总结:
贝叶斯决策理论的核心思想是选择高概率对应的类别，即选择具有最高概率的决策。忽略P(X)。
运用贝叶斯定理
分类算法忽略P(X)而比较其他概率的高低，从而做出分类判断。
算法实现
下面做一个简单的留言板分类，自动判别留言类别：侮辱类和非侮辱类，分别使用1和0表示。下面来做一下这个实验。以下函数全部写在一个叫bayes.py文件中，后面的实验室通过导入bayes.py，调用里面的函数来做的。
1.加载数据集
该函数返回的是词条切分集合和类标签。
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
2.根据样本创建一个词库
下面的函数是根据上面给出来的样本数据所创建出来的一个词库。
def createVocabList(dataSet):
vocabSet = set([]) #create empty set
for document in dataSet:
vocabSet = vocabSet | set(document) #union of the two sets
return list(vocabSet)
3.统计每个样本在词库中的出现情况
下面的函数功能是把单个样本映射到词库中去，统计单个样本在词库中的出现情况，1表示出现过，0表示没有出现，函数如下：
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
4.计算条件概率和类标签概率
def trainNB0(trainMatrix,trainCategory):
numTrainDocs = len(trainMatrix)
numWords = len(trainMatrix[0])
pAbusive = sum(trainCategory)/float(numTrainDocs) #计算某个类发生的概率
p0Num = ones(numWords); p1Num = ones(numWords) #初始样本个数为1，防止条件概率为0，影响结果
p0Denom = 2.0; p1Denom = 2.0 #作用同上
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) #计算类标签为1时的其它属性发生的条件概率
p0Vect = log(p0Num/p0Denom) #计算标签为0时的其它属性发生的条件概率
return p0Vect,p1Vect,pAbusive #返回条件概率和类标签为1的概率
5.训练贝叶斯分类算法
该算法包含四个输入，vec2Classify表示待分类的样本在词库中的映射集合，p0Vec表示条件概率P(wi|c=0)，p1Vec表示条件概率P(wi|c=1)，pClass1表示类标签为1时的概率P(c=1)。
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
其中p1和p0表示的是lnp(w1|c=1)p(w2|c=1)…p(wn|c=1)∗p(c=1)和lnp(w1|c=0)p(w2|c=0)…p(wn|c=0)∗p(c=0),取对数是因为防止p(w_1|c=1)p(w_2|c=1)p(w_3|c=1)…p(w_n|c=1)多个小于1的数相乘结果值下溢。
6.文档词袋模型,修改函数setOfWords2Vec
词袋模型主要修改上面的第三个步骤，因为有的词可能出现多次，所以在单个样本映射到词库的时候需要多次统计。
def bagOfWords2VecMN(vocabList, inputSet):
returnVec = [0]*len(vocabList)
for word in inputSet:
if word in vocabList:
returnVec[vocabList.index(word)] += 1
return returnVec
7.测试函数
#step1：加载数据集和类标号
# 导入数据
listOPosts,listClasses = bayes.loadDataSet()
print(listOPosts)
print("----------------")
print(listClasses)
#[['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']]
#----------------
#[0, 1, 0, 1, 0, 1]
#step2：创建词库
# 求出总词集myVocabList
myVocabList = bayes.createVocabList(listOPosts)
myVocabList
#['mr',
# 'to',
# 'licks',
# 'worthless',
# 'buying',
# 'garbage',
# 'ate',
# 'take',
# 'not',
# 'how',
# 'please',
# 'is',
# 'steak',
# 'quit',
# 'so',
# 'has',
# 'stop',
# 'flea',
# 'problems',
# 'stupid',
# 'help',
# 'cute',
# 'posting',
# 'I',
# 'love',
# 'park',
# 'my',
# 'dog',
# 'dalmation',
# 'food',
# 'maybe',
# 'him']
#step3：计算每个样本在词库中的出现情况
# 求出训练集trainMat
trainMat=[]
for postinDoc in listOPosts:
trainMat.append(bayes.setOfWords2Vec(myVocabList, postinDoc))
