About the multidimensional competitive learning vector quantization algorithm with constant gain

DOI10.1214/aoap/1034801249zbMath0892.60082OpenAlexW2006444496MaRDI QIDQ1370999

Gilles Pagès, Catherine Bouton

Publication date: 9 August 1998

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

Full work available at URL: https://doi.org/10.1214/aoap/1034801249

zbMATH Keywords

neural networksMarkov chainvector quantizationuniform ergodicity

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Limit theorems in probability theory (60F99)

Related Items

A space quantization method for numerical integration, Bridging the gap between constant step size stochastic gradient descent and Markov chains, Limit theorems for random normalized distortion, Average Competitive Learning Vector Quantization, Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension, Error analysis of the optimal quantization algorithm for obstacle problems., Simulated annealing with a potential function with discontinuous gradient on \(\mathbb R^d\), Numerical Methods for the Exit Time of a Piecewise-Deterministic Markov Process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov chains and stochastic stability
• Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli
• Self-organization and associative memory
• Étude d'un processus d'auto-organisation. (Study of a self-organization process)
• Analysis of a simple self-organizing process
• A self-organizing cluster process
• On the a.s. convergence of the Kohonen algorithm with a general neighborhood function
• Exponential rate of convergence for Lloyd's method I
• Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions
• Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform