Asymptotic Behaviour of Self-Organizing Maps with Non-Uniform Stimuli Distribution

  • Here the almost sure convergence of one dimensional Kohonen" s algorithm in its general form, namely, 2k point neightbour setting with a non-uniform stimuli distribution is proved. We show that the asymptotic behaviour of the algorithm is governed by a cooperative system of differential equations which in general is irreducible. The system of differential equation has an asymptotically stable fixed point which a compact subset of its domain of attraction will be visited by the state variable Xn infinitely often.

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Author:Ali A. Sadeghi
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5691
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (166)
Document Type:Preprint
Language of publication:English
Year of Completion:1996
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/06/23
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011