Convergence of a Neural Network Classifier

In this paper, we prove that the vectors in the LVQ learning algorithm converge.  We do this by showing that the learning algorithm performs stochastic approximation.  Convergence is then obtained by identifying the appropriate conditions in the learning rate and on the underlying statistics of the classification problem.  We also present a modification to the learning algorithm which we argue results in convergence of the LVQ error to the Bayesian optimal error as the appropriate parameters become large.