preprint available

[Michael Biehl]

 FTP-host:      archive.cis.ohio-state.edu
 FTP-filename:  /pub/neuroprose/biehlmietzner.pancakes.ps.Z


The following paper has been placed in the Neuroprose archive
(see above for ftp-host) as a compressed postscript file named

          biehlmietzner.pancakes.ps.Z     (15 pages of output)

email addresses of authors :  biehl at physik.uni-wuerzburg.de
                           mietzner at physik.uni-wuerzburg.de 


****  Hardcopies  cannot be provided   **** 

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  "Statistical Mechanics of Unsupervised Structure Recognition"
  
    Michael Biehl and Andreas Mietzner
    Physikalisches Institut der Universitaet
    Am Hubland
  D-97074 Wuerzburg
    Germany  

Abstract:

A model of unsupervised learning is studied, where the
environment provides N-dimensional input examples that are drawn
from two overlapping Gaussian clouds. We consider the
optimization of two different objective functions: the search
for the direction of the largest variance in the data and the
largest separating gap (stability) respectively.
By means of a statistical mechanics analysis, we investigate how
well the underlying structure is inferred from a set of
examples. The performance of the learning algorithms depends
crucially on the actual shape of the input distribution. A
generic result is the existence of a critical number of examples
needed for successful learning. The learning strategies are
compared with methods different in spirit,  such as the estimation
of parameters in a model distribution and an information
theoretic approach. 
 
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