Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli

DOI10.1016/0304-4149(93)90017-XzbMath0779.60075MaRDI QIDQ689465

Catherine Bouton, Gilles Pagès

Publication date: 19 January 1994

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Markov chainsneural networksnumerical simulations

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (12)

Self-organization of the batch Kohonen network under quantization effects ⋮ Convergence rate of optimal quantization grids and application to empirical measure ⋮ Study of the Kohonen network with a discrete state space ⋮ A self-organizing cluster process ⋮ Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options ⋮ About the multidimensional competitive learning vector quantization algorithm with constant gain ⋮ A space quantization method for numerical integration ⋮ Convergence theorems for the Kohonen feature mapping algorithms with VLRPs ⋮ Kohonen neural networks and genetic classification ⋮ Theoretical analysis of the batch variant of the self-organizing feature map algorithm for 1-d networks mapping a continuous 1-d input space ⋮ Computational intelligence: From mathematical point of view ⋮ Asymptotic behavior of self-organizing maps with nonuniform stimuli distribution

Cites Work

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• Self-organization and associative memory
• Étude d'un processus d'auto-organisation. (Study of a self-organization process)
• Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne. (Gaussian approximation of stochastic algorithms)
• Analysis of a simple self-organizing process
• Quasi-Monte Carlo methods and pseudo-random numbers
• A Stochastic Approximation Method

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