R10

			Hierarchical Clustering


# A sample Dataset

x1 <- c(1, 2, 3, 4, 7, 8, 10)
x2 <- c(8, 2, 3, 1, 11, 8, 10)
X <- cbind(x1, x2)
plot(X, pch=16)
identify(X, labels=1:7)


X.d <- dist(X)
X.d

X.hc.s <- hclust(X.d, method="single")

win.graph()

plot(X.hc.s)

dev.set(2)

cutree(X.hc.s, 3)

plot(X, pch=cutree(X.hc.s, 3), col=cutree(X.hc.s, 3))

dev.off(3)

# Iris Data

iris.s <- scale(iris[,-5])
iris.d <- dist(iris.s)
species <- iris[,5]

iris.hc.s <- hclust(iris.d, method="single")

plot(iris.hc.s)

pairs(iris[,-5], pch=cutree(iris.hc.s,6), col=cutree(iris.hc.s,6))

pairs(iris[,-5], pch=unclass(species), col=cutree(iris.hc.s,6))


iris.hc.c <- hclust(iris.d, method="complete")

plot(iris.hc.c)

pairs(iris[,-5], pch=cutree(iris.hc.c,6), col=cutree(iris.hc.c,6))

pairs(iris[,-5], pch=unclass(species), col=cutree(iris.hc.c,6))

# Artificial data - 4 clusters

X <- matrix(rnorm(320), 80, 4)
X[1:20,1] <- X[1:20,1]+10
X[21:40,2] <- X[21:40,2]+10
X[41:60,3] <- X[41:60,3]+10
X <- scale(X)
pairs(X)

library(rgl)
plot3d(X[,1],X[,2],X[,3], type="s", size=.25, col="red")

plot3d(X[,1],X[,2],X[,3], type="s", size=.25, col=rep(1:4, c(20,20,20,20)))

rot <- eigen(cor(iris[,-5]))$vectors	# Arbitrary rotation matrix to hide structure

Y <- scale(X %*% rot)
pairs(Y)

plot3d(Y[,1],Y[,2],Y[,3], type="s", size=.25, col="red")

plot3d(Y[,1],Y[,2],Y[,3], type="s", size=.25, col=rep(1:4, c(20,20,20,20)))

Y.d <- dist(Y)

Y.hc.s <- hclust(Y.d, method="single")
plot(Y.hc.s)
Y.hc.c <- hclust(Y.d, method="complete")
plot(Y.hc.c)
Y.hc.a <- hclust(Y.d, method="average")
plot(Y.hc.a)
Y.hc.w <- hclust(Y.d, method="ward")
plot(Y.hc.w)

pairs(Y, pch=cutree(Y.hc.w,4), col=cutree(Y.hc.w,4))

Y.pca <- prcomp(Y)
plot(Y.pca)

pairs(Y.pca$x[,1:3], pch=cutree(Y.hc.w,4), col=cutree(Y.hc.w,4))


# Swiss canton data

pairs(swiss, pch=16)

swiss.d <- dist(scale(swiss))

plot(hclust(swiss.d, method="single"))

plot(hclust(swiss.d, method="complete"))
plot(hclust(swiss.d, method="ward"))
plot(hclust(swiss.d, method="average"))

swiss.hc.w <- hclust(swiss.d, method="ward")
pairs(swiss, pch=cutree(swiss.hc.w, 3), col=cutree(swiss.hc.w, 3))

swiss.pca <- prcomp(swiss, scale=T)
plot(swiss.pca)
swiss.pca$rotation
pairs(swiss.pca$x[,1:4], pch=cutree(swiss.hc.w, 3), col=cutree(swiss.hc.w, 3))

swiss.hc.c <- hclust(swiss.d, method="complete")
pairs(swiss, pch=cutree(swiss.hc.c, 2), col=cutree(swiss.hc.c, 2))
pairs(swiss, pch=cutree(swiss.hc.c, 4), col=cutree(swiss.hc.c, 4))

pairs(swiss.pca$x[,1:4], pch=cutree(swiss.hc.c, 4), col=cutree(swiss.hc.c, 4))