Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli
This paper shows that the 2-neighbour Kohonen algorithm is self-organizing under pretty general assumptions on the stimuli distribution [mu] (supp([mu]c) contains a non-empty open set) and is a.s. convergent--in a weakened sense--as soon as [mu] admits a log-concave density. The 0-neighbour algorithm is shown to have similar converging properties. Some numerical simulations illustrate the theoretical results and a counter-example provided by a specific class of density functions.
Year of publication: |
1993
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Authors: | Bouton, Catherine ; Pagès, Gilles |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 47.1993, 2, p. 249-274
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Publisher: |
Elsevier |
Keywords: | Neural networks Stochastic algorithms Markov chains |
Saved in:
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