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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Verfasserangaben: Ali A. Sadeghi urn:nbn:de:hbz:386-kluedo-5691 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (166) Preprint Englisch 1996 1996 Technische Universität Kaiserslautern 23.06.2000 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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