Spline-based methods for functional data on multivariate domains

Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the a...
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Autor*in:	Basna, Rani [verfasserIn] Nassar, Hiba [verfasserIn] Podgórski, Krzysztof [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Splinets Tensor spline bases Orthonormal bases Binary regression trees Image classification

Anmerkung:	© The Author(s) 2024

Übergeordnetes Werk:	Enthalten in: Journal of mathematics in industry - Springer Berlin Heidelberg, 2011, 14(2024), 1 vom: 30. Juli
Übergeordnetes Werk:	volume:14 ; year:2024 ; number:1 ; day:30 ; month:07

Links:	Volltext

DOI / URN:	10.1186/s13362-024-00153-w

Katalog-ID:	SPR05679262X

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520			\|a Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods.
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allfields	10.1186/s13362-024-00153-w doi (DE-627)SPR05679262X (SPR)s13362-024-00153-w-e DE-627 ger DE-627 rakwb eng 510 VZ Basna, Rani verfasserin aut Spline-based methods for functional data on multivariate domains 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. Splinets (dpeaa)DE-He213 Tensor spline bases (dpeaa)DE-He213 Orthonormal bases (dpeaa)DE-He213 Binary regression trees (dpeaa)DE-He213 Image classification (dpeaa)DE-He213 Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin (orcid)0000-0003-0043-1532 aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 30. Juli (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:30 month:07 https://dx.doi.org/10.1186/s13362-024-00153-w X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 30 07
spelling	10.1186/s13362-024-00153-w doi (DE-627)SPR05679262X (SPR)s13362-024-00153-w-e DE-627 ger DE-627 rakwb eng 510 VZ Basna, Rani verfasserin aut Spline-based methods for functional data on multivariate domains 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. Splinets (dpeaa)DE-He213 Tensor spline bases (dpeaa)DE-He213 Orthonormal bases (dpeaa)DE-He213 Binary regression trees (dpeaa)DE-He213 Image classification (dpeaa)DE-He213 Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin (orcid)0000-0003-0043-1532 aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 30. Juli (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:30 month:07 https://dx.doi.org/10.1186/s13362-024-00153-w X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 30 07
allfields_unstemmed	10.1186/s13362-024-00153-w doi (DE-627)SPR05679262X (SPR)s13362-024-00153-w-e DE-627 ger DE-627 rakwb eng 510 VZ Basna, Rani verfasserin aut Spline-based methods for functional data on multivariate domains 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. Splinets (dpeaa)DE-He213 Tensor spline bases (dpeaa)DE-He213 Orthonormal bases (dpeaa)DE-He213 Binary regression trees (dpeaa)DE-He213 Image classification (dpeaa)DE-He213 Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin (orcid)0000-0003-0043-1532 aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 30. Juli (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:30 month:07 https://dx.doi.org/10.1186/s13362-024-00153-w X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 30 07
allfieldsGer	10.1186/s13362-024-00153-w doi (DE-627)SPR05679262X (SPR)s13362-024-00153-w-e DE-627 ger DE-627 rakwb eng 510 VZ Basna, Rani verfasserin aut Spline-based methods for functional data on multivariate domains 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. Splinets (dpeaa)DE-He213 Tensor spline bases (dpeaa)DE-He213 Orthonormal bases (dpeaa)DE-He213 Binary regression trees (dpeaa)DE-He213 Image classification (dpeaa)DE-He213 Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin (orcid)0000-0003-0043-1532 aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 30. Juli (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:30 month:07 https://dx.doi.org/10.1186/s13362-024-00153-w X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 30 07
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language	English
source	Enthalten in Journal of mathematics in industry 14(2024), 1 vom: 30. Juli volume:14 year:2024 number:1 day:30 month:07
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topic_facet	Splinets Tensor spline bases Orthonormal bases Binary regression trees Image classification
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author	Basna, Rani
spellingShingle	Basna, Rani ddc 510 misc Splinets misc Tensor spline bases misc Orthonormal bases misc Binary regression trees misc Image classification Spline-based methods for functional data on multivariate domains
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topic_title	510 VZ Spline-based methods for functional data on multivariate domains Splinets (dpeaa)DE-He213 Tensor spline bases (dpeaa)DE-He213 Orthonormal bases (dpeaa)DE-He213 Binary regression trees (dpeaa)DE-He213 Image classification (dpeaa)DE-He213
topic	ddc 510 misc Splinets misc Tensor spline bases misc Orthonormal bases misc Binary regression trees misc Image classification
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title	Spline-based methods for functional data on multivariate domains
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title_sort	spline-based methods for functional data on multivariate domains
title_auth	Spline-based methods for functional data on multivariate domains
abstract	Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. © The Author(s) 2024
abstractGer	Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. © The Author(s) 2024
abstract_unstemmed	Abstract Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. © The Author(s) 2024
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title_short	Spline-based methods for functional data on multivariate domains
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Spline-based methods for functional data on multivariate domains

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