simuldata <- function(m,m2=m){
z<- c(rbinom(1,m,1/3))
z[2]<-rbinom(1,m-z[1],1/2)
v<- c(rbinom(1,m,1/3))
v[2]<-rbinom(1,m-v[1],1/2)
x <- c(rnorm(z[1])/2+2, rnorm(z[2])+6, rnorm(m-z[1]-z[2])/2+3, rnorm(v[1])/1+4, rnorm(v[2])/3+1,
rnorm(m-v[1]-v[2])+8)
y <- c(rnorm(z[1])/2+1, rnorm(z[2])/3+1, rnorm(m-z[1]-z[2])/2+1.5, rnorm(v[1])/3+2, rnorm(v[2])/3+2,
rnorm(m-v[1]-v[2])/3+1.5)
typ <- c(rep("blue",m),rep("red",m2))
return(data.frame(x,y,typ))
}

lerndaten <- simuldata(200)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

dev.print(pdf,file="lerndaten.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern1.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern2.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern2.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern3.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern4.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern5.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern6.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern7.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern8.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern9.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern10.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern11.pdf")

punkt <- simuldata(1)[runif(1,1,2.99999999),]
points(punkt$x,punkt$y,pch=20,cex=2)
dev.print(pdf,file="lern12.pdf")

points(punkt$x,punkt$y,pch=20,col=as.vector(punkt$typ))
dev.print(pdf,file="lern13.pdf")

plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

blaudichte <- function(x) {
.3333*dnorm(x[1],2,.5)*dnorm(x[2],1,.5)+
.3333*dnorm(x[1],6,1)*dnorm(x[2],1,1/3)+
.3333*dnorm(x[1],3,0.5)*dnorm(x[2],1.5,.5)
}

rotdichte <- function(x) {
.3333*dnorm(x[1],4,1)*dnorm(x[2],2,1/3)+
.3333*dnorm(x[1],1,1/3)*dnorm(x[2],2,1/3)+
.3333*dnorm(x[1],8,1)*dnorm(x[2],1.5,1/3)
}

library(MASS)
L <- lda(typ~.,lerndaten)
a <- rep(1:100/10,90)
b <- rep(1:90/30,rep(100,90))
P <- predict(L,data.frame("x"=a,"y"=b),type="probs")
points(a,b,pch=46,col=as.vector(P$class))

contour(1:100/10,1:90/30,matrix(P[[2]][,1]-P[[2]][,2],100),
add=T,levels=0,labex=c())

dev.print(pdf,file="lda.pdf")

Q<- qda(typ~.,lerndaten)
P2<-predict(Q,data.frame("x"=a,"y"=b),type="probs")$class
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
points(a,b,pch=46,col=as.vector(P2))

Pp<-predict(Q,data.frame("x"=a,"y"=b),type="probs")
contour(1:100/10,1:90/30,matrix(Pp[[2]][,1]-Pp[[2]][,2],100),
add=T,levels=0,labex=0)

dev.print(pdf,file="qda.pdf")

library(class)
knn(lerndaten[,1:2],data.frame("x"=a,"y"=b),lerndaten$typ,k=1)->einnachb
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ),pch=20)
points(a,b,pch=42,col=as.vector(einnachb))

dev.print(pdf,file="knn1.pdf")

knn(lerndaten[,1:2],data.frame("x"=a,"y"=b),lerndaten$typ,k=5)->fuenfnachb
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ),pch=20)
points(a,b,pch=42,col=as.vector(fuenfnachb))

dev.print(pdf,file="knn5.pdf")

knn(lerndaten[,1:2],data.frame("x"=a,"y"=b),lerndaten$typ,k=20)->zwoelfnachb
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ),pch=20)
points(a,b,pch=42,col=as.vector(zwoelfnachb))
points(lerndaten$x,lerndaten$y,col=lerndaten$typ)

dev.print(pdf,file="knn12.pdf")

library(nnet)
nnet(typ~x+y,lerndaten,size=5,maxit=1000)->netz
pnn<-predict(netz,data.frame("x"=a,"y"=b))
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
#points(lerndaten$x,lerndaten$y,col=lerndaten$typ,pch=20)
contour(1:100/10,1:90/30,matrix(pnn,100),
add=T,levels=0.5,labex=0)

dev.print(pdf,file="nn1.pdf")

nnet(typ~x+y,lerndaten,size=5,maxit=1000)->netz
pnn<-predict(netz,data.frame("x"=a,"y"=b))
contour(1:100/10,1:90/30,matrix(pnn,100),
add=T,levels=0.5,labex=0)

dev.print(pdf,file="nn2.pdf")

nnet(typ~x+y,lerndaten,size=5,maxit=1000)->netz
pnn<-predict(netz,data.frame("x"=a,"y"=b))
contour(1:100/10,1:90/30,matrix(pnn,100),
add=T,levels=0.5,labex=0)

dev.print(pdf,file="nn3.pdf")

