Fort, Jean-Claude; Pagès, Gilles On the a.s. convergence of the Kohonen algorithm with a general neighborhood function. (English) Zbl 0861.60076 Ann. Appl. Probab. 5, No. 4, 1177-1216 (1995). 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) Cited in 15 Documents MSC: 60J05 Discrete-time Markov processes on general state spaces 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.) Keywords:self-organization; quantization; self-organizing neural network; stability and instability results PDFBibTeX XMLCite \textit{J.-C. Fort} and \textit{G. Pagès}, Ann. Appl. Probab. 5, No. 4, 1177--1216 (1995; Zbl 0861.60076) Full Text: DOI