I'm not sure the problem that needed to be addressed is what we think it
is. I saw an email in the last couple of days from the original poster of
the problem and believe the issue is to generate 3 random samples (without
replacement) from a small number of observations such that each sample has
the same distribution as the original data.

I might be confusing this and maybe the original poster can resend a
description of the problem to the list.

Bill Shannon

On Thu, 24 Oct 2002, F. James Rohlf wrote:

> I agree. I don't yet see the point of why this should be done.
>
> > -----Original Message-----
> > From: Classification, clustering, and phylogeny estimation
> > [mailto:[log in to unmask]]On Behalf Of Murray Jorgensen
> > Sent: Thursday, October 24, 2002 8:21 PM
> > To: [log in to unmask]
> > Subject: Re: classification comparison/R=R1=R2=R3
> >
> >
> > At 15:36 24/10/02 +0200, Christian Hennig wrote:
> >
> > >2) On clustering with R1=R2=R3=R. k-means clustering implicitly assumes
> > >   clusters to have unit matrix correlation. So transforming the data to
> > >   unit covariance and then applying 3-means will give clusters with
> > >   approximately R1=R2=R3=R.
> >
> > R1=R2=R3, maybe but =R???
> >
> > Surely it is most unlikely that the overall correlation structure
> > would mirror
> > the within-cluster structure? It is also hard to think why that might be
> > desirable. If it were then an obvious way to achieve it would be
> > to randomly
> > allocate the data points to the three clusters.
> >
> > Murray Jorgensen
> >
> >
> > May be even better with a Gausiian mixture
> > >   model where covariance matrices of the clusters are restricted to cI,
> > >   where I is unit matrix and c may depend on the cluster. This again has
> > >   to be applied to data which is sphered, i.e. transformed to unit
> > >   covariance first. I hope this "covariance model" can be found
> > in mclust,
> > >   mentioned previously in this discussion.
> > >
> > >Christian Hennig
> > >
> > >
> > >
> > >--
> > >***********************************************************************
> > >Christian Hennig
> > >Seminar fuer Statistik, ETH-Zentrum (LEO), CH-8092 Zuerich (current)
> > >and Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
> > >[log in to unmask], http://stat.ethz.ch/~hennig/
> > >[log in to unmask], http://www.math.uni-hamburg.de/home/hennig/
> > >#######################################################################
> > >ich empfehle www.boag.de
> > >
> > Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
> > Department of Statistics, University of Waikato, Hamilton, New Zealand
> > Email: [log in to unmask]                            Fax +64-7 838 4155
> > Phone  +64-7 838 4773 wk    +64 7 849 6486 home     Mobile 021 395 862
> >
>