# cmahal: Generation of tuning constant for Mahalanobis fixed point clusters.

## Description

Generates tuning constants `ca`

for `fixmahal`

dependent on
the number of points and variables of the current fixed point cluster
(FPC).

This is experimental and only thought for use in `fixmahal`

.

## Usage

cmahal(n, p, nmin, cmin, nc1, c1 = cmin, q = 1)

## Arguments

n

positive integer. Number of points.

p

positive integer. Number of variables.

nmin

integer larger than 1. Smallest number of points for which
`ca`

is computed. For smaller FPC sizes, `ca`

is set to
the value for `nmin`

.

cmin

positive number. Minimum value for `ca`

.

nc1

positive integer. Number of points at which `ca=c1`

.

c1

positive numeric. Tuning constant for `cmahal`

.
Value for `ca`

for FPC size equal to `nc1`

.

q

numeric between 0 and 1. 1 for steepest possible descent of
`ca`

as function of the FPC size. Should presumably always be 1.

## Value

A numeric vector of length `n`

, giving the values for `ca`

for all FPC sizes smaller or equal to `n`

.

## Details

Some experiments suggest that the tuning constant `ca`

should
decrease with increasing FPC size and increase with increasing
`p`

in `fixmahal`

. This is to prevent too small
meaningless FPCs while maintaining the significant larger
ones. `cmahal`

with `q=1`

computes `ca`

in such a way
that as long as `ca>cmin`

, the decrease in `n`

is as steep
as possible in order to maintain the validity of the convergence
theorem in Hennig and Christlieb (2002).

## References

Hennig, C. and Christlieb, N. (2002) Validating visual clusters in
large datasets: Fixed point clusters of spectral features,
*Computational Statistics and Data Analysis* 40, 723-739.

## Examples

# NOT RUN {
plot(1:100,cmahal(100,3,nmin=5,cmin=qchisq(0.99,3),nc1=90),
xlab="FPC size", ylab="cmahal")
# }