how different definition of distance changes our view of clustering

viewpoints.r

# you can run this script with the following R command:
# source('https://gist.githubusercontent.com/tdunning/badb88043d41d916a3148c669f2fb0cd/raw/8d3289fdbf2a7999bd5d9687002488b904e1d82f/viewpoints.r')

set.seed(1)
noise = matrix(nrow=2000, ncol=8, data=rnorm(4*8*500))
offsets = matrix(
    c(rep(-1,1000), rep(1,1000),
      rep(-1, 500), rep(1, 500), rep(-1, 500), rep(1, 500)),
    ncol=2)
xy = rbind(matrix(nrow=2000, ncol=2, data=rnorm(2*2000))) + offsets * 8
x = cbind(xy, noise)

c1 = rbind(matrix(0, nrow=2, ncol=2), matrix(rnorm(2*8), nrow=8))
c2 = rbind(matrix(c(1,0,0,0,0,1), nrow=3,byrow=T), matrix(0, nrow=7, ncol=2))
c3 = rbind(matrix(c(0.5,0,-0.5,0,0,0.8), nrow=3,byrow=T), matrix(0, nrow=7, ncol=2))
c4 = diag(nrow=10, ncol=2)

par(mar=c(1,1,1,1), mfrow=c(2,2))

show = function(data) {
    plot(data, col=NA, bg=rgb(0,0,0,0.2), pch=21,
         xlab=NA, ylab=NA, xlim=c(-12, 12), ylim=c(-12, 12),
         xaxt='n', yaxt='n')
}

show(x %*% c1)
show(x %*% c2)
show(x %*% c3)
show(x %*% c4)