TY - JOUR

T1 - Generalised rational approximation and its application to improve deep learning classifiers

AU - Peiris, V.

AU - Sharon, N.

AU - Sukhorukova, N.

AU - Ugon, J.

N1 - Publisher Copyright:
© 2020

PY - 2021/1/15

Y1 - 2021/1/15

N2 - A rational approximation (that is, approximation by a ratio of two polynomials) is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non-Lipschitz functions, where polynomial approximations are not efficient. We prove that the optimisation problems appearing in the best uniform rational approximation and its generalisation to a ratio of linear combinations of basis functions are quasiconvex even when the basis functions are not restricted to monomials. Then we show how this fact can be used in the development of computational methods. This paper presents a theoretical study of the arising optimisation problems and provides results of several numerical experiments. We apply our approximation as a preprocessing step to deep learning classifiers and demonstrate that the classification accuracy is significantly improved compared to the classification of the raw signals.

AB - A rational approximation (that is, approximation by a ratio of two polynomials) is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non-Lipschitz functions, where polynomial approximations are not efficient. We prove that the optimisation problems appearing in the best uniform rational approximation and its generalisation to a ratio of linear combinations of basis functions are quasiconvex even when the basis functions are not restricted to monomials. Then we show how this fact can be used in the development of computational methods. This paper presents a theoretical study of the arising optimisation problems and provides results of several numerical experiments. We apply our approximation as a preprocessing step to deep learning classifiers and demonstrate that the classification accuracy is significantly improved compared to the classification of the raw signals.

KW - Chebyshev approximation

KW - Data analysis

KW - Deep learning

KW - Generalised rational approximation

KW - Quasiconvex functions

KW - Rational approximation

UR - http://www.scopus.com/inward/record.url?scp=85089187351&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2020.125560

DO - 10.1016/j.amc.2020.125560

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AN - SCOPUS:85089187351

SN - 0096-3003

VL - 389

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 125560

ER -