THE AS CONVERGENCE OF THE ONE-DIMENSIONALKOHONEN ALGORITHM

Authors
BENAIM M FORT JC PAGES G
Citation
M. Benaim et al., THE AS CONVERGENCE OF THE ONE-DIMENSIONALKOHONEN ALGORITHM, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(12), 1997, pp. 1407-1412
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
324
Issue
12
Year of publication
1997
Pages
1407 - 1412
Database
ISI
SICI code
0764-4442(1997)324:12<1407:TACOTO>2.0.ZU;2-J
Abstract
We prove the a.s. convergence of the one dimensional Kohonen algorithm after self-organization and with decreasing step. Under some mild asu mption of log-concavity on the input probability distribution, we firs t show the uniqueness of the limit and then the a.s. convergence. The proof relies on the index formula for a vector field on a manifold and a result by M. Hirsh about the convergence of cooperative dynamical s ystems applied to the ODE.