基于概率论的分类方法：朴素贝叶斯

 

前两章我们要求分类器做出决策，给出“该数据实例属于哪一类”这类问题的明确答案。

不过，分类器有时会产生错误结果，这时可以要求分类器给出一个最优的类别猜测结果，同时给出这个猜测的概率估计值。

假设有一个数据集，由两类数据组成，如下所示

用p1(x,y)表示数据点(x,y)属于类别1(圆点)的概率

用p2(x,y)表示数据点(x,y)属于类别2(三角形点)的概率

那么对于一个新的数据点(x,y)，可以用下面的规则判断它的类别：

if p1(x,y)>p2(x,y),then class1

if p2(x,y)>p1(x,y),then class2

也就是说，选择高概率对应的类别。这就是贝叶斯决策理论的核心思想，即选择具有最高概率的决策。

 

这里需要用到条件概率公式，来源百度百科

 

朴素贝叶斯是用于文档分类的常用算法。我们可以观察文档中出现的词，并把每个词的出现或不出现作为一个特征，这样得到的特征数目就会跟词汇表中得到的特征数目一样多。

朴素贝叶斯分类器中的另一个假设是，每个特征同等重要。这里即单词出现的可能性与它和其他单词相邻没有关系。

 

一个例子，使用Python进行文本分类。

1.词表到向量的转换函数

# 返回进行词条切分后的文档集合和人工标注的类别标签的集合
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代表存在侮辱性的文字，0代表不存在
    return postingList, classVec


# 统计所有文档中出现的词条
def createVocabList(dataSet):
    vocabSet = set([])
    for document in dataSet:
        # 创建两个集合的并集
        vocabSet = vocabSet | set(document)
    return list(vocabSet)


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)
            # 输出文档向量，向量的每一元素为1或0
            # 分别表示词汇表中的单词在输入文档中是否出现
    return returnVec

测试运行

 

2.训练算法：从词向量计算概率

伪代码：

计算每个类别中的文档数目

对每篇训练文档：

　　对每个类别：

　　　　如果词条出现在文档中->增加该词条的计数值

　　　　增加所有词条的计数值

　　对每个类别：

　　　　对每个词条：

　　　　　　将该词条出现的数目除以总词条数目得到条件概率

返回每个类别的条件概率

# 朴素贝叶斯分类器训练函数
def trainNB0(trainMatrix, trainCategory):
    # 获取文档总数
    numTrainDocs = len(trainMatrix)
    # 获取词条向量的长度
    numWords = len(trainMatrix[0])
    # 类1占所有文档的比例
    pAbusive = sum(trainCategory) / float(numTrainDocs)
    # p0Num=zeros(numWords)
    # p1Num=zeros(numWords)
    # p0Denom=0.0
    # p1Denom=0.0
    p0Num = ones(numWords)
    p1Num = ones(numWords)
    p0Denom = 2.0
    p1Denom = 2.0
    for i in range(numTrainDocs):
        if trainCategory[i] == 1:
            # 向量加法，统计所有类别为1的词条向量中各个词条出现的次数
            p1Num += trainMatrix[i]
            # 统计类别为1的词条向量中出现的所有词条的总数
            # 即统计类1所有文档中出现单词的数目
            p1Denom += sum(trainMatrix[i])
        else:
            p0Num += trainMatrix[i]
            p0Denom += sum(trainMatrix[i])
    # 利用NumPy数组计算p(wi|c1)
    # p1Vect = p1Num / p1Denom
    # p0Vect = p0Num / p0Denom
    p1Vect = log(p1Num / p1Denom)
    p0Vect = log(p0Num / p0Denom)
    return p0Vect, p1Vect, pAbusive

测试运行

 

3.测试算法：根据现实情况修改分类器

 （1）

p0Num=ones(numWords);
p1Num=ones(numWords)
p0Denom=2.0;
p1Denom=2.0

（2）解决下溢出：用ln(f(x))替换f(x)

分类函数

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

测试

listOPosts, listClasses = loadDataSet()
    myVocabList = createVocabList(listOPosts)
    print(myVocabList)
    print(listOPosts[0])
    print(setOfWords2Vec(myVocabList, listOPosts[0]))
    print(listOPosts[3])
    print(setOfWords2Vec(myVocabList, listOPosts[3]))
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
    p0V, p1V, pAb = trainNB0(trainMat, listClasses)
    print(p0V)
    print(p1V)
    print(pAb)

    testEntry = ['love', 'my', 'dalmation']
    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))

