Hello World for Clustering methods

A hello world program can be a useful sanity test to make sure that the procedure/methods you are analyzing "works" at least for very basic tasks. For this purpose, I create an artificial data set from 4 different 2-dimensional normal distributions to check how well the 4 clusters can be recognized by common clustering methods.

set1 <- matrix(cbind(rnorm(100,0,2),rnorm(100,0,2)),100,2)
set2 <- matrix(cbind(rnorm(100,0,2),rnorm(100,8,2)),100,2)
set3 <- matrix(cbind(rnorm(100,8,2),rnorm(100,0,2)),100,2)
set4 <- matrix(cbind(rnorm(100,8,2),rnorm(100,8,2)),100,2)
dati <- list(values=rbind(set1,set2,set3,set4),classes=c(rep(1,100),rep(2,100),rep(3,100),rep(4,100))) # clustering - common methods
op <- par(mfcol = c(2, 2))
par(las =1)
plot(dati$values, col = as.integer(dati$classes), xlim=c(-6,14), ylim = c(-6,14), xlab="", ylab="", main = "True Groups")
party <- kmeans(dati$values,4)
plot(dati$values, col = party$cluster, xlab = "", ylab = "", main = "kmeans")
hc = hclust(dist(dati$values), method = "ward")
memb <- cutree(hc, k = 4)
plot(dati$values, col = memb, xlab = "", ylab = "", main = "hclust Euclidean ward") hc = hclust(dist(dati$values), method = "complete")
memb <- cutree(hc, k = 4)
plot(dati$values, col = memb, xlab = "", ylab = "", main = "hclust Euclidean complete")
par(op)



From Similarity To Distance matrix


# This function returns an object of class "dist"
sim2dist <- function(mx) as.dist(sqrt(outer(diag(mx), diag(mx), "+") - 2*mx)) # from similarity to distance matrix d.mx = as.matrix(d.mx) d.mx = sim2dist(d.mx) # The distance matrix can be used to visualize # hierarchical clustering results as dendrograms hc = hclust(d.mx) plot(hc)

See Multivariate Analysis (Probability and Mathematical Statistics) for the statistical theory.