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February 1998 Asymptotic behavior of self-organizing maps with nonuniform stimuli distribution
Ali A. Sadeghi
Ann. Appl. Probab. 8(1): 281-299 (February 1998). DOI: 10.1214/aoap/1027961044

Abstract

Here the almost sure convergence of one-dimensional Kohonen's algorithm in its general form, namely, the 2k-neighbor setting with a nonuniform stimuli distribution, is proved. We show that the asymptotic behavior of the algorithm is governed by a cooperative system of differential equations which is irreducible. The system of differential equations possesses an asymptotically stable equilibrium, a compact subset of whose domain of attraction will be visited by the state variable $X^n$ infinitely often. The assumptions on the stimuli distribution and the neighborhood functions are weakened, too.

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Ali A. Sadeghi. "Asymptotic behavior of self-organizing maps with nonuniform stimuli distribution." Ann. Appl. Probab. 8 (1) 281 - 299, February 1998. https://doi.org/10.1214/aoap/1027961044

Information

Published: February 1998
First available in Project Euclid: 29 July 2002

zbMATH: 0939.60080
MathSciNet: MR1620374
Digital Object Identifier: 10.1214/aoap/1027961044

Subjects:
Primary: 60J05
Secondary: 92B20 , 93D20

Keywords: neural networks , stochastic approximation , theory of differential equations

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 1 • February 1998
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