rFace {fpc}

"Face-shaped" clustered benchmark datasets

Description

Generates "face-shaped" clustered benchmark datasets. This is based on a collaboration with Martin Maechler.

Usage

rFace(n, p = 6, nrep.top = 2, smile.coef = 0.6, dMoNo = 1.2, dNoEy = 1)

Arguments

n

integer greater or equal to 10. Number of points.

p

integer greater or equal to 2. Dimension.

nrep.top

integer. Number of repetitions of the hair-top point.

smile.coef

numeric. Coefficient for quadratic term used for generation of mouth-points. Positive values=>smile.

dMoNo

number. Distance from mouth to nose.

dNoEy

number. Minimum vertical distance from mouth to eyes.

Details

The function generates a nice benchmark example for cluster analysis. There are six "clusters" in this data, of which the first five are clearly homogeneous patterns, but with different distributional shapes and different qualities of separation. The clusters are distinguished only in the first two dimensions. The attribute grouping is a factor giving the cluster numbers, see below. The sixth group of points corresponds to some hairs, and is rather a collection of outliers than a cluster in itself. This group contains nrep.top+2 points. Of the remaining points, 20% belong to cluster 1, the chin (quadratic function plus noise). 10% belong to cluster 2, the right eye (Gaussian). 30% belong to cluster 3, the mouth (Gaussian/squared Gaussian). 20% belong to cluster 4, the nose (Gaussian/gamma), and 20% belong to cluster 5, the left eye (uniform).

The distributions of the further variables are homogeneous over all points. The third dimension is exponentially distributed, the fourth dimension is Cauchy distributed, all further distributions are Gaussian.

Please consider the source code for exact generation of the clusters.

Value

An n times p numeric matrix with attributes

grouping

a factor giving the cluster memberships of the points.

indexlist

a list of six vectors containing the indices of points belonging to the six groups.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

Examples

  set.seed(4634)
  face <- rFace(600,dMoNo=2,dNoEy=0)
  grface <- as.integer(attr(face,"grouping"))
  plot(face, col = grface)
#  pairs(face, col = grface, main ="rFace(600,dMoNo=2,dNoEy=0)")