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

Author

Chen, Tianping ; Chen, Hong

Author_Institution

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

Volume

2

fYear

1993

fDate

25-29 Oct. 1993

Firstpage

1439

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 an RBF network is that the function is not an even polynomial. (2) The capability of approximating nonlinear functionals and operators by RBF networks is revealed, using sample data either in the frequency domain or in the time domain.

Keywords

approximation theory; feedforward neural nets; function approximation; functional equations; activation function; approximation capability; frequency domain; necessary and sufficient condition; nonlinear functionals; operators; radial basis function neural networks; time domain; Convolution; Feedforward neural networks; Intelligent networks; Kernel; Mathematics; Multi-layer neural network; Neural networks; Polynomials; Radial basis function networks; Radiofrequency interference;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks, 1993. IJCNN '93-Nagoya. Proceedings of 1993 International Joint Conference on

Print_ISBN

0-7803-1421-2

Type

conf

DOI

10.1109/IJCNN.1993.716815

Filename

716815