ICANN ’94 pp 318-321 | Cite as

About the convergence of the generalized Kohonen algorithm

  • Jean-Claude Fort
  • Gilles Pagès
Conference paper

Abstract

The Kohonen algorithm was originally devised and studied by Kohonen in 1982 (see [4], [5]). Unfortunately, as far as mathematical treatment is concerned, rigourous results are not so easy to establish. For instance, any simulation in a one dimensional setting (i.e. with scalar inputs) shows the existence of a self-organization property. Nevertheless, the proof of such a property requires some non trivial Markov material. It was first carried out in [2] for uniformly distributed stimuli and then was extended to general distributions in [1]. Many open questions related to the one dimensional self-organization still remain, and no similar result was proved in higher dimension so far.

Keywords

Rium 

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References

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    C. Bouton, G. Pagès, Self-organization and convergence of the one-dimensional Kohonen algorithm with non uniformly distributed stimuli, Stoch. Proc. and their Appl, 47, 1993, p.249–274.CrossRefMATHGoogle Scholar
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Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Jean-Claude Fort
    • 1
    • 2
  • Gilles Pagès
    • 3
    • 4
  1. 1.Fac. SciencesUniv. Nancy IVandœuvre-Lès-Nancy Cedex & SamosFrance
  2. 2.Univ. Paris IParis Cedex 13France
  3. 3.Lab. de Proba.URA 224, Univ. Paris 6Paris Cedex 05France
  4. 4.Univ. Paris 12Créteil CedexFrance

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