On the A.S. Convergence of the Kohonen Algorithm with a General Neighborhood Function

Some existence and stability results for the equilibrium points of the one-dimensional Kohonen self-organizing neural network with two neighbors are extended to most nonincreasing neighborhood functions. All the functions mentioned in the neural literature are included. The assumption on the stimuli distribution is weakened, too. In the multidimensional setting, we derive from a general formula various stability and instability results.