R09

		Multidimensional Scaling (MDS)


# From your book, a set of distances between European cities

cities.dist <- read.table("F:/S5600/Data sets/ASCII/Ch07/CITIES.txt", row.names=1)
cities.dist
cities <- rownames(cities.dist)
colnames(cities.dist) <- cities
cities.dist

cities.mds <- cmdscale(cities.dist, k=2)
plot(cities.mds)
identify(cities.mds, labels=cities)


# A similar example from R

eurodist

euro.mds <- cmdscale(eurodist, k=2)
plot(euro.mds, type="n")
text(euro.mds, rownames(euro.mds))
euro.mds[,2] <- -1*euro.mds[,2]
plot(euro.mds, type="n")
text(euro.mds, rownames(euro.mds))

euro.sh <- Shepard(as.dist(eurodist),euro.mds)
plot(euro.sh$y, euro.sh$x, pch=16)		# Book's orientation
points(euro.sh$yf, euro.sh$x, pch=3,col="red")

# Examine States by Voting Patterns, 1960-1976

library(cluster)
data(votes.repub)
repub <- votes.repub[,27:31]
head(repub)

pairs(repub)

repub.dist <- dist(repub)     # create a distance matrix
repub.mds <- cmdscale(repub.dist, k=2)
plot(repub.mds, type="n")
text(repub.mds, state.abb)

repub.pca <- prcomp(repub)
plot(-repub.pca$x[,1],repub.pca$x[,2], type="n")
text(-repub.pca$x[,1],repub.pca$x[,2], state.abb)
text(repub.mds, state.abb, col="red")



# Nonmetric MDS - Car Dissimilarity Data

library(MASS)		# Needed for nonmetric MDS

car.dis <- read.tri("F:/S5600/Data sets/ASCII/Ch07/CAR.txt")
rownames(car.dis) <- c("BMW","Ford","Infiniti","Jeep","Lexus",
	"Chrysler","Mercedes","Saab","Porsche","Volvo")
colnames(car.dis) <- rownames(car.dis)
car.dis

car.nmds <- isoMDS(car.dis, k=2)

plot(car.nmds$points)
identify(car.nmds$points, labels=rownames(car.dis))
car.nmds$stress

# Shepard diagram

delta <- as.dist(car.dis)
delta

d <- dist(car.nmds$points)
d

plot(d, delta, pch=16)

car.sh <- Shepard(delta, car.nmds$points)
plot(car.sh$y, car.sh$x, pch=16)		# Book's orientation
points(car.sh$yf, car.sh$x, pch=3,col="red")

# Drug Use Data - Correlations as Variable Similarities

drug.cor <- read.tri("F:/S5600/Data sets/ASCII/Ch04/DRUG_USE.txt")
rownames(drug.cor) <- c("Cigarettes","Beer","Wine","Liquor","Cocaine",
	"Tranquillizers","Medication","Heroin","Marijuana","Hashish",
	"Inhalants","Hallucinogenics","Amphetamines")
colnames(drug.cor) <- rownames(drug.cor)
head(drug.cor)

# Convert to distances - method 1 (works well for correlations)

drug.dist <- 1-drug.cor
head(drug.dist)

drug.nmds <- isoMDS(drug.dist, k=2)

plot(drug.nmds$points)
identify(drug.nmds$points, labels=rownames(drug.dist))

drug.sh <- Shepard(as.dist(drug.dist), drug.nmds$points)
plot(drug.sh$y, drug.sh$x, pch=16)
points(drug.sh$yf, drug.sh$x, pch=3,col="red")


# Convert to distances - method 2 (more general)

drug.dist2 <-matrix(0, nrow=13, ncol=13)

for (i in 1:13) for (j in 1:13)
	drug.dist2[i,j] <- sqrt(drug.cor[i,i]-2*drug.cor[i,j]+drug.cor[j,j])

plot(drug.dist, drug.dist2)

drug.nmds2 <- isoMDS(drug.dist2, k=2)

plot(drug.nmds2$points)
identify(drug.nmds2$points, labels=rownames(drug.dist))

drug.sh2 <- Shepard(as.dist(drug.dist), drug.nmds2$points)
plot(drug.sh2$y, drug.sh2$x, pch=16)
points(drug.sh2$yf, drug.sh2$x, pch=3,col="red")