Asymptotic behavior of self-organizing maps with nonuniform stimuli distribution

DOI10.1214/aoap/1027961044zbMath0939.60080OpenAlexW2051277574MaRDI QIDQ1296630

Ali A. Sadeghi

Publication date: 5 July 2000

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1027961044

zbMATH Keywords

neural networksstochastic approximationtheory of differential equations

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Neural networks for/in biological studies, artificial life and related topics (92B20) Asymptotic stability in control theory (93D20)

Related Items (1)

Stochastic approximation, cooperative dynamics and supermodular games

Cites Work

• Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli
• Étude d'un processus d'auto-organisation. (Study of a self-organization process)
• Self-organizing maps: Ordering, convergence properties and energy functions
• Stochastic approximation methods for constrained and unconstrained systems
• On the a.s. convergence of the Kohonen algorithm with a general neighborhood function
• Stability and convergence in strongly monotone dynamical systems.
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform
• Self-organizing maps.
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