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)