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
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Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
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