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October 2002

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Subject:
From:
"F. James Rohlf" <[log in to unmask]>
Reply To:
Classification, clustering, and phylogeny estimation
Date:
Thu, 24 Oct 2002 21:12:02 -0400
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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
>

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