# Aufgabe 1

o<-read.table("Desktop/olives.txt",TRUE)
attach(o)

m<-data.frame(stearic=min(stearic),oleic=min(oleic))
for (i in min(stearic)+0:30/30*(max(stearic)-min(stearic)))
for (j in min(oleic)+0:30/30*(max(oleic)-min(oleic))) m<-rbind(m,c(i,j))
l<-lda(Region~stearic+oleic)
pc<-predict(l,m)$class
plot(stearic,oleic,col=unclass(Region))
points(m,col=as.integer(pc),pch=3)

# Aufgabe 2

q<-qda(Region~stearic+oleic)
table(predict(l)$class, Region)
table(predict(q)$class, Region)

plot(stearic,oleic,col=unclass(Region))
points(m,col=as.integer(predict(q,m)$class),pch=3)

ccr.lda<-sum(predict(l)$class==Region)/length(Region)
ccr.qda<-sum(predict(q)$class==Region)/length(Region)

#Aufgabe 3

x <- c(0,1,1,0,0,1,1,0)
y <- c(0,0,1,1,0,0,1,1)
z <- c(0,0,0,0,1,1,1,1)
m <- matrix(c(x,y,z),,3)

e<-c(1:4,1,5:8,4,8,5,6,2,6,7,3)

cs<-cmdscale(dist(m))
plot(cs)
lines(cs[e,])

cs<-sammon(dist(m))$points
plot(cs)
lines(cs[e,])

cs<-isoMDS(dist(m))$points
plot(cs)
lines(cs[e,])

###xtra:
# cs<-isoMDS(dist(m),cbind(runif(8),runif(8)))$points
# plot(cs)
# lines(cs[e,])

m<-as.matrix(o[3:10])
cs<-sammon(dist(t(m)))
plot(cs$points)
text(cs$points,names(o[3:10]))

nd <- function(x) (x-mean(x))/sd(x)

# Aufgabe 4

crabs <- read.table("Desktop/crabs.txt",TRUE)
attach(crabs)
nc<-crabs
for (i in 4:8) nc[i]<-nd(nc[i])
m<-nc[4:8]
cs<-isoMDS(dist(m))$points
plot(cs,col=sp-1+2*(sex-1)+1)

cs<-isoMDS(dist(m),cbind(runif(200),runif(200)),maxit=100)$points
plot(cs,col=sp-1+2*(sex-1)+1)

cs<-isoMDS(dist(m),cbind(runif(200)+c(rep(-5,100),rep(5,100)),runif(200)+c(rep(-5,50),rep(5,50),rep(-5,50),rep(1,50))))$points
plot(cs,col=sp-1+2*(sex-1)+1)

# Aufgabe 5

km<-kmeans(crabs[4:8], 4)
pairs(crabs[4:8], col=km$cluster, pch=sp-1+2*(sex-1)+1)

pc<-as.data.frame(predict(princomp(crabs[4:8])))
km<-kmeans(pc[2:3],4)
pairs(crabs[4:8], col=km$cluster, pch=sp-1+2*(sex-1)+1)

pairs(pc[1:3], col=km$cluster, pch=sp-1+2*(sex-1)+1)