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 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

代码及数据集下载：贝叶斯

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