R: Generation of tuning constant for Mahalanobis fixed point...

cmahal {fpc} | R Documentation

## 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.

### 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).

### Value

A numeric vector of length `n`, giving the values for `ca` for all FPC sizes smaller or equal to `n`.

### Author(s)

Christian Hennig c.hennig@ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/

### 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.

### See Also

`fixmahal`

### Examples

      plot(1:100,cmahal(100,3,nmin=5,cmin=qchisq(0.99,3),nc1=90),
           xlab="FPC size", ylab="cmahal")

[Package fpc version 2.1-10 Index]