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August 1997 About the multidimensional competitive learning vector quantization algorithm with constant gain
Catherine Bouton, Gilles Pagès
Ann. Appl. Probab. 7(3): 679-710 (August 1997). DOI: 10.1214/aoap/1034801249

Abstract

The competitive learning vector quantization (CLVQ) algorithm with constant step ε>0--also known as the Kohonen algorithm with 0 neighbors--is studied when the stimuli are i.i.d. vectors. Its first noticeable feature is that, unlike the one-dimensional case which has n! absorbing subsets, the CLVQ algorithm is "irreducible on open sets" whenever the stimuli distribution has a path-connected support with a nonempty interior. Then the Doeblin recurrence (or uniform ergodicity) of the algorithm is established under some convexity assumption on the support. Several properties of the invariant probability measure νε are studied, including support location and absolute continuity with respect to the Lebesgue measure. Finally, the weak limit set of νε as ε0 is investigated.

Citation

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Catherine Bouton. Gilles Pagès. "About the multidimensional competitive learning vector quantization algorithm with constant gain." Ann. Appl. Probab. 7 (3) 679 - 710, August 1997. https://doi.org/10.1214/aoap/1034801249

Information

Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 0892.60082
MathSciNet: MR1459266
Digital Object Identifier: 10.1214/aoap/1034801249

Subjects:
Primary: 60J20
Secondary: 60F99 , 60J10

Keywords: Markov chain , neural networks , uniform ergodicity , Vector quantization

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.7 • No. 3 • August 1997
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