R11

				  Distances and 
				k-Means Clustering

# Alternative Distance Measures


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
dist(X)		# default - Euclidean (2 norm)
sqrt((1-2)^2+(8-2)^2)	# d(1,2)

dist(X, method="manhattan")	# 1 norm
abs(1-2)+abs(8-2)	# d(1,2)

dist(X, method="maximum")	# sup (infinity) norm
max(abs(1-2),abs(8-2))	# d(1,2)

dist(X, method="minkowski", p = 3)	# 3 norm
(abs(1-2)^3+abs(8-2)^3)^(1/3)	# d(1,2)


pairs(swiss, pch=16)
swiss.d2 <- dist(scale(swiss))
swiss.hc.c2 <- hclust(swiss.d2, method="complete")
plot(swiss.hc.c2)
pairs(swiss, pch=cutree(swiss.hc.c2, 4), col=cutree(swiss.hc.c2, 4))

swiss.d1 <- dist(scale(swiss), "manhattan")
swiss.hc.c1 <- hclust(swiss.d1, method="complete")
plot(swiss.hc.c1)
pairs(swiss, pch=cutree(swiss.hc.c1, 4), col=cutree(swiss.hc.c1, 4))

swiss.pca <- prcomp(swiss, scale=T)
pairs(swiss.pca$x[,1:4], pch=cutree(swiss.hc.c2, 4), col=cutree(swiss.hc.c2, 4))
pairs(swiss.pca$x[,1:4], pch=cutree(swiss.hc.c1, 4), col=cutree(swiss.hc.c1, 4))

# Compare assignments from different distances

table(data.frame(c2=cutree(swiss.hc.c2,4),c1=cutree(swiss.hc.c1,4)))

swiss.dsup <- dist(scale(swiss), "maximum")
swiss.hc.csup <- hclust(swiss.d1, method="complete")
plot(swiss.hc.csup)
pairs(swiss, pch=cutree(swiss.hc.csup, 4), col=cutree(swiss.hc.csup, 4))

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

table(data.frame(c2=cutree(swiss.hc.c2,4),csup=cutree(swiss.hc.csup,4)))
table(data.frame(c1=cutree(swiss.hc.c1,4),csup=cutree(swiss.hc.csup,4)))



# Natural Modality: Bimodal vs Unimodal

library(MASS)
mu1 <- c(3,3)
mu2 <- c(6,6)
Sigma1 <- matrix(c(1,0,0,1),nrow=2)
bimodal <- rbind(mvrnorm(25,mu=mu1,Sigma=Sigma1),mvrnorm(25,mu=mu2,Sigma=Sigma1))
plot(bimodal, pch=16)

mu3 <- c(4.5, 4.5)
Sigma2 <- matrix(c(2.25,1.5,1.5,2.25),nrow=2)
unimodal <- mvrnorm(50, mu=mu3, Sigma=Sigma2)
plot(unimodal, pch=16)


bim.d2 <- dist(bimodal)
unim.d2 <- dist(unimodal)

plot(hclust(bim.d2, method="complete"))
plot(hclust(unim.d2, method="complete"))

plot(hclust(bim.d2, method="single"))
plot(hclust(unim.d2, method="single"))

plot(hclust(bim.d2, method="ward"))
plot(hclust(unim.d2, method="ward"))


bim.d1 <- dist(bimodal, "manhattan")
unim.d1 <- dist(unimodal, "manhattan")

plot(hclust(bim.d1, method="complete"))
plot(hclust(unim.d1, method="complete"))

plot(hclust(bim.d1, method="single"))
plot(hclust(unim.d1, method="single"))

plot(hclust(bim.d1, method="ward"))
plot(hclust(unim.d1, method="ward"))


# Kth Nearest Neighbor Density Distance

source("F:/S5600/knn.dist.txt")

bim.dk.10 <- knn.dist(bimodal, 10)
unim.dk.10 <- knn.dist(unimodal, 10)

plot(hclust(bim.dk.10, method="single"))
plot(hclust(unim.dk.10, method="single"))


bim.dk.5 <- knn.dist(bimodal, 5)
unim.dk.5 <- knn.dist(unimodal, 5)

plot(hclust(bim.dk.5, method="single"))
plot(hclust(unim.dk.5, method="single"))