 

4.准备词袋模型

 

def bagOfWords2VecMN(vocabList, inputSet):
    returnVec = [0] * len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] += 1
    return returnVec

 

5.使用朴素贝叶斯过滤垃圾邮件

def textParse(bigString):
    import re
    listOfTokens = re.split(r'W*', bigString)
    return [tok.lower() for tok in listOfTokens if len(tok) > 2]


def spanTest():
    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 = list(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('classification error')
    print('the error rate is: ', float(errorCount) / len(testSet))

运行，每次结果不尽相同

6.使用朴素贝叶斯分类器从个人广告中获取区域倾向

 需要安装feedparser包

（1）收集数据：导入RSS源

RSS源分类器及高频词去除函数

# 实例：使用朴素贝叶斯分类器从个人广告中获取区域倾向
# RSS源分类器及高频词去除函数
def calcMostFreq(vocabList, fullText):
    freqDict = {}
    for token in vocabList:
        # 计算每个单词出现的次数
        freqDict[token] = fullText.count(token)
    # 按照逆序从大到小对freqDict进行排序
    sortedFreq = sorted(freqDict.items(), key=operator.itemgetter(1), reverse=True)
    # 返回前30个高频单词
    return sortedFreq[:30]


def localWords(feed1, feed0):
    docList = [];
    classList = [];
    fullText = []
    # 求两个源长度较小的那个长度值
    minLen = min(len(feed1['entries']), len(feed0['entries']))
    for i in range(minLen):
        # 每次访问一条RSS源
        wordList = textParse(feed1['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(1)
        wordList = textParse(feed0['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(0)
    vocabList = createVocabList(docList)
    # 得到在两个源中出现次数最高的30个单词
    top30Words = calcMostFreq(vocabList, fullText)
    for pairW in top30Words:
        if pairW[0] in vocabList:
            # 从词汇表中把高频的30个词移除
            vocabList.remove(pairW[0])
    trainingSet = list(range(2 * minLen))
    testSet = []
    # 从两个rss源中挑出20条作为测试文本
    for i in range(20):
        randIndex = int(random.uniform(0, len(trainingSet)))
        testSet.append(trainingSet[randIndex])
        del (trainingSet[randIndex])
        trainMat = []
        trainClasses = []
        # 训练文本
        for docIndex in trainingSet:
            trainMat.append(bagOfWords2VecMN(vocabList, docList[docIndex]))
            trainClasses.append(classList[docIndex])
        p0V, p1V, pSpam = trainNB0(array(trainMat), array(trainClasses))
        errorCount = 0
        # 计算分类，和错误率
        for docIndex in testSet:
            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

（2）分析数据：显示地狱相关的用词

最具表征性的词汇显示函数

def getTopWords(ny, sf):  # 返回频率大于某个阈值的所有值
    vocabList, p0V, p1V = localWords(ny, sf)
    topNY = []
    topSF = []
    for i in range(len(p0V)):
        if p0V[i] > -4.5:
            topSF.append((vocabList[i], p0V[i]))
        if p1V[i] > -4.5:
            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")
    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")
    for item in sortedNY:
        print(item[0])

完整代码

from numpy import *
import feedparser
import operator


# 返回进行词条切分后的文档集合和人工标注的类别标签的集合
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代表存在侮辱性的文字，0代表不存在
    return postingList, classVec


# 统计所有文档中出现的词条
def createVocabList(dataSet):
    vocabSet = set([])
    for document in dataSet:
        # 创建两个集合的并集
        vocabSet = vocabSet | set(document)
    return list(vocabSet)


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)
            # 输出文档向量，向量的每一元素为1或0
            # 分别表示词汇表中的单词在输入文档中是否出现
    return returnVec


def bagOfWords2VecMN(vocabList, inputSet):
    returnVec = [0] * len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] += 1
    return returnVec


