Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks

Author

Chen, Tianping ; Chen, Hong

Author_Institution

Dept. of Math., Fudan Univ., Shanghai, China

Volume

6

Issue

4

fYear

1995

fDate

7/1/1995 12:00:00 AM

Firstpage

904

Lastpage

910

Abstract

The purpose of this paper is to explore the representation capability of radial basis function (RBF) neural networks. The main results are: 1) the necessary and sufficient condition for a function of one variable to be qualified as an activation function in RBF network is that the function is not an even polynomial, and 2) the capability of approximation to nonlinear functionals and operators by RBF networks is revealed, using sample data either in frequency domain or in time domain, which can be used in system identification by neural networks

Keywords

approximation theory; feedforward neural nets; function approximation; identification; activation function; function approximation; necessary condition; nonlinear functionals; radial basis function neural networks; sufficient condition; system identification; Feedforward neural networks; Frequency domain analysis; Kernel; Multi-layer neural network; Multilayer perceptrons; Neural networks; Polynomials; Radial basis function networks; Sufficient conditions; System identification;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.392252

Filename

392252