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 > > >