数据分析与挖掘 - R语言：贝叶斯分类算法（案例一）

一个简单的例子！
环境：CentOS6.5
Hadoop集群、Hive、R、RHive，具体安装及调试方法见博客内文档。

名词解释：

先验概率：由以往的数据分析得到的概率, 叫做先验概率。

后验概率：而在得到信息之后，再重新加以修正的概率叫做后验概率。贝叶斯分类是后验概率。

贝叶斯分类算法步骤：

第一步：准备阶段

该阶段为朴素贝叶斯分类做必要的准备。主要是依据具体情况确定特征属性，并且对特征属性进行适当划分。然后就是对一部分待分类项进行人工划分，以确定训练样本。

这一阶段的输入是所有的待分类项，输出特征属性和训练样本。分类器的质量很大程度上依赖于特征属性及其划分以及训练样本的质量。

第二步：分类器训练阶段

主要工作是计算每个类别在训练样本中出现频率以及每个特征属性划分对每个类别的条件概率估计。输入是特征属性和训练样本，输出是分类器。

第三步：应用阶段

这个阶段的任务是使用分类器对待分类项进行分类，其输入是分类器和待分类项，输出是待分类项与类别的映射关系。

特别要注意的是：朴素贝叶斯的核心在于它假设向量的所有分量之间是独立的。

实例编写R脚本：

#!/usr/bin/Rscript
#构造训练集
data <- matrix(c("sunny","hot","high","weak","no",
                 "sunny","hot","high","strong","no",
                 "overcast","hot","high","weak","yes",
                 "rain","mild","high","weak","yes",
                 "rain","cool","normal","weak","yes",
                 "rain","cool","normal","strong","no",
                 "overcast","cool","normal","strong","yes",
                 "sunny","mild","high","weak","no",
                 "sunny","cool","normal","weak","yes",
                 "rain","mild","normal","weak","yes",
                 "sunny","mild","normal","strong","yes",
                 "overcast","mild","high","strong","yes",
                 "overcast","hot","normal","weak","yes",
                 "rain","mild","high","strong","no"),
                 byrow = TRUE,
                 dimnames = list(day = c(),condition = c("outlook","temperature","humidity","wind","playtennis")),
                 nrow=14,
                 ncol=5);  

#计算先验概率
prior.yes = sum(data[,5] == "yes") / length(data[,5]);
prior.no  = sum(data[,5] == "no")  / length(data[,5]);  

#贝叶斯模型
naive.bayes.prediction <- function(condition.vec) {
    # Calculate unnormlized posterior probability for playtennis = yes.
    playtennis.yes <-
        sum((data[,1] == condition.vec[1]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(outlook = f_1 | playtennis = yes)
        sum((data[,2] == condition.vec[2]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(temperature = f_2 | playtennis = yes)
        sum((data[,3] == condition.vec[3]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(humidity = f_3 | playtennis = yes)
        sum((data[,4] == condition.vec[4]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(wind = f_4 | playtennis = yes)
        prior.yes; # P(playtennis = yes)  

    # Calculate unnormlized posterior probability for playtennis = no.
    playtennis.no <-
        sum((data[,1] == condition.vec[1]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(outlook = f_1 | playtennis = no)
        sum((data[,2] == condition.vec[2]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(temperature = f_2 | playtennis = no)
        sum((data[,3] == condition.vec[3]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(humidity = f_3 | playtennis = no)
        sum((data[,4] == condition.vec[4]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(wind = f_4 | playtennis = no)
        prior.no; # P(playtennis = no)  

    return(list(post.pr.yes = playtennis.yes,
            post.pr.no  = playtennis.no,
            prediction  = ifelse(playtennis.yes >= playtennis.no, "yes", "no")));
}  

#预测
naive.bayes.prediction(c("overcast", "mild", "normal", "weak"));  

结果：

$post.pr.yes
[1] 0.05643739

$post.pr.no
[1] 0

$prediction
[1] "yes"

预测结果为：yes