- Title
- Generalised rational approximation and its application to improve deep learning classifiers
- Creator
- Peiris, V; Sharon, Nir; Sukhorukova, Nadezda; Ugon, Julien
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/173692
- Identifier
- vital:14734
- Identifier
-
https://doi.org10.1016/j.amc.2020.125560
- Identifier
- ISBN:0096-3003 (ISSN)
- 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. © 2020; This research was supported by the Australian Research Council (ARC), Solving hard Chebyshev approximation problems through nonsmooth analysis (Discovery Project DP180100602 ). This research was partially sponsored by Tel Aviv-Swinburne Research Collaboration Grant (2019).
- Publisher
- Elsevier Inc.
- Relation
- Applied Mathematics and Computation Vol. 389, no. (2021), p.; https://purl.org/au-research/grants/arc/DP180100602
- Rights
- Copyright © 2020 Elsevier Inc. All rights reserved.
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0802 Computation Theory and Mathematics; Chebyshev approximation; Data analysis; Deep learning; Generalised rational approximation; Quasiconvex functions; Rational approximation
- Reviewed
- Funder
- This research was supported by the Australian Research Council (ARC), Solving hard Chebyshev approximation problems through nonsmooth analysis (Discovery Project DP180100602 ). This research was partially sponsored by Tel Aviv-Swinburne Research Collaboration Grant (2019).
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