# Aufgabe 2

# a)

#Einlesen des Datensatzes
euro <- read.table("https://www.elab.moodle.elearning.lmu.de/pluginfile.php/21443/mod_resource/content/1/europa.txt",header=T)
Xeuro <- data.frame(euro[,-1],row.names=euro[,1])

#standardisieren der Daten
euroscaled <- scale(Xeuro,scale=T,center=T)

# b) 

# quadrierte euklidische Distanzen
dist_eucl2 <- dist(euroscaled, method="euclidean")^2

# Single Linkage mit allen Kovariablen 
sl   <- hclust(dist_eucl2, method="single")

# c) 

# Zentroid mit allen Kovariablen 
cent <- hclust(dist_eucl2, method="centroid")

# d) 

S <- var(euroscaled)
dist_mahal <- matrix(NA,nrow=24,ncol=24)
for(i in 1:24){
  dist_mahal[i,] <- mahalanobis(euroscaled, euroscaled[i,],S)
}
rownames(dist_mahal) <- colnames(dist_mahal) <- labels(dist_eucl2)
dist_mahal <- as.dist(dist_mahal)

cl <- hclust(dist_mahal, method="complete")

# e) 
par(mfrow=c(1,3))
plot(sl)
plot(cent)
plot(cl)