# 朴素贝叶斯分类器训练函数
def trainNB0(trainMatrix, trainCategory):
    # 获取文档总数
    numTrainDocs = len(trainMatrix)
    # 获取词条向量的长度
    numWords = len(trainMatrix[0])
    # 类1占所有文档的比例
    pAbusive = sum(trainCategory) / float(numTrainDocs)
    # p0Num=zeros(numWords)
    # p1Num=zeros(numWords)
    # p0Denom=0.0
    # p1Denom=0.0
    p0Num = ones(numWords)
    p1Num = ones(numWords)
    p0Denom = 2.0
    p1Denom = 2.0
    for i in range(numTrainDocs):
        if trainCategory[i] == 1:
            # 向量加法，统计所有类别为1的词条向量中各个词条出现的次数
            p1Num += trainMatrix[i]
            # 统计类别为1的词条向量中出现的所有词条的总数
            # 即统计类1所有文档中出现单词的数目
            p1Denom += sum(trainMatrix[i])
        else:
            p0Num += trainMatrix[i]
            p0Denom += sum(trainMatrix[i])
    # 利用NumPy数组计算p(wi|c1)
    # p1Vect = p1Num / p1Denom
    # p0Vect = p0Num / p0Denom
    p1Vect = log(p1Num / p1Denom)
    p0Vect = log(p0Num / p0Denom)
    return p0Vect, p1Vect, 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 textParse(bigString):
    import re
    listOfTokens = re.split(r'W*', bigString)
    return [tok.lower() for tok in listOfTokens if len(tok) > 2]


def spanTest():
    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 = list(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('classification error')
    print('the error rate is: ', float(errorCount) / len(testSet))


# 实例：使用朴素贝叶斯分类器从个人广告中获取区域倾向
# RSS源分类器及高频词去除函数
def calcMostFreq(vocabList, fullText):
    freqDict = {}
    for token in vocabList:
        # 计算每个单词出现的次数
        freqDict[token] = fullText.count(token)
    # 按照逆序从大到小对freqDict进行排序
    sortedFreq = sorted(freqDict.items(), key=operator.itemgetter(1), reverse=True)
    # 返回前30个高频单词
    return sortedFreq[:30]


def localWords(feed1, feed0):
    docList = [];
    classList = [];
    fullText = []
    # 求两个源长度较小的那个长度值
    minLen = min(len(feed1['entries']), len(feed0['entries']))
    for i in range(minLen):
        # 每次访问一条RSS源
        wordList = textParse(feed1['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(1)
        wordList = textParse(feed0['entries'][i]['summary'])
        docList.append(wordList)
        fullText.extend(wordList)
        classList.append(0)
    vocabList = createVocabList(docList)
    # 得到在两个源中出现次数最高的30个单词
    top30Words = calcMostFreq(vocabList, fullText)
    for pairW in top30Words:
        if pairW[0] in vocabList:
            # 从词汇表中把高频的30个词移除
            vocabList.remove(pairW[0])
    trainingSet = list(range(2 * minLen))
    testSet = []
    # 从两个rss源中挑出20条作为测试文本
    for i in range(20):
        randIndex = int(random.uniform(0, len(trainingSet)))
        testSet.append(trainingSet[randIndex])
        del (trainingSet[randIndex])
        trainMat = []
        trainClasses = []
        # 训练文本
        for docIndex in trainingSet:
            trainMat.append(bagOfWords2VecMN(vocabList, docList[docIndex]))
            trainClasses.append(classList[docIndex])
        p0V, p1V, pSpam = trainNB0(array(trainMat), array(trainClasses))
        errorCount = 0
        # 计算分类，和错误率
        for docIndex in testSet:
            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):  # 返回频率大于某个阈值的所有值
    vocabList, p0V, p1V = localWords(ny, sf)
    topNY = []
    topSF = []
    for i in range(len(p0V)):
        if p0V[i] > -4.5:
            topSF.append((vocabList[i], p0V[i]))
        if p1V[i] > -4.5:
            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")
    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")
    for item in sortedNY:
        print(item[0])


if __name__ == '__main__':
    listOPosts, listClasses = loadDataSet()
    myVocabList = createVocabList(listOPosts)
    print(myVocabList)
    print(listOPosts[0])
    print(setOfWords2Vec(myVocabList, listOPosts[0]))
    print(listOPosts[3])
    print(setOfWords2Vec(myVocabList, listOPosts[3]))
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
    p0V, p1V, pAb = trainNB0(trainMat, listClasses)
    print(p0V)
    print(p1V)
    print(pAb)

    testEntry = ['love', 'my', 'dalmation']
    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))

    spanTest()
    spanTest()

    ny = feedparser.parse('http://newyork.craigslist.org/stp/index.rss')
    sf = feedparser.parse('http://sfbay.craigslist.org/stp/index.rss')
    # (ny, sf)
    getTopWords(ny, sf)