Finite-Sample Convergence Properties of the LVQ1 Algorithm and the Batch LVQ1 Algorithm

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.