##################################################
## Classical Multidimensional Scaling
##################################################
setwd("/u/kalisch/teaching/12/ams/vorlesung/v1.1/")
dat <- read.csv(file = "USairpollution.csv", header = TRUE, row.names = 1)
str(dat)
summary(dat)
## scale
xs <- apply(dat, 2, function(x) (x - min(x))/(diff(range(x))))
summary(xs)

## compute distance matrix
head(xs)
poldist <- dist(xs)
poldist
## reduce to 2 dimensions
pol.mds <- cmdscale(poldist, k = 2, eig = TRUE)
pol.mds
## reduce to 3 dimensions
pol.mds3 <- cmdscale(poldist, k = 3, eig = TRUE)
pol.mds3

## plot
x <- pol.mds$points
plot(x[,1], x[,2], type = "n")
text(x[,1], x[,2], labels = rownames(x), cex = 0.7)

x11()
stars(xs, draw.segments = TRUE, key.loc = c(15,2))

##################################################
## Non-metric MDS
##################################################
## Voting: 15 US congressman in Rep/Democrat party voted in 19 votes
## Recorded is the number of votes in which each pair of congressmen disagreed
load("/u/kalisch/teaching/12/ams/vorlesung/v4.1/voting.rda")
voting

library(MASS)
mdsRes <- isoMDS(voting, k = 2)
str(mdsRes)

mycol <- c(1,1,2,2,1,1,1,2,2,2,2,1,1,2,2) ## color code for Repub/Demo.
plot(mdsRes$points, type = "n", xlim = c(-15,10))
text(mdsRes$points, labels = rownames(mdsRes$points), col = mycol)