SELF-ORGANIZATION AND AS CONVERGENCE OF THE ONE-DIMENSIONAL KOHONEN ALGORITHM WITH NONUNIFORMLY DISTRIBUTED STIMULI

被引：42

作者：

BOUTON, C

PAGES, G

机构：

[1] UNIV PARIS 01,UFR 27,90 RUE TOLBIAC,F-75634 PARIS 13,FRANCE

[2] UNIV PARIS 06,PROBABIL & APPLICAT LAB,F-75230 PARIS 05,FRANCE

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1993年 / 47卷 / 02期

关键词：

NEURAL NETWORKS; STOCHASTIC ALGORITHMS; MARKOV CHAINS;

D O I：

10.1016/0304-4149(93)90017-X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper shows that the 2-neighbour Kohonen algorithm is self-organizing under pretty general assumptions on the stimuli distribution mu (supp(mu(c)) contains a non-empty open set) and is a.s. convergent-in a weakened sense-as soon as mu admits a log-concave density. The 0-neighbour algorithm is shown to have similar converging properties. Some numerical simulations illustrate the theoretical results and a counter-example provided by a specific class of density functions.

引用

页码：249 / 274

页数：26

共 19 条

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