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
以及条件概率为
Xl表示第l个特征，由于特征条件独立的假设，可得
条件概率的极大似然估计为
根据贝叶斯定理
则由上式可以得到条件概率P(Y=ck|X=x)。
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
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。
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：
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
完整代码如下;
import numpy as np
import re
import feedparser
import operator
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 is abusive, 0 not
return postingList,classVec
def 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 returnList
def 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,pAbusive
def 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 0
def textParse(bigString): #文本解析
splitdata = re.split(r'\W+',bigString)
splitdata = [token.lower() for token in splitdata if len(token) > 2]
return splitdata
def 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
代码及数据集下载：贝叶斯
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