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On the a.s. convergence of the Kohonen algorithm with a general neighborhood function. (English) Zbl 0861.60076

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, various stability and instability results are derived from a general formula.
Reviewer: Wu Rong (Tianjin)

MSC:

60J05 Discrete-time Markov processes on general state spaces
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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