朴素贝叶斯法大概是最简单的一种挖掘算法了，《统计学习方法》在第四章做了很详细的叙述，无非是对于输入特征x，利用通过学习得到的模型计算后验概率分布，将后验概率最大的分类作为输出。
根据贝叶斯定理，后验概率P(Y=cx | X=x) = 条件概率P(X=x | Y=cx) * 先验概率P(Y = ck) / P(X=x)，取P(X=x | Y=cx) * P(Y = ck)最大的分类作为输出。
#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]);
#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("rain", "hot", "high", "strong"));
naive.bayes.prediction(c("sunny", "mild", "normal", "weak"));
naive.bayes.prediction(c("overcast", "mild", "normal", "weak"));