trainMat
#[[0,
# 0,
# .....
# 0,
# 0],
# .....
# [0,
# 0,
# .....
# 1,
# 0]]
#step4：调用第四步函数，计算条件概率
# 训练模型
p0V,p1V,pAb = bayes.trainNB0(array(trainMat),array(listClasses))
print(p0V)
print("----------------")
print(p1V)
print("----------------")
print(pAb)
#[-2.56494936 -2.56494936 -2.56494936 -3.25809654 -3.25809654 -3.25809654
# -2.56494936 -3.25809654 -3.25809654 -2.56494936 -2.56494936 -2.56494936
# -2.56494936 -3.25809654 -2.56494936 -2.56494936 -2.56494936 -2.56494936
# -2.56494936 -3.25809654 -2.56494936 -2.56494936 -3.25809654 -2.56494936
# -2.56494936 -3.25809654 -1.87180218 -2.56494936 -2.56494936 -3.25809654
# -3.25809654 -2.15948425]
#----------------
#[-3.04452244 -2.35137526 -3.04452244 -1.94591015 -2.35137526 -2.35137526
# -3.04452244 -2.35137526 -2.35137526 -3.04452244 -3.04452244 -3.04452244
# -3.04452244 -2.35137526 -3.04452244 -3.04452244 -2.35137526 -3.04452244
# -3.04452244 -1.65822808 -3.04452244 -3.04452244 -2.35137526 -3.04452244
# -3.04452244 -2.35137526 -3.04452244 -1.94591015 -3.04452244 -2.35137526
# -2.35137526 -2.35137526]
#----------------
#0.5
#step5
# 测试模型1
testEntry = ['love', 'my', 'dalmation']
thisDoc = array(bayes.setOfWords2Vec(myVocabList, testEntry))
print(thisDoc)
print("----------------")
print (testEntry,'classified as: ',bayes.classifyNB(thisDoc,p0V,p1V,pAb))
#[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0]
#----------------
#['love', 'my', 'dalmation'] classified as: 0
# 测试模型2
testEntry = ['stupid', 'garbage']
thisDoc = array(bayes.setOfWords2Vec(myVocabList, testEntry))
print(thisDoc)
print("----------------")
print (testEntry,'classified as: ',bayes.classifyNB(thisDoc,p0V,p1V,pAb))
#[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
#----------------
#['stupid', 'garbage'] classified as: 1
#PS:拆解classifyNB(vec2Classify, p0Vec, p1Vec, pClass1)
#比较sum(p0VthisDoc)和sum(p1VthisDoc)
p0V
#array([-2.56494936, -2.56494936, -2.56494936, -3.25809654, -3.25809654,
# -3.25809654, -2.56494936, -3.25809654, -3.25809654, -2.56494936,
# -2.56494936, -2.56494936, -2.56494936, -3.25809654, -2.56494936,
# -2.56494936, -2.56494936, -2.56494936, -2.56494936, -3.25809654,
# -2.56494936, -2.56494936, -3.25809654, -2.56494936, -2.56494936,
# -3.25809654, -1.87180218, -2.56494936, -2.56494936, -3.25809654,
# -3.25809654, -2.15948425])
thisDoc
#array([0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
# 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
p0V*thisDoc
#array([-0. , -0. , -0. , -0. , -0. ,
# -3.25809654, -0. , -0. , -0. , -0. ,
# -0. , -0. , -0. , -0. , -0. ,
# -0. , -0. , -0. , -0. , -3.25809654,
# -0. , -0. , -0. , -0. , -0. ,
# -0. , -0. , -0. , -0. , -0. ,
# -0. , -0. ])
sum(p0V*thisDoc)
#-6.516193076042964
sum(p1V*thisDoc)
#-4.00960333376701