Self-organizing map algorithm and distortion measure

被引：9

作者：

Rynkiewicz, Joseph ^{[1
]}

机构：

[1] Univ Paris 01, SAMOS, MATISSE, F-75013 Paris, France

来源：

NEURAL NETWORKS | 2006年 / 19卷 / 6-7期

关键词：

distortion measure; asymptotic convergence; consistency; self-organizing map; empirical processes; Glivenko-Cantelli class; uniform law of large numbers; general neighborhood function;

D O I：

10.1016/j.neunet.2006.05.016

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of the distortion measure. If we assume that the observations and the map lie in a compact Euclidean space, we prove the strong consistency of the map which almost minimizes the empirical distortion. Moreover, after calculating the derivatives of the theoretical distortion measure, we show that the points minimizing this measure and the equilibria of the Kohonen map do not match in general. We illustrate, with a simple example, how this occurs. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：830 / 837

页数：8

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