Convergence of the one-dimensional Kohonen algorithm

We show in a very general framework the a.s. convergence of the one-dimensional Kohonen algorithm–after self-organization–to its unique equilibrium when the learning rate decreases to 0 in a suitable way. The main requirement is a log-concavity assumption on the stimuli distribution which includes a...

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Veröffentlicht in:	Advances in applied probability 1998-09, Vol.30 (3), p.850-869
Hauptverfasser:	Benaïm, Michel, Fort, Jean-Claude, Pagès, Gilles
Format:	Artikel
Sprache:	eng
Schlagworte:	34C35 62L20 Algorithms cooperative dynamical system Dynamical systems Eigenvalues General Applied Probability Kohonen algorithm Martingales Mathematical functions Mathematical vectors Odes Ordinary differential equations Partial derivatives Perceptron convergence procedure Probability stochastic algorithm Stochastic models Studies Uniqueness
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