Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data

Research output: Chapter in Book/Conference paperConference paper

1 Citation (Scopus)

Abstract

The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symbolic computation within Mathematica software is used to generate the relevant optimization scheme for estimating the missing interpolation knots. Experiments confirm the theoretical input of this work and enable numerical comparisons (again with the aid of Mathematica) between various schemes used in the optimization step. Modelling and/or fitting reduced sparse data constitutes a common problem in natural sciences (e.g. biology) and engineering (e.g. computer graphics).

Original languageEnglish
Title of host publicationComputer Algebra in Scientific Computing
Subtitle of host publication19th International Workshop, CASC 2017, Proceedings
EditorsVladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
Place of PublicationBeijing
PublisherSpringer
Pages257-271
Number of pages15
Volume10490 LNCS
ISBN (Print)9783319663197
DOIs
Publication statusPublished - 2017
Event19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 - Beijing, China
Duration: 18 Sep 201722 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10490 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
CountryChina
CityBeijing
Period18/09/1722/09/17

Fingerprint

Non-convexity
Knot
Mathematica
Nonlinearity
Optimization
Interpolate
Interpolation
Sparse Data
Symbolic Computation
Numerical Comparisons
Computer graphics
Natural sciences
Biology
Euclidean space
Optimization Problem
Engineering
Unknown
Software
Arbitrary
Modeling

Cite this

Kozera, R., & Noakes, L. (2017). Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. In V. P. Gerdt, W. Koepf, W. M. Seiler, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings (Vol. 10490 LNCS, pp. 257-271). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10490 LNCS). Beijing: Springer. https://doi.org/10.1007/978-3-319-66320-3_19
Kozera, Ryszard ; Noakes, Lyle. / Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings. editor / Vladimir P. Gerdt ; Wolfram Koepf ; Werner M. Seiler ; Evgenii V. Vorozhtsov. Vol. 10490 LNCS Beijing : Springer, 2017. pp. 257-271 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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abstract = "The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symbolic computation within Mathematica software is used to generate the relevant optimization scheme for estimating the missing interpolation knots. Experiments confirm the theoretical input of this work and enable numerical comparisons (again with the aid of Mathematica) between various schemes used in the optimization step. Modelling and/or fitting reduced sparse data constitutes a common problem in natural sciences (e.g. biology) and engineering (e.g. computer graphics).",
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Kozera, R & Noakes, L 2017, Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. in VP Gerdt, W Koepf, WM Seiler & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings. vol. 10490 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10490 LNCS, Springer, Beijing, pp. 257-271, 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, Beijing, China, 18/09/17. https://doi.org/10.1007/978-3-319-66320-3_19

Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. / Kozera, Ryszard; Noakes, Lyle.

Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings. ed. / Vladimir P. Gerdt; Wolfram Koepf; Werner M. Seiler; Evgenii V. Vorozhtsov. Vol. 10490 LNCS Beijing : Springer, 2017. p. 257-271 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10490 LNCS).

Research output: Chapter in Book/Conference paperConference paper

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T1 - Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data

AU - Kozera, Ryszard

AU - Noakes, Lyle

PY - 2017

Y1 - 2017

N2 - The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symbolic computation within Mathematica software is used to generate the relevant optimization scheme for estimating the missing interpolation knots. Experiments confirm the theoretical input of this work and enable numerical comparisons (again with the aid of Mathematica) between various schemes used in the optimization step. Modelling and/or fitting reduced sparse data constitutes a common problem in natural sciences (e.g. biology) and engineering (e.g. computer graphics).

AB - The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symbolic computation within Mathematica software is used to generate the relevant optimization scheme for estimating the missing interpolation knots. Experiments confirm the theoretical input of this work and enable numerical comparisons (again with the aid of Mathematica) between various schemes used in the optimization step. Modelling and/or fitting reduced sparse data constitutes a common problem in natural sciences (e.g. biology) and engineering (e.g. computer graphics).

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KW - Knots selection

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VL - 10490 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Kozera R, Noakes L. Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. In Gerdt VP, Koepf W, Seiler WM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings. Vol. 10490 LNCS. Beijing: Springer. 2017. p. 257-271. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-66320-3_19