Kohonen's Learning Vector Quantization is a nonparametric classification scheme which classifies observations by comparing them to k templates called Voronoi vectors. The locations of these vectors are determined from past labeled data through a learning algorithm. When learning is complete, the class of a new observation is the same as the class of the closest Voronoi vector. Hence LVQ is similar to nearest neighbors, except that instead of all of the past observations being searched only the k Voronoi vectors are searched.
In this paper, we show that the LVQ learning algorithm converges to asymptotically stable zeros of an ordinary differential eqüation. 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. We also present a modification to the learning algorithm which results in more robust convergence.