I don't really believe that there is any satisfactory definition of the "true number of clusters" let along a procedure that would reliably find it.

Murray Jorgensen


Martin Maechler wrote:


Back from my vacation, I haven't seen an R-help answer on this
  (Christian, where have you been ? ;-)


"GiampS" == Giampiero Salvi <[EMAIL PROTECTED]>
   on Sat, 7 Feb 2004 23:40:36 +0100 (CET) writes:


    GiampS> Hi all, I'm doing a study on predicting the "true"
    GiampS> number of clusters in a hierarchical clustering
    GiampS> scheme. My main reference is at the moment

    GiampS> Milligan GW and Cooper MC (1985) "An examination of
    GiampS> procedures for determining the number of clusters in
    GiampS> a data set" Psychometrika vol 50 no 2 pp 159-179

GiampS> and all the references included in that paper.

(not available to me)

    GiampS> I'm planning to perform a similar comparison on a
    GiampS> number of indexes, but on a much larger data set (in
    GiampS> the order of 3000 points), and with a much higher
    GiampS> "true" number of clusters (in the order of some
    GiampS> hundreds), to see if the properties of the indexes
    GiampS> scale accordingly.

    GiampS> I was wondering if the set of indexes described in
    GiampS> the reference are still "state of the art" (most of
    GiampS> them were introduced in the '60s and '70s), or if
    GiampS> there are new indexes and methods I could include in
    GiampS> my study. I would really appreciate if you could
    GiampS> point me to some newer references addressing this problem.

Gordon's 2nd edition,

  author =       {A. D. Gordon},
  title =        {Classification, 2nd Edition},
  publisher =    {Chappman \& Hall/CRC},
  year =         1999,
  series =       {Monographs on Statistics and Applied Probability 82},
  edition =      {2nd edition}

has a whole chapter (one of the last ones in the book) on this.

R's cluster package has a generic silhouette() function (with 2 methods),
and plot.silhouette() method --- all are improvements from
Kaufman & Rousseeuw's original code.

A recent research paper using "CLEST" (Fridyland & Dudoit),
mentioning "GAP" (Tibshirani) etc etc  still find silhouette
among the best "indices" for determining the number of clusters.

A student's (master) thesis here seems to point in the same
direction.

GiampS> I also read Milligan's chapter in the book
GiampS> "Clustering and Classification" from 1995, (which book? author?)


    GiampS> but didn't find information on this subject that wasn't
    GiampS> included in the previous paper.

Regards,
Martin Maechler <[EMAIL PROTECTED]>       http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum  LEO C16    Leonhardstr. 27
ETH (Federal Inst. Technology)  8092 Zurich     SWITZERLAND
phone: x-41-1-632-3408          fax: ...-1228                   <><

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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 Email: [EMAIL PROTECTED] Fax 7 838 4155 Phone +64 7 838 4773 wk +64 7 849 6486 home Mobile 021 1395 862

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