机器学习--朴素贝叶斯分类算法学习笔记

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一、基于贝叶斯决策理论的分类方法

优点：在数据较少的情况下仍然有效，可以处理多类别问题。

缺点：对于输入数据的准备方式较为敏感。

适用数据类型：标称型数据。

现在假设有一个数据集，它由两类数据构成。

用p1(c1 | x,y)表示数据点(x,y)属于类别1的概率，用p2(c2 | x,y)表示数据点(x,y)属于类别2的概率。

那么对于一个新的数据点(x,y)，可以用下面的规则来判断它的类别。

• 如果p1(c1 | x,y) > p2(c2 | x,y)，则属于类别1。
• 如果p1(c1 | x,y) < p2(c2 | x,y)，则属于类别2。

这就是朴素贝叶斯理论的核心思想，即选择具有最高概率的决策。

条件概率的计算使用贝叶斯准则。

二、使用朴素贝叶斯进行文档分类

2.1 准备数据

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]
    return postingList, classVec

def createVocabList(dataSet):
    vocabSet = set([])
    for document in dataSet:
        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 Vacabulary!" %word)
    return returnVec

2.2 训练算法

def trainNB0(trainMatrix, trainCategory):
    numTrainDocs = len(trainMatrix)
    numWords = len(trainMatrix[0])
    pAbusive = sum(trainCategory)/float(numTrainDocs)
    p0Num = ones(numWords)
    p1Num = ones(numWords)
    p0Denom = 2.0
    p1Denom = 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)
    p0Vect = log(p0Num/p0Denom)
    return p0Vect, p1Vect, pAbusive

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

2.3 测试算法

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 testingNB():
    list0Posts, listClasses = loadDataSet()
    myVacabList = createVocabList(listOPosts)
    trainMat = []
    for postinDoc in listOPosts:
        trainMat.append(setOfWords2Vec(myVacabList, postinDoc))
    p0V, p1V, pAb = trainNB0(array(trainMat), array(listClasses))
    testEntry = ['love', 'my', 'dalmation']
    thisDoc = array(setOfWords2Vec(myVacabList, testEntry))
    print("{} classified as: {}".format(testEntry, classifyNB(thisDoc, p0V, p1V, pAb)))
    testEntry = ['stupid', 'garbage']
    thisDoc = array(setOfWords2Vec(myVacabList, testEntry))
    print("{} classified as: {}".format(testEntry, classifyNB(thisDoc, p0V, p1V, pAb)))

调用 

testingNB()

输出：