A view of unconstrained optimization
Optimization
Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Self-organizing maps
On-line learning and stochastic approximations
On-line learning in neural networks
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Learning with Nearest Neighbour Classifiers
Neural Processing Letters
Local Averaging of Ensembles of LVQ-Based Nearest Neighbor Classifiers
Applied Intelligence
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This letter addresses the asymptotic convergence of Kohonen's LVQ1 algorithm when the number of training samples are finite with an analysis that uses the dynamical systems and optimisation theories. It establishes the sufficient conditions to ensure the convergence of LVQ1 near a minimum of its cost function for constant step sizes and cyclic sampling. It also proposes a batch version of LVQ1 based on the very fast Newton optimisation method that cancels the dependence of the on-line version on the order of supplied training samples.