#===================
# IMPURITY MEASURES
#===================

n <- 1000
misclass <- entropy <- gini <- rep(0,n)
for (i in 1:n){
    p <- i/n
    misclass[i] <- min(p, 1-p)
    entropy[i] <- - p * log(p) - (1-p)*log(1-p)
    gini[i] <- p*(1-p)
}

par(bg="lightblue", mar=rep(5,4), mfrow=c(1,1))
plot(x=(1:n)/n, y=entropy, ann=T, type="l",
    main="", xlab="p", ylab="impurity", lty=1, lwd=2, col="blue")
lines(x=(1:n)/n, y=misclass, lty=1, lwd=2, col="red")
lines(x=(1:n)/n, y=gini, lty=1, lwd=2, col="purple")
segments(0.5, -.02, .5, -2*0.5*log(0.5), lty=2)
text(x=.56, y=.27, "Gini")
text(x=.67, y=.42, "Misclass")
text(x=.79, y=.6, "Entropy")



# ======================
# Splitting Illustration??
# ======================