朴素贝叶斯

朴素贝叶斯：朴素指的是统计意义上的独立，即一个特征或者单词出现的可能性和其它词没有关联。

$$p(c_i|\omega) = \frac {p(\omega|c_i)p(c_i)}{p(\omega)}$$

from numpy import *


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(dataSet):
    vocabSet = set([])  # create empty set
    for document in dataSet:
        vocabSet = vocabSet | set(document)  # union of the two sets
    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)
    return returnVec


def trainNB0(trainMatrix, trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory) / float(numTrainDocs)
    p0Num = ones(numWords);
    p1Num = ones(numWords)  # change to ones()
    p0Denom = 2.0;
    p1Denom = 2.0  # change to 2.0
    for i in range(numTrainDocs):
        if trainCategory[i] == 1:
            p1Num += trainMatrix[i]
            p1Denom += sum(trainMatrix[i])
        else:
            p0Num += trainMatrix[i]
            p0Denom += sum(trainMatrix[i])
    p1Vect = log(p1Num / p1Denom)  # change to log()
    p0Vect = log(p0Num / p0Denom)  # change to log()
    return p0Vect, p1Vect, pAbusive

def classifyNB(vec2Classify, p0Vec, p1Vec, pClass1):
    p1 = sum(vec2Classify * p1Vec) + log(pClass1)  # element-wise mult
    p0 = sum(vec2Classify * p0Vec) + log(1.0 - pClass1)
    if p1 > p0:
        return 1
    else:
        return 0

注意1：在上面的函数中，进行比较的不是$\frac {p(\omega|c_i)p(c_i)}{p(\omega)}$,而是$p(\omega|c_i)p(c_i)$。
注意2：为了防止下溢出以及浮点数舍入导致的错误，我们对乘积取自然对数。

def bagOfWords2VecMN(vocabList, inputSet):
    """
    文档词袋模型
    :param vocabList:
    :param inputSet:
    :return:
    """
    returnVec = [0] * len(vocabList)
    for word in inputSet:
        if word in vocabList:
            returnVec[vocabList.index(word)] += 1
    return returnVec


def testingNB():
    listOPosts, listClasses = loadDataSet()
    myVocabList = createVocabList(listOPosts)
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
    p0V, p1V, pAb = trainNB0(array(trainMat), array(listClasses))

    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))
    classifyResult = classifyNB(thisDoc, p0V, p1V, pAb)
    print(testEntry, 'classified as: ', classifyResult)


if __name__ == '__main__':
    testingNB()

参考书籍：
哈林顿李锐. 机器学习实战 : Machine learning in action[M]. 人民邮电出版社, 2013.