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November, 1995 On the A.S. Convergence of the Kohonen Algorithm with a General Neighborhood Function
Jean-Claude Fort, Gilles Pages
Ann. Appl. Probab. 5(4): 1177-1216 (November, 1995). DOI: 10.1214/aoap/1177004611

Abstract

Some existence and stability results for the equilibrium points of the one-dimensional Kohonen self-organizing neural network with two neighbors are extended to most nonincreasing neighborhood functions. All the functions mentioned in the neural literature are included. The assumption on the stimuli distribution is weakened, too. In the multidimensional setting, we derive from a general formula various stability and instability results.

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Jean-Claude Fort. Gilles Pages. "On the A.S. Convergence of the Kohonen Algorithm with a General Neighborhood Function." Ann. Appl. Probab. 5 (4) 1177 - 1216, November, 1995. https://doi.org/10.1214/aoap/1177004611

Information

Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0861.60076
MathSciNet: MR1384371
Digital Object Identifier: 10.1214/aoap/1177004611

Subjects:
Primary: 60J05
Secondary: 60K30

Keywords: neural networks , quantization , self-organization , stochastic algorithms

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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