary']        docList.append(doc1)        classList.append(1)        fullText.extend(doc1)        doc0 = feed0['entries'][i]['summary']        docList.append(doc0)        classList.append(0)        fullText.extend(doc0)    vocabList = createVocabList(docList)    top30Words = calcMostFreq(vocabList,fullText)    for word in top30Words:        if word[0] in vocabList:            vocabList.remove(word[0])    trainingSet = list(range(2*numList))    testSet = []    for i in range(20):        randnum = int(np.random.uniform(0,len(trainingSet)-5))        testSet.append(trainingSet[randnum])        del(trainingSet[randnum])    trainMat = []    trainClass = []    for i in trainingSet:        trainClass.append(classList[i])        trainMat.append(setofWords2Vec(vocabList,docList[i]))    p0V,p1V,pSpam = trainNB0(trainMat,trainClass)    errCount = 0    for i in testSet:        testData = setofWords2Vec(vocabList,docList[i])        if classList[i] != classifyNB(testData,p0V,p1V,pSpam):            errCount += 1    return errCount/len(testData)if __name__=="__main__":    ny = feedparser.parse('http://newyork.craigslist.org/stp/index.rss')    sf = feedparser.parse('http://sfbay.craigslist.org/stp/index.rss')    print(localWords(ny,sf))

编程技巧：
1.两个集合的并集

vocab = vocab | set(document)

2.创建元素全为零的向量

vec = [0]*10