lrec <- read.csv("http://archive.ics.uci.edu/ml/machine-learning-databases/letter-recognition/letter-recognition.data", header=F)
# go to  http://archive.ics.uci.edu/ml/machine-learning-databases/letter-recognition/letter-recognition.names for more information on the data

summary(lrec)
library(rpart)
library(help=rpart)
help(rpart)

lrec.t1 <- rpart(V1~., data=lrec, method="class")
plot(lrec.t1)
text(lrec.t1)

require(ggplot2)
qplot(V12, binwidth=2.5, geom="histogram", data=lrec, fill=V1)

qplot(V12, binwidth=2.5, geom="histogram", position="fill", data=lrec, fill=V1)

qplot(V10, binwidth=0.5, geom="histogram", data=subset(lrec, V12 <=2.5), fill=V1)

qplot(V10, binwidth=1, geom="histogram", position="fill", data=subset(lrec, V12 <=2.5), fill=V1)

Y <- lrec$V1
X <- lrec$V2

qplot(V2, data=lrec)

gini <- function(Y) {
	ns <- table(Y)
	probs <- ns/sum(ns)
	return(sum(probs*(1-probs)))
}
gini(Y)
gini(Y[X<=1])
gini(Y[X<=2])
gini(Y[X<=3])

X <- lrec$V12
gini(Y[X<=1])
gini(Y[X>1])

gini(Y[X<=2])
gini(Y[X<=3])
gini(Y[X<=4])

entropy <- function(Y) {
	ns <- table(Y)
	probs <- ns/sum(ns)
	lprobs <- log(probs)
	lprobs[which(probs==0)] <- 0
	return(-2*sum(probs*lprobs))
}

method <- entropy
method <- gini
library(plyr)
res <- ldply(2:ncol(lrec), function(x) {
	X <- lrec[,x]
	res <- ldply((min(X)+.5):(max(X)-.5), function(i) 	{
		return(c(x=i, li=sum(X <= i), left=method(Y[X <= i]), ri=sum(X > i), right=method(Y[X > i])))
	})
	res$var <- names(lrec)[x]
	return(res)
})

res <- subset(res, (li>=20) &(ri >=20))
res[which.min(res$left+res$right),]

qplot(V11, fill=V1, data=lrec)
qplot(x, left+right, data=subset(res, var=="V11"))

qplot(var, left+right, data=res)

##############
# not particularly helpful - list of each split
summary(lrec.t1)

# inspect output object
str(lrec.t1)

lrec$tree <- predict(lrec.t1, type="class")
qplot(tree, data=lrec)
ggfluctuation(xtabs(~V1+tree, data=lrec))

lrec.t2 <- rpart(V1~., data=lrec[,1:17], method="class", control=list(cp=0.005))
plot(lrec.t2)
text(lrec.t2)
lrec$t2 <- predict(lrec.t2, type="class")
qplot(t2, data=lrec)
ggfluctuation(xtabs(~V1+t2, data=lrec))

loss <- matrix(1, ncol=26, nrow=26)
diag(loss) <- 0 # same as default

# assume it's 5 times as bad to mistake Gs and Os for each other
loss[7,13] <- 5 
loss[13,7] <- 5 

lrec.t3 <- rpart(V1~., data=lrec[,1:17], method="class", parms=list(loss=loss))
plot(lrec.t3)
text(lrec.t3)
lrec$t3 <- predict(lrec.t3, type="class")
ggfluctuation(xtabs(~V1+t3, data=lrec))