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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 Xn infinitely often. The assumptions on the stimuli distribution and the neighborhood functions are weakened, too.

Citation

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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

Vol.8 • No. 1 • February 1998
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