nnet(typ~x+y,lerndaten,size=5,maxit=1000)->netz
pnn<-predict(netz,data.frame("x"=a,"y"=b))
contour(1:100/10,1:90/30,matrix(pnn,100),
add=T,levels=0.5,labex=0)

dev.print(pdf,file="nn4.pdf")

nnet(typ~x+y,lerndaten,size=5,maxit=1000)->netz
pnn<-predict(netz,data.frame("x"=a,"y"=b))
contour(1:100/10,1:90/30,matrix(pnn,100),
add=T,levels=0.5,labex=0)

dev.print(pdf,file="nn5.pdf")

library(e1071)
sv<-svm(typ~x+y,lerndaten)
svp<-predict(sv,data.frame("x"=a,"y"=b))
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
points(a,b,pch=42,col=as.vector(svp))
points(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ),pch=20)

dev.print(pdf,file="svm.pdf")

lerndaten <- simuldata(200)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten2.pdf")

lerndaten <- simuldata(200)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten3.pdf")

contour(1:100/10,1:90/30,matrix(apply(cbind(a,b),1,rotdichte),100),
add=T,col="red",nlevels=20)
dev.print(pdf,file="rotdichte.pdf")

contour(1:100/10,1:90/30,matrix(apply(cbind(a,b),1,blaudichte),100),
add=T,col="blue",nlevels=20)
dev.print(pdf,file="blaudichte.pdf")

contour(1:100/10,1:90/30,matrix(apply(cbind(a,b),1,rotdichte)-apply(cbind(a,b),1,blaudichte),100),add=T,levels=0,labex=0,lwd=5)

dev.print(pdf,file="optimal.pdf")

lerndaten <- simuldata(10)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten10.pdf")

lerndaten <- simuldata(20)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten20.pdf")

lerndaten <- simuldata(50)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten50.pdf")

lerndaten <- simuldata(1000)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))
dev.print(pdf,file="lerndaten1000.pdf")

simuldata2 <- function(m){
x <- c(rnorm(m)/4, rnorm(m))
y <- c(rnorm(m)/4, rnorm(m))
typ <- c(rep("blue",m),rep("red",m))
return(data.frame(x,y,typ))
}

simuldata3 <- function(m){
x <- c(rnorm(m), rnorm(m))
y <- c(rnorm(m)+1, rnorm(m)-1)
typ <- c(rep("blue",m),rep("red",m))
return(data.frame(x,y,typ))
}

simuldata4 <- function(m){
x <- c(rnorm(m)/2, rnorm(m))
y <- c(rnorm(m)/2+1, rnorm(m)-1)
typ <- c(rep("blue",m),rep("red",m))
return(data.frame(x,y,typ))
}

lerndaten <- simuldata4(200)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

bewerte<-function(simfunct,n,wdh){
svmbew <- c()
nnetbew <- c()
ldabew <-c()
knnbew <-c()
qdabew <- c()
for(i in 1:wdh) {
lerndaten <- simfunct(n)
testdaten<-simfunct(100)
svmbew[i]<-sum(predict(svm(typ~x+y,lerndaten),testdaten[,1:2])!=testdaten$typ)/200
nnetbew[i]<-sum(round(predict(nnet(typ~x+y,lerndaten,size=5,maxit=1000),testdaten[,1:2]))!=rep(c(0,1),c(100,100)))/200
ldabew[i] <-sum(predict(lda(typ~.,lerndaten),testdaten[,1:2])$class!=testdaten$typ)/200
knnbew[i] <-sum(knn(lerndaten[,1:2],testdaten[,1:2],lerndaten$typ,k=1)!=testdaten$typ)/200
qdabew[i] <-sum(predict(qda(typ~.,lerndaten),testdaten[,1:2],type="probs")$class!=testdaten$typ)/200
}
return(data.frame(ldabew,qdabew,knnbew,nnetbew,svmbew))
}

bew10<-bewerte(simuldata,10,50)
bew20<-bewerte(simuldata,20,50)
bew50<-bewerte(simuldata,50,50)
bew100<-bewerte(simuldata,100,50)
bew200<-bewerte(simuldata,200,50)
bew500<-bewerte(simuldata,500,50)
bew1000<-bewerte(simuldata,1000,50)

