TCB Publications - Abstract

Edgar Erwin, Klaus Obermayer, and Klaus Schulten. Convergence properties of self-organizing maps. In Teuvo Kohonen, Kai Mäkisara, Olli Simula, and Jari Kangas, editors, Artificial Neural Networks, pp. 409-414. Elsevier, Amsterdam, 1991.

ERWI91 We investigate the convergence properties, in particular convergence time and number and characteristics of metastable states, of the self-organizing feature map algorithm for a simple, but very instructive case: the representation of the unit interval by a linear Kohonen chain. We find that convergence times are minimal for a Gaussian neighborhood function with a width of the order of the number of neurons in the chain. Metastable states, which may "trap" Kohonen maps for a long time during the ordering process, arise for concave-shaped neighborhood functions. An extension of Kohonen's proof of ordering to include all neighborhood functions which are monotonically decreasing with distance is introduced.

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