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October 2002

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Subject:
From:
Christian Hennig <[log in to unmask]>
Reply To:
Classification, clustering, and phylogeny estimation
Date:
Fri, 25 Oct 2002 10:33:50 +0200
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> > > 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???

...we look for clusters with unit correlation in data with unit correlation...

> > >
> > > 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

OK, my suggestion will usually not give perfectly R1=R2=R3=R and not a very
good clustering, but to a certain amount it tries to do both
simultaneously.

> I apologise if the matter is not strictly related with cluster analysis.
> Maybe it can be considered an allocation-optimization problem.
>
> Kind regards
> max

However, clustering does not seem to be in any sense Max'
aim (not only "not strictly"), and therefore all this does not really help.
I guess that under usual conditions my suggestion will match R1=R2=R3=R
worse then random allocation.

Christian

--
***********************************************************************
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/
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