Generalised rational approximation and its application to improve deep learning classifiers

V. Peiris, N. Sharon, N. Sukhorukova, J. Ugon

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number125560
JournalApplied Mathematics and Computation
Volume389
DOIs
StatePublished - 15 Jan 2021

Keywords

  • Chebyshev approximation
  • Data analysis
  • Deep learning
  • Generalised rational approximation
  • Quasiconvex functions
  • Rational approximation

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