简介
贝叶斯分类算法是一大类分类算法的总称
贝叶斯分类算法以样本可能属于某类的概率来作为分类依据
朴素贝叶斯分类算法是贝叶斯分类算法中最简单的一种
注:朴素的意思是条件概率独立性
此处要想真正理解,需要有概率论的基础知识
P(A|x1x2x3x4)=p(A|x1)*p(A|x2)p(A|x3)p(A|x4)则为条件概率独立
P(xy|z)=p(xyz)/p(z)=p(xz)/p(z)*p(yz)/p(z)
算法
如果一个事物在一些属性条件发生的情况下,事物属于A的概率大于属于B的概率,则判定事物属于A
公式
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步骤
1、分解各类先验样本数据中的特征
2、计算各类数据中,各特征的条件概率
(比如:特征1出现的情况下,属于A类的概率p(A|特征1),属于B类的概率p(B|特征1),属于C类的概率p(C|特征1)......)
3、分解待分类数据中的特征(特征1、特征2、特征3、特征4......)
4、计算各特征的各条件概率的乘积,如下所示:
判断为A类的概率:p(A|特征1)*p(A|特征2)*p(A|特征3)*p(A|特征4).....
判断为B类的概率:p(B|特征1)*p(B|特征2)*p(B|特征3)*p(B|特征4).....
判断为C类的概率:p(C|特征1)*p(C|特征2)*p(C|特征3)*p(C|特征4).....
5、结果中的最大值就是该样本所属的类别
代码
object NaiveBayes {
/**
* 先验数据
*/
def dataSet(): (Array[Array[String]], Array[Int]) ={
val dataList = Array(Array("my", "dog", "has", "flea", "problems", "help", "please"),
Array("maybe", "not", "take", "him", "to", "dog", "park", "stupid"),
Array("my", "dalmation", "is", "so", "cute", "I", "love", "him"),
Array("stop", "posting", "stupid", "worthless", "garbage"),
Array("mr", "licks", "ate", "my", "steak", "how", "to", "stop", "him"),
Array("quit", "buying", "worthless", "dog", "food", "stupid"))
//分类
val dataType=Array(0, 1, 0, 1, 0, 1)
(dataList,dataType)
}
/**
* 设置分类
* @param dataList 数据集合
* @param inputSet 输入类型
*/
def setWordsType(dataList:Array[String],inputSet:Array[String]): Array[Int] ={
/***
* 先验数据
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
*
*
*/
val returnList=new Array[Int](dataList.length)
val dataIndex = dataList.zipWithIndex
for(word <- inputSet){
if(dataList.contains(word)){
//println(dataIndex.filter(_._1 == word).toBuffer)
//与inputSet数据相等的为1
returnList(dataIndex.filter(_._1 == word)(0)._2) = 1
}else {
println("the word: %s is not in my Vocabulary!\n",word)
}
}
returnList
}
/**
* 先验数据
* @param trainData 训练数据
* @param trainType 训练类型
*/
def trainSet(trainData:Array[Array[Int]],trainType:Array[Int]): (Array[Double], Array[Double], Double) ={
/**
* 0 = {int[32]@797}
* 1 = {int[32]@798}
* 2 = {int[32]@799}
* 3 = {int[32]@800}
* 4 = {int[32]@801}
* 5 = {int[32]@802}
*
* ArrayBuffer(0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
* ArrayBuffer(0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0)
* ArrayBuffer(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
* ArrayBuffer(0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
* ArrayBuffer(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
* ArrayBuffer(1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
*
*/
val trainLength=trainData.length
val wordsNum=trainData(0).length
//每个分类的概率,这里分类只有0/1,所以只返回一个类别1的概率
val pType=trainType.sum/trainLength.toDouble
var p0Num=Array.fill(wordsNum)(1)
var p1Num=Array.fill(wordsNum)(1)
var p0Denom = 2.0
var p1Denom = 2.0
/**
* for 循环 0~5
* p0Denom:2.0
p1Denom:2.0
p0Denom:9.0
p1Denom:2.0
p0Denom:9.0
p1Denom:10.0
p0Denom:17.0
p1Denom:10.0
p0Denom:17.0
p1Denom:15.0
p0Denom:26.0
p1Denom:15.0
*/
for (i <- 0 until trainLength) {
if (trainType(i) == 1) {
var cnt = 0
//
p1Num = p1Num.map { x =>
val v = x + trainData(i)(cnt)
cnt += 1
v
}
p1Denom += trainData(i).sum
} else {
var cnt = 0
p0Num = p0Num.map { x =>
val v = x + trainData(i)(cnt)
cnt += 1
v
}
p0Denom += trainData(i).sum
}
}
/**
* p1Num
* ArrayBuffer(2, 2, 3, 3, 2, 4, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1)
* p1Denom 21.0
*
* p0Num
* ArrayBuffer(1, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2)
* p0Denom 26.0
*/
(p1Num.map(x => Math.log(x / p1Denom)), p0Num.map(x => Math.log(x / p0Denom)), pType)
}
def classifyNB(vec2Classify: Array[Int], p0Vec: Array[Double], p1Vec: Array[Double], pClass1: Double): Int = {
var cnt = 0
val p1 = vec2Classify.map { x =>
val v = x * p1Vec(cnt)
cnt += 1
v
}.sum + math.log(pClass1)
cnt = 0
val p0 = vec2Classify.map { x =>
val v = x * p0Vec(cnt)
cnt += 1
v
}.sum + math.log(1.0 - pClass1)
//log(p(w/c0)p(c0))=log(p(w/c0))+log(p(c0))= sum(vec2Classify * p0Vec) + log(1.0 - pClass1)
if (p1 > p0) 1 else 0
}
def main(args: Array[String]): Unit = {
val DataSet = dataSet()
val listOPosts = DataSet._1
val listClasses = DataSet._2
val myVocabList = listOPosts.reduce((a1, a2) => a1.++:(a2)).distinct
/**
* myVocabList的数据
* ArrayBuffer(quit, buying, worthless, dog, food, stupid, mr, licks, ate, my, steak, how, to, stop, him, posting, garbage, dalmation, is, so, cute, I, love, maybe, not, take, park, has, flea, problems, help, please)
*/
var trainMat = new ArrayBuffer[Array[Int]](listOPosts.length)
listOPosts.foreach(postinDoc => trainMat.append(setWordsType(myVocabList, postinDoc)))
//训练集
val p = trainSet(trainMat.toArray, listClasses)
val p0V = p._2
val p1V = p._1
val pAb = p._3
val testEntry = Array("love", "my", "dalmation")
val thisDoc = setWordsType(myVocabList, testEntry)
println(testEntry.mkString(",") + " classified as: " + classifyNB(thisDoc, p0V, p1V, pAb))
val testEntry2 = Array("stupid", "garbage")
val thisDoc2 = setWordsType(myVocabList, testEntry2)
println(testEntry2.mkString(",") + " classified as: " + classifyNB(thisDoc2, p0V, p1V, pAb))
}
}
posted @
2018-09-09 18:38
Dlimeng
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