Generation of tuning constant for Mahalanobis fixed point clusters.
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.
cmahal(n, p, nmin, cmin, nc1, c1 = cmin, q = 1)
n |
positive integer. Number of points. |
p |
positive integer. Number of variables. |
nmin |
integer larger than 1. Smallest number of points for which
|
cmin |
positive number. Minimum value for |
nc1 |
positive integer. Number of points at which |
c1 |
positive numeric. Tuning constant for |
q |
numeric between 0 and 1. 1 for steepest possible descent of
|
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).
A numeric vector of length n, giving the values for ca
for all FPC sizes smaller or equal to n.
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.
plot(1:100,cmahal(100,3,nmin=5,cmin=qchisq(0.99,3),nc1=90),
xlab="FPC size", ylab="cmahal")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.