Weight convergence and weight density of the multi-dimensional SOFM algorithm

Siming Lin, Jennie Si

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

In this paper, we analyze convergence properties of the self-organizing feature map (SOFM) with multi-dimensional input using Robbins-Monro stochastic approximation principle. It is shown that the SOFM algorithm optimizes a well defined energy function and converges almost truly (i.e. with probability one) if the input data is from a discrete stochastic distribution. For the case of multi-dimensional inputs generated from continuous distributions, it is shown that the weights of the SOFM algorithm converge almost truly to the centroids of the cells of a Voronoi partition of the input space if the neighborhood function satisfies some reasonable conditions. The density of the weight space in the equilibrium states is also investigated.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
PublisherIEEE
Pages2404-2408
Number of pages5
Volume4
StatePublished - 1997
EventProceedings of the 1997 American Control Conference. Part 3 (of 6) - Albuquerque, NM, USA
Duration: Jun 4 1997Jun 6 1997

Other

OtherProceedings of the 1997 American Control Conference. Part 3 (of 6)
CityAlbuquerque, NM, USA
Period6/4/976/6/97

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Lin, S., & Si, J. (1997). Weight convergence and weight density of the multi-dimensional SOFM algorithm. In Proceedings of the American Control Conference (Vol. 4, pp. 2404-2408). IEEE.