paper available

[Michael Biehl]

FTP-host: archive.cis.ohio-state.edu
FTP-file: pub/neuroprose/marangi.clusters.ps.Z

The following paper has been placed in the Neuroprose archive in file
marangi.clusters.ps.Z (8 pages).  Hardcopies are not available.

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        SUPERVISED LEARNING FROM CLUSTERED INPUT EXAMPLES 

                        Carmela Marangi
          Dipartimento di Fisica dell' Universita' di Bari
                   and I.N.F.N., Sez. di Bari
                Via Orabona 4, 70126 Bari, Italy  

		  Michael Biehl ^ and Sara Solla 
                 CONNECT, The Niels Bohr Institute
              Blegdamsvej 17, 2100 Copenhagen, Denmark

               ^ email: biehl at physik.uni-wuerzburg.de


                  submitted to Europhysics Letters

                
                            ABSTRACT

In this paper we analyse the effect of introducing a structure in the input
distribution on the generalzation ability of a simple perceptron. The simple
case of two clusters of input data and a linearly separable rule is
considered. We find that the generalization ability improves with the
separation between the clusters, and is bounded from below by the result for
the unstructured case. The asymptotic behavior for large training sets,
however, is the same for structured and unstructured input distributions. For
small training sets, the dependence of the generalization error on the number
of examples is observed to be nonmonotonic for certain values of the model
parameters. 


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---  Michael Biehl   biehl at physik.uni-wuerzburg.de