Convergence of Kohonen´s learning vector quantization

It is shown that the learning vector quantization (LVQ) algorithm (T. Kohonen, 1986), converges to locally asymptotic stable equilibria of an ordinary differential equation. It is shown that the learning algorithm performs stochastic approximation. Convergence of the vectors is guaranteed under the appropriate conditions on the underlying statistics of the classification problem. Also presented is a modification to the learning algorithm which results in more robust convergence. With this modification, it is possible to show that as the appropriate parameters go to infinity, the decision regions associated with the modified LVQ algorithm approach the Bayesian optimal