###########
## Neural Nets introduction code.
###########

###########
## First generate some fake data to illustrate the ideas.
## Probabilities that Y = 1 are given by a sin curve
## A 0/1 observation is then generated with the sin curve probabilities
###########

x <- seq(0,1,length=1500)
y <- rbinom(1500,1,(sin(x * 2 * 3.14 * 3) * .5) + .5)
plot(x,(sin(x * 2 * 3.14 * 3) * .5) + .5)


###########
## This code sets up a graph sheet with a 3 by 3 grid of images
###########

win.graph()
par(mfrow=c(3,3))



for(i in 0:8){
## This line fits the nueral network with "i" units in the hidden layer.
nnet.out <- nnet(x,y,size=i,entropy=T,decay=0.001,skip=T)

## Now print out the value of the fitting criterion.
## The analog of the sums of squares error in regression

print(nnet.out$value)
plot(x,y)

## Now predict the probabilities from the trained network
##  Hopefully they should be close to a sin curve.
 
points(x,predict.nnet(nnet.out,matrix(x,ncol=1)),col=i+1)
}



##################################
## Now use neural nets on the internet demographics dataset
##################################

win.graph()
 
m1 <- max(uva$Age)
m2 <- max(uva$Inc)
prediction.grid <- expand.grid(seq(5,80,length=40)/m1,seq(1000,150000,length=40)/m2)
names(prediction.grid) <- c("Age","Income")
prediction.grid <- as.data.frame(prediction.grid)
par(mfrow=c(3,3))
for(i in 1:9){
nnet.out <- nnet(
	cbind(uva$Age/m1, uva$Inc/m2),
		as.factor(uva$Newbie),size=i,skip=T,decay=.0005,entropy=T)
print(nnet.out$value)
persp(seq(5,80,length=40)/m1, seq(1000,150000,length=40)/m2,
matrix(predict.nnet(nnet.out,prediction.grid),ncol=40))
}



#################################
## Add some gold to this data to see how successful the nnet is in 
## identifying it.
#################################

fakedata <- uva


fakedata[1:1000,1] <- 1
fakedata[1:1000,2] <- sample(c(35:45),1000,replace=T)
fakedata[1:1000,11] <- sample(c(35000:45000),1000,replace=T)
 
m1 <- max(fakedata$Age)
m2 <- max(fakedata$Inc)
prediction.grid <- expand.grid(seq(5,80,length=40)/m1,seq(1000,150000,length=40)/m2)
names(prediction.grid) <- c("Age","Income")
prediction.grid <- as.data.frame(prediction.grid)
par(mfrow=c(3,3))
for(i in 1:9){
nnet.out <- nnet(
cbind(fakedata$Age/m1, fakedata$Inc/m2),
as.factor(fakedata$Newbie),size=i,skip=T,entropy=T,decay=0.0001)
print(nnet.out$value)
persp(seq(5,80,length=40)/m1, seq(1000,150000,length=40)/m2,
matrix(predict.nnet(nnet.out,prediction.grid),ncol=40))}