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APPROXIMATION BY SPHERICAL NEURAL NETWORKS WITH ZONAL FUNCTIONS

Part of: Approximations and expansions

Published online by Cambridge University Press:  26 April 2017

ZHIXIANG CHEN  and
FEILONG CAO
ZHIXIANG CHEN
Affiliation:
Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang Province, PR China email czx@usx.edu.cn
FEILONG CAO*
Affiliation:
Department of Applied Mathematics, China Jiliang University, Hangzhou 310018, Zhejiang Province, PR China email feilongcao@gmail.com
*
✉feilongcao@gmail.com
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Abstract

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We address the construction and approximation for feed-forward neural networks (FNNs) with zonal functions on the unit sphere. The filtered de la Vallée-Poussin operator and the spherical quadrature formula are used to construct the spherical FNNs. In particular, the upper and lower bounds of approximation errors by the FNNs are estimated, where the best polynomial approximation of a spherical function is used as a measure of approximation error.

Keywords

approximationneural networkszonal functionerror

MSC classification

Primary: 41A25: Rate of convergence, degree of approximation
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 238 - 246
Copyright
© 2017 Australian Mathematical Society 

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