####
#
# train simple NNet with just one neuron

nu <- 0.5 
x  <- matrix(c(1,0,0,1,1,0,1,0,1,1,1,1), 4, 3, byrow=T)
y  <- matrix(c(0,0,0,1), 4,1)
w  <- matrix(1,3,1)

for( k in 1:1000 ) {
      i <- sample(4,1)
      j <- sample(3,1)
      if( w[1] + w[2]*x[i, 2] + w[3]*x[i, 3] >= 0 )
         hy<-1
      else
         hy<-0
      dw <- nu*(y[i] - hy)* x[i, j]
      w[j] <- w[j] + dw
}

###
#
# fit NNet for olive data

library(nnet)

attach(olives)

on<-nnet(cbind(olives[,8], olives[,11]), olives[,2],  
                  data=olives, size=3, decay=0.0005, linout=T, skip=T, maxit=1000)
                                                     
table(Region, round(predict(on)))

plot(linoleic, eicosenoic, col=round(predict(on)), pch=olives$Region)

rast.x<- rep(seq(min(linoleic), max(linoleic),length=75), 75)
rast.y<- rep(seq(min(eicosenoic), max(eicosenoic), length=75), rep(75, 75))

pred<-predict(on, newdata=cbind(rast.x, rast.y))
points(rast.x, rast.y, col=round(pred), pch="+")