## Bivariate Data Set with 3 Clusters

### Description

An artificial data set consisting of 3000 points in 3 quite well-separated
clusters.

### Usage

data(xclara)

### Format

A data frame with 3000 observations on 2 numeric variables (named
`V1`

and `V2`

) giving the
*x* and *y* coordinates of the points, respectively.

### Note

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.

### Source

Sample data set accompanying the reference below (file
‘xclara.dat’ in side ‘clus_examples.tar.gz’).

### References

Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996)
Clustering in an Object-Oriented Environment.
*Journal of Statistical Software* **1**.
http://www.jstatsoft.org/v01/i04

### Examples

## 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)