Best approximation to C2 functions and its error bounds using Gaussian hidden units

Binfan Liu, Jennie Si

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

1 Scopus citations

Abstract

In the present paper we prove that any C2 function of m real variables with support in the unit hypercube can be approximated by a Gaussian radial basis network. This network uses a single layer of N Gaussian radial basis functions. The centers of the Gaussian functions are uniformly distributed on the unit hypercube. From the view point of the best approximation theory, an upper bound of this approximation O(σ2+N-2) is obtained, where σ is the deviation of Gaussians. Our results provide an explicit expression of the relationship between the number of hidden nodes and the approximation error.

Original languageEnglish (US)
Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
PublisherPubl by IEEE
Pages188-191
Number of pages4
ISBN (Print)0780312813
StatePublished - Jan 1 1993
Event1993 IEEE International Symposium on Circuits and Systems - Chicago, IL, USA
Duration: May 3 1993May 6 1993

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
Volume1
ISSN (Print)0271-4310

Other

Other1993 IEEE International Symposium on Circuits and Systems
CityChicago, IL, USA
Period5/3/935/6/93

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Liu, B., & Si, J. (1993). Best approximation to C2 functions and its error bounds using Gaussian hidden units. In Proceedings - IEEE International Symposium on Circuits and Systems (pp. 188-191). (Proceedings - IEEE International Symposium on Circuits and Systems; Vol. 1). Publ by IEEE.