Bivariate Data Set with 3 Clusters
An artificial data set consisting of 3000 points in 3 quite well-separated clusters.
data(xclara)
A data frame with 3000 observations on 2 numeric variables (named
V1 and V2) giving the
x and y coordinates of the points, respectively.
Our version of the xclara is slightly more rounded than the one
from read.table("xclara.dat") and the relative
difference measured by all.equal is 1.15e-7 for
V1 and 1.17e-7 for V2 which suggests that our
version has been the result of a options(digits = 7)
formatting.
Previously (before May 2017), it was claimed the three cluster were
each of size 1000, which is clearly wrong. pam(*, 3)
gives cluster sizes of 899, 1149, and 952, which apart from seven
“outliers” (or “mislabellings”) correspond to
observation indices 1:900, 901:2050, and
2051:3000, see the example.
Sample data set accompanying the reference below (file ‘xclara.dat’ in side ‘clus_examples.tar.gz’).
Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996) Clustering in an Object-Oriented Environment. Journal of Statistical Software 1. doi: 10.18637/jss.v001.i04
## Visualization: Assuming groups are defined as {1:1000}, {1001:2000}, {2001:3000}
plot(xclara, cex = 3/4, col = rep(1:3, each=1000))
p.ID <- c(78, 1411, 2535) ## PAM's medoid indices == pam(xclara, 3)$id.med
text(xclara[p.ID,], labels = 1:3, cex=2, col=1:3)
px <- pam(xclara, 3) ## takes ~2 seconds
cxcl <- px$clustering ; iCl <- split(seq_along(cxcl), cxcl)
boxplot(iCl, range = 0.7, horizontal=TRUE,
main = "Indices of the 3 clusters of pam(xclara, 3)")
## Look more closely now:
bxCl <- boxplot(iCl, range = 0.7, plot=FALSE)
## We see 3 + 2 + 2 = 7 clear "outlier"s or "wrong group" observations:
with(bxCl, rbind(out, group))
## out 1038 1451 1610 30 327 562 770
## group 1 1 1 2 2 3 3
## Apart from these, what are the robust ranges of indices? -- Robust range:
t(iR <- bxCl$stats[c(1,5),])
## 1 900
## 901 2050
## 2051 3000
gc <- adjustcolor("gray20",1/2)
abline(v = iR, col = gc, lty=3)
axis(3, at = c(0, iR[2,]), padj = 1.2, col=gc, col.axis=gc)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.