决策树（ID3,C4.5,C5.0,CART算法）以及条件推理决策树R语言实现

### 10.2.1 ID3算法基本原理  ###
mtcars2 <- within(mtcars[,c('cyl','vs','am','gear')], {
  am <- factor(am, labels = c("automatic", "manual"))
  vs <- factor(vs, labels = c("V", "S"))
  cyl  <- ordered(cyl)
  gear <- ordered(gear)
})
 
table(mtcars2$am) # 查看因变量的类别数量
 
I_am <- -19/32*log2(19/32)-13/32*log2(13/32) # 计算因变量的信息熵
I_am
 
 
# 自定义函数计算信息熵、信息增益
information_gain <- function(x,y){
  m1 <- matrix(table(y))
  entropy_y <- sum(-(m1/sum(m1))*log2(m1/sum(m1)))
  t <- table(x,y)
  m <- matrix(t,length(unique(x)),length(unique(y)),
              dimnames = list(levels(x),levels(y)))
  freq <- -rowSums((m/rowSums(m))*log2(m/rowSums(m)))
  entropy <- sum(rowSums(