CONVERGENCE IN DISTRIBUTION OF THE ONE-DIMENSIONAL KOHONEN ALGORITHMS WHEN THE STIMULI ARE NOT UNIFORM

被引：20
|
作者：
BOUTON, C
PAGES, G
机构：
[1] UNIV PARIS 06,PROBABILITES LAB,URA 224,F-75252 PARIS 05,FRANCE
[2] UNIV PARIS 01,UFR 27,F-75634 PARIS 13,FRANCE
来源：
ADVANCES IN APPLIED PROBABILITY | 1994年 / 26卷 / 01期
关键词：
MARKOV CHAINS; DOEBLIN RECURRENCE; NEURAL NETWORKS;
D O I：
10.2307/1427581
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：
We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step epsilon) is a Doeblin recurrent Markov chain provided that the stimuli distribution mu is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure nu(epsilon) (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as epsilon down 0 and its robustness with respect to mu.
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页码：80 / 103
页数：24
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