M <- matrix(c(mean(bew10),mean(bew20),mean(bew50),mean(bew100),mean(bew200),mean(bew500),mean(bew1000)),ncol=7)
plot(c(10,20,50,100,200,500,1000),M[1,],t='b',col='red',ylim=c(0,max(M)),xlim=c(10,1200),ylab="Fehlerrate",xlab="Anzahl Lenrdaten",log="x")
points(c(10,20,50,100,200,500,1000),M[2,],t='b',col='green')
points(c(10,20,50,100,200,500,1000),M[3,],t='b',col='blue')
points(c(10,20,50,100,200,500,1000),M[4,],t='b')
points(c(10,20,50,100,200,500,1000),M[5,],t='b',col="orange")
text(rep(1200,5),c(M[1,7],M[2,7],M[3,7],M[4,7],M[5,7]),labels=c("lda","qda","knn","nnet","svm"),col=c("red","green","blue","black","orange"))

dev.print(pdf,file="contest1.pdf")

lerndaten <- simuldata3(1000)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

dev.print(pdf,file="vert2.pdf")

bew10n<-bewerte(simuldata3,10,50)
bew20n<-bewerte(simuldata3,20,50)
bew50n<-bewerte(simuldata3,50,50)
bew100n<-bewerte(simuldata3,100,50)
bew200n<-bewerte(simuldata3,200,50)
bew500n<-bewerte(simuldata3,500,50)
bew1000n<-bewerte(simuldata3,1000,50)

M <- matrix(c(mean(bew10n),mean(bew20n),mean(bew50n),mean(bew100n),mean(bew200n),mean(bew500n),mean(bew1000n)),ncol=7)
plot(c(10,20,50,100,200,500,1000),M[1,],t='b',col='red',ylim=c(0,max(M)),xlim=c(10,1200),ylab="Fehlerrate",xlab="Anzahl Lerndaten",log="x")
points(c(10,20,50,100,200,500,1000),M[2,],t='b',col='green')
points(c(10,20,50,100,200,500,1000),M[3,],t='b',col='blue')
points(c(10,20,50,100,200,500,1000),M[4,],t='b')
points(c(10,20,50,100,200,500,1000),M[5,],t='b',col="orange")
text(rep(1200,5),c(M[1,7]-.012,M[2,7]-.006,M[3,7],M[4,7]+.005,M[5,7]),labels=c("lda","qda","knn","nnet","svm"),col=c("red","green","blue","black","orange"))

dev.print(pdf,file="contest2.pdf")

lerndaten <- simuldata2(200)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

dev.print(pdf,file="vert3.pdf")

bew10n2<-bewerte(simuldata2,10,50)
bew20n2<-bewerte(simuldata2,20,50)
bew50n2<-bewerte(simuldata2,50,50)
bew100n2<-bewerte(simuldata2,100,50)
bew200n2<-bewerte(simuldata2,200,50)
bew500n2<-bewerte(simuldata2,500,50)
bew1000n2<-bewerte(simuldata2,1000,50)

M <- matrix(c(mean(bew10n2),mean(bew20n2),mean(bew50n2),mean(bew100n2),mean(bew200n2),mean(bew500n2),mean(bew1000n2)),ncol=7)
plot(c(10,20,50,100,200,500,1000),M[1,],t='b',col='red',ylim=c(0,max(M)),xlim=c(10,1200),ylab="Fehlerrate",xlab="Anzahl Lerndaten",log="x")
points(c(10,20,50,100,200,500,1000),M[2,],t='b',col='green')
points(c(10,20,50,100,200,500,1000),M[3,],t='b',col='blue')
points(c(10,20,50,100,200,500,1000),M[4,],t='b')
points(c(10,20,50,100,200,500,1000),M[5,],t='b',col="orange")
text(rep(1200,5),c(M[1,7],M[2,7]-0.01,M[3,7],M[4,7]+0.005,M[5,7]),labels=c("lda","qda","knn","nnet","svm"),col=c("red","green","blue","black","orange"))

dev.print(pdf,file="contest3.pdf")

lerndaten <- simuldata4(500)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ))

dev.print(pdf,file="vert4.pdf")

bew10n4<-bewerte(simuldata4,10,20)
bew20n4<-bewerte(simuldata4,20,20)
bew50n4<-bewerte(simuldata4,50,20)
bew100n4<-bewerte(simuldata4,100,20)
bew200n4<-bewerte(simuldata4,200,20)
bew500n4<-bewerte(simuldata4,500,20)
bew1000n4<-bewerte(simuldata4,1000,20)

M <- matrix(c(mean(bew10n4),mean(bew20n4),mean(bew50n4),mean(bew100n4),mean(bew200n4),mean(bew500n4),mean(bew1000n4)),ncol=7)
plot(c(10,20,50,100,200,500,1000),M[1,],t='b',col='red',ylim=c(0,max(M)),xlim=c(10,1200),ylab="Fehlerrate",xlab="Anzahl Lerndaten",log="x")
points(c(10,20,50,100,200,500,1000),M[2,],t='b',col='green')
points(c(10,20,50,100,200,500,1000),M[3,],t='b',col='blue')
points(c(10,20,50,100,200,500,1000),M[4,],t='b')
points(c(10,20,50,100,200,500,1000),M[5,],t='b',col="orange")
text(rep(1200,5),c(M[1,7],M[2,7]-0.002,M[3,7],M[4,7]+0.002,M[5,7]),labels=c("lda","qda","knn","nnet","svm"),col=c("red","green","blue","black","orange"))

dev.print(pdf,file="contest4.pdf")