Approximation by spherical neural networks with zonal functions

Zhixiang Chen, Feilong Cao

Abstract


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.

doi:10.1017/S1446181117000104

Keywords


approximation, neural networks, zonal function, error.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11098



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.