Fitting Dense and Sparse Reduced Data

Ryszard Kozera, Artur Wiliński

Research output: Chapter in Book/Conference paperConference paper

Abstract

This paper addresses the topic of fitting reduced data represented by the sequence of interpolation points (Formula Presented) in arbitrary Euclidean space Em. The parametric curve γ together with its knots (Formula Presented) (for which (Formula Presented)) are both assumed to be unknown. We look at some recipes to estimate T in the context of dense versus sparse M for various choices of interpolation schemes (Formula Presented). For M dense, the convergence rate to approximate γ with (Formula Presented) is considered as a possible criterion to force a proper choice of new knots (Formula Presented). The latter incorporates the so-called exponential parameterization “retrieving” the missing knots T from the geometrical spread of M. We examine the convergence rate in approximating γ by commonly used interpolants (Formula Presented) based here on M and exponential parameterization. In contrast, for M sparse, a possible optional strategy is to select (Formula Presented) which optimizes a certain cost function depending on the family of admissible knots (Formula Presented). This paper focuses on minimizing “an average acceleration” within the family of natural splines (Formula Presented) fitting M with (Formula Presented) admitted freely in the ascending order. Illustrative examples and some applications listed supplement theoretical component of this work.

Original languageEnglish
Title of host publicationAdvances in Soft and Hard Computing
EditorsJanusz Kacprzyk, Jerzy Pejaś, Imed El Fray, Tomasz Hyla
PublisherSpringer-Verlag Berlin
Pages3-17
Number of pages15
ISBN (Print)9783030033132
DOIs
Publication statusPublished - 1 Jan 2019
Event21st International Multi-Conference on Advanced Computer Systems, ACS 2018 - Międzyzdroje, Poland
Duration: 24 Sep 201826 Sep 2018
http://acs.zut.edu.pl/

Publication series

NameAdvances in Intelligent Systems and Computing
Volume889
ISSN (Print)2194-5357

Conference

Conference21st International Multi-Conference on Advanced Computer Systems, ACS 2018
Abbreviated titleACS2018
CountryPoland
CityMiędzyzdroje
Period24/09/1826/09/18
OtherArtificial intelligence, software technologies, biometrics and IT security are established fields of computer science of both theoretical and practical significance.

The aim of ACS 2018 Multi-Conference is to bring artificial intelligence, software technologies, biometrics, IT security and open and distance learning researchers in contact with the ACS community, and to give ACS attendees an opportunity to exchange some significant knowledge according to this areas of interest. Industrial and systems presentations bearing new ideas and solution paradigms are welcome as well.
Internet address

Fingerprint

Parameterization
Interpolation
Cost functions
Splines

Cite this

Kozera, R., & Wiliński, A. (2019). Fitting Dense and Sparse Reduced Data. In J. Kacprzyk, J. Pejaś, I. El Fray, & T. Hyla (Eds.), Advances in Soft and Hard Computing (pp. 3-17). (Advances in Intelligent Systems and Computing; Vol. 889). Springer-Verlag Berlin. https://doi.org/10.1007/978-3-030-03314-9_1
Kozera, Ryszard ; Wiliński, Artur. / Fitting Dense and Sparse Reduced Data. Advances in Soft and Hard Computing. editor / Janusz Kacprzyk ; Jerzy Pejaś ; Imed El Fray ; Tomasz Hyla. Springer-Verlag Berlin, 2019. pp. 3-17 (Advances in Intelligent Systems and Computing).
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Kozera, R & Wiliński, A 2019, Fitting Dense and Sparse Reduced Data. in J Kacprzyk, J Pejaś, I El Fray & T Hyla (eds), Advances in Soft and Hard Computing. Advances in Intelligent Systems and Computing, vol. 889, Springer-Verlag Berlin, pp. 3-17, 21st International Multi-Conference on Advanced Computer Systems, ACS 2018, Międzyzdroje, Poland, 24/09/18. https://doi.org/10.1007/978-3-030-03314-9_1

Fitting Dense and Sparse Reduced Data. / Kozera, Ryszard; Wiliński, Artur.

Advances in Soft and Hard Computing. ed. / Janusz Kacprzyk; Jerzy Pejaś; Imed El Fray; Tomasz Hyla. Springer-Verlag Berlin, 2019. p. 3-17 (Advances in Intelligent Systems and Computing; Vol. 889).

Research output: Chapter in Book/Conference paperConference paper

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PB - Springer-Verlag Berlin

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Kozera R, Wiliński A. Fitting Dense and Sparse Reduced Data. In Kacprzyk J, Pejaś J, El Fray I, Hyla T, editors, Advances in Soft and Hard Computing. Springer-Verlag Berlin. 2019. p. 3-17. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-030-03314-9_1