Translation-Invariant Kernels for Multivariable Approximation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00532708" target="_blank" >RIV/67985807:_____/21:00532708 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TNNLS.2020.3026720" target="_blank" >http://dx.doi.org/10.1109/TNNLS.2020.3026720</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TNNLS.2020.3026720" target="_blank" >10.1109/TNNLS.2020.3026720</a>
Alternative languages
Result language
angličtina
Original language name
Translation-Invariant Kernels for Multivariable Approximation
Original language description
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)
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA18-23827S" target="_blank" >GA18-23827S: Capabilities and limitations of shallow and deep networks</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Neural Networks and Learning Systems
ISSN
2162-237X
e-ISSN
2162-2388
Volume of the periodical
32
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
5072-5081
UT code for WoS article
000711638200028
EID of the result in the Scopus database
2-s2.0-85092915493