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Translation-Invariant Kernels for Multivariable Approximation
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SYSNO ASEP 0532708 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Translation-Invariant Kernels for Multivariable Approximation Author(s) Kůrková, Věra (UIVT-O) RID, SAI, ORCID
Coufal, David (UIVT-O) RID, SAI, ORCIDNumber of authors 2 Source Title IEEE Transactions on Neural Networks and Learning Systems - ISSN 2162-237X
Roč. 32, č. 11 (2021), s. 5072-5081Number of pages 10 s. Language eng - English Country US - United States Keywords Classification ; Fourier and Hankel transforms ; 17 function approximation ; radial kernels ; translation-invariant kernels Subject RIV IN - Informatics, Computer Science OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GA18-23827S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000711638200028 EID SCOPUS 85092915493 DOI 10.1109/TNNLS.2020.3026720 Annotation Suitability of shallow (one-hidden-layer) networks with translation-invariant kernel units for function approximation and classification tasks is investigated. It is shown that a critical property influencing the capabilities of kernel networks is how the Fourier transforms of kernels converge to zero. The Fourier transforms of kernels suitable for multivariable approximation can have negative values but must be almost everywhere nonzero. In contrast, the Fourier transforms of kernels suitable for maximal margin classification must be everywhere nonnegative but can have large sets where they are equal to zero (e.g., they can be compactly supported). The behavior of the Fourier transforms of multivariable kernels is analyzed using the Hankel transform. The general results are illustrated by examples of both univariable and multivariable kernels (such as Gaussian, Laplace, rectangle, sinc, and cut power kernels) Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022 Electronic address http://dx.doi.org/10.1109/TNNLS.2020.3026720
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