朴素贝叶斯方法（二分类）[机器学习实战]
数据链接
解析
设一个点(x,y)，对(x,y)进行分类(1,2)，我们可以设每个点分别属于两个类别的概率：
如果p1(x,y) > p2(x,y),那么类别为1
如果p1(x,y) < p2(x,y),那么类别为2
由贝叶斯概率我们有
\[p(c|x,y) = \frac {p(x,y|c)p(c)}{p(x,y)}\dots（1）
\]
对于二分类可见
$$p1 \rightarrow p(1|x,y)$$
$$p2 \rightarrow p(2|x,y)$$
观察公式一右边.
根据大数定理，当数据集具有一定规模时，我们可以以频率逼近概率。
右边的概率可以由统计而得
因此朴素贝叶斯法则主要在于对数据的统计，步骤如下：
- 分词，生成词向量空间（英文文本无需如此，中文文本可以使用jieba分词工具）
- 对于每个向量，计算其向量空间坐标(每个特征词出现次数，即词袋)
1)计算出p(c)，即每个类别出现概率
2)对于p(x,y)，可以统计出所有的单变量，再使用乘法原理即可
3)对于p(x,y|c)可以统计类别c下的所有(x,y)的出现次数
- 计算对于给定词向量的p1,p2，答案为其中值较大者
《机器学习实战中》给出了一个优化：
考虑概率很小以及一些为0的值会导致乘完出现0，所以使用对数代替p（由于对数函数是单调递增函数，因此同样很好度量）
from numpy import *
def textParse1(vec):
return 1 if vec[0] == 'spam' else 0,vec[1:];
def textParse2(vec):
return vec[0],vec[1:];
def bagOfWords2VecMN(vocabList, inputSet):
returnVec = [0]*len(vocabList)
for word in inputSet:
if word in vocabList:
returnVec[vocabList.index(word)] += 1
return returnVec
def setOfWords2VecMN(vocabList, inputSet):
returnVec = [0]*len(vocabList)
for word in inputSet:
if word in vocabList:
returnVec[vocabList.index(word)] = 1
return returnVec
def createVocabList(dataSet):
vocabSet = set([])
for document in dataSet:
vocabSet = vocabSet | set(document)
return list(vocabSet)
def tfIdf(trainMatrix,setMatrix):
n = len(trainMatrix)
m = len(trainMatrix[0])
d = [n]*n;
tb = sum(trainMatrix,axis=1)
tc = sum(setMatrix,axis=0)
b = array(tb,dtype='float')
c = array(tc,dtype='float')
weight = []
for i in range(m):
a = trainMatrix[:,i]
tf = a/b
weight.append(tf * log(d/(c[i])))
returnVec = array(weight).transpose()
return returnVec
def trainNB0(trainMatrix,trainCategory,weight):
numTrainDocs = len(trainMatrix)
numWords = len(trainMatrix[0])
pAbusive = sum(trainCategory)/float(numTrainDocs)
p0Num = ones(numWords); p1Num = ones(numWords)
p0Denom = 2.0; p1Denom = 2.0
a = 0;b = 0
a += trainMatrix[0];b += sum(trainMatrix[0])
for i in range(numTrainDocs):
if trainCategory[i] == 1:
p1Num += trainMatrix[i]*weight[i]
p1Denom += sum(trainMatrix[i]*weight[i])
else:
p0Num += trainMatrix[i]*weight[i]
p0Denom += sum(trainMatrix[i]*weight[i])
p1Vect = log(p1Num/p1Denom)
p0Vect = log(p0Num/p0Denom)
return p0Vect,p1Vect,pAbusive
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 spamTest():
trainFile = './train.csv'
testFile = './test.csv'
import csv
docList=[]; classList = []; fullText =[]
in1 = open(trainFile);in1.readline()
fr1 = csv.reader(in1)
trainData = [row for row in fr1]
#prepare trainData
n = 0
for i in trainData:
label,wordList = textParse1(i)
docList.append(wordList)
classList.append(label)
n += 1
vocabList = createVocabList(docList)
trainMat = [];trainClasses = []
setMat = []
for docIndex in range(n):
trainMat.append(bagOfWords2VecMN(vocabList,docList[docIndex]))
setMat.append(setOfWords2VecMN(vocabList,docList[docIndex]))
trainClasses.append(classList[docIndex])
#traiing by bayes
weight = tfIdf(array(trainMat),array(setMat))
p0V,p1V,pSpam = trainNB0(array(trainMat),array(trainClasses),array(weight))
#prepare testData
in2 = open(testFile);in2.readline()
fr2 = csv.reader(in2)
fw = csv.writer(open('predict.csv', 'w'))
name = ['SmsId','Label']
fw.writerow(name)
testData = [row for row in fr2]
#predict testData
for i in testData:
id,wordList = textParse2(i)
wordVector = bagOfWords2VecMN(vocabList, wordList)
fw.writerow([id,'spam' if classifyNB(array(wordVector),p0V,p1V,pSpam) else 'ham'])
#print 'fianl point'
