Two theorems for the Kohonen mapping neural network

The authors provide a rigorous treatment of the convergence of the topology preserving neural network which was first proposed by Kohonen. The problem is formulated for a more general case of selecting the neighborhood amplitude of interaction rather than the uniform amplitude. The proof of convergence is based on the well-known Gladyshev theorem which uses Lyapunov´s function method. This proof also provides the relation between the boundary neurons weight vectors and the number of neurons in the network