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Translation-Invariant Kernels for Multivariable Approximation

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    0532708 - ÚI 2022 RIV US eng J - Článek v odborném periodiku
    Kůrková, Věra - Coufal, David
    Translation-Invariant Kernels for Multivariable Approximation.
    IEEE Transactions on Neural Networks and Learning Systems. Roč. 32, č. 11 (2021), s. 5072-5081. ISSN 2162-237X. E-ISSN 2162-2388
    Grant CEP: GA ČR(CZ) GA18-23827S
    Institucionální podpora: RVO:67985807
    Klíčová slova: Classification * Fourier and Hankel transforms * 17 function approximation * radial kernels * translation-invariant kernels
    Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    Impakt faktor: 14.255, rok: 2021
    Způsob publikování: Omezený přístup
    http://dx.doi.org/10.1109/TNNLS.2020.3026720

    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)
    Trvalý link: http://hdl.handle.net/11104/0311119

     
     
Počet záznamů: 1