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The following manuscript is now available via anonymous ftp
(see below for the retrieval procedure), or, alternatively from 
http://www.physik.uni-wuerzburg.de/~biehl

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  "Specialization processes in on-line unsupervised learning"

  Michael Biehl, Ansgar Freking, Georg Reents, and Enno Schl"osser

   Contribution to the 
   Minerva Workshop on Mesoscopics, Fractals and Neural Networks
   Eilat, Israel,  March 1997

   Ref: WUE-ITP-97-003


                         Abstract
From the recent analysis of supervised learning by on-line gradient 
descent in multilayered neural networks it is known that the necessary 
process of student specialization can be delayed significantly.  We 
demonstrate that this phenomenon also occurs in various models of
unsupervised learning.  A solvable model of competitive learning is 
presented, which identifies prototype vectors suitable for the repre-
sentation of high--dimensional data. The specific case of two overlapping 
clusters of data and a matching number of prototype vectors exhibits non-
trivial behavior like almost stationary plateau configurations.  As a 
second example scenario we investigate the application of Sanger's 
algorithm for principal component analysis in the presence of two relevant
directions in input space. Here, the fast learning of the first principal 
component may lead to an almost complete loss of initial knowledge about 
the second one.  

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Retrieval procedure:

     unix> ftp  ftp.physik.uni-wuerzburg.de
     Name: anonymous  Password: {your e-mail address}
     ftp>  cd pub/preprint/1997
     ftp>  binary
     ftp>  get WUE-ITP-97-003.ps.gz           (*)   
     ftp>  quit
     unix> gunzip WUE-ITP-97-003.ps.gz
e.g. unix> lp WUE-ITP-97-003.ps                     [10 pages]             

(*) can be replaced by "get WUE-ITP-97-003.ps". The file will then
    be uncompressed before transmission (slow!). 
_____________________________________________________________________ 

-- 

Michael Biehl     
Institut fuer Theoretische Physik              
Julius-Maximilians-Universitaet Wuerzburg
Am Hubland
D-97074 Wuerzburg 

email:     biehl@physik.uni-wuerzburg.de
homepage:  http://www.physik.uni-wuerzburg.de/~biehl 
Tel.:      (+49) (0)931 888 5865   
             "      "    "  5131
Fax :      (+49) (0)931 888 5141