Abstract
We present the now well-known ODE method in a general framework. We state a global convergence theorem when the ODE has no “pseudocycle” which could apply in many cases. We note that the Kohonen algorithm in dimension 1 (units and stimuli) after self-organization is a cooperative dynamical system and prove the uniqueness of its equilibrium point. We then derive results of convergence (a.s and in distribution) for a very general class of stimuli distributions and neighbourhood functions.
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© 1997 Springer-Verlag Berlin Heidelberg
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Fort, JC., Pagès, G. (1997). Convergences of the Kohonen maps: a dynamical system approach. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020225
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DOI: https://doi.org/10.1007/BFb0020225
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