###
#
# Euro Distances

data(eurodist)

###
#
# Layout in 1-d via PCA

loc <- cmdscale(eurodist, k=1)
x <- loc[,1]
plot(x, rep(0,length(loc[,1])), ylim=c(0,1), pch="+", xlab="", ylab="", main="cmdscale(eurodist)")
text(x, (1:21)/21, names(eurodist), cex=0.8)

###
#
# Layout in 2-d via PCA

loc <- cmdscale(eurodist, k=2)
x <- loc[,1]
y <- (-loc[,2])
plot(x, y, pch="+", xlab="", ylab="", main="cmdscale(eurodist)")
text(x, y+100, names(eurodist), cex=0.8)

###
#
# Layout the Euro Cities under stress, i.e. 1-d (with random start config for non-metric)

par(mfrow=c(1,3))

plot(rep(0,21), cmdscale(eurodist, k=1), type="n")
text(rep(0,21), cmdscale(eurodist, k=1), names(eurodist))

plot(rep(0,21), sammon(eurodist, k=1)$points, type="n")
text(rep(0,21), sammon(eurodist, k=1)$points, names(eurodist))

plot(rep(0,21), isoMDS(eurodist, d<-matrix(runif(21,-2000,2000),21,1), k=1)$points, type="n")
text(rep(0,21), isoMDS(eurodist, d, k=1)$points, names(eurodist))

###
#
# Remaining Stress for Crabs Data in 1:7 Dimensions

stress <- 1:7
crd <- dist(normdf(crabs[4:8]))
for ( i in 1:7 )
    stress[i] <- sammon(crd, k=i)$stress

plot(stress, type="l", xlab="Dimensionen")

####
#
# Find a layout for the crabs data from a random start
# (finds the four groups at a minimal stress value of 0.327986!!! - runs long!)

plot(as.data.frame(isoMDS(crd, matrix(runif(600), 200, 3), k=3, maxit=200)$points), col=sp-1+2*(sex-1)+1)

###
#
# Compare fitted an original distances in 2-d and label them

fit <- dist(sammon(eurodist, k=2)$points)

plot(eurodist, fit, pch="+")

n1 <- length(names(eurodist))

fit.mat <- as.matrix(fit)
for( i in 1:n1)
  for( j in 1:n1)
     if( i<=j )
        fit.mat[i,j] <- 0

fit.df <- as.data.frame(as.table(fit.mat))

dist.mat <- as.matrix(eurodist)
for( i in 1:n1)
  for( j in 1:n1)
     if( i<=j )
        dist.mat[i,j] <- 0

dist.df <- as.data.frame(as.table(dist.mat))

diffs <- abs(dist.df$Freq - fit.df$Freq)

text(dist.df$Freq[diffs>500], fit.df$Freq[diffs>500]+75, 
     paste(fit.df$Var1[diffs>500], "-", fit.df$Var2[diffs>500]))

###
#
# A layout for the olive oil data in 2-d, colored for the 3 Regions

ofit <- sammon(dist(olives[4:11]), k=2)$points     
     
plot(ofit, col=olives[,2])