Data driven orthogonal basis selection for functional data analysis

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may hav...
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Autor*in:	Basna, Rani [verfasserIn] Nassar, Hiba [verfasserIn] Podgórski, Krzysztof [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Functional data analysis Machine learning Splines

Übergeordnetes Werk:	Enthalten in: Journal of multivariate analysis - Orlando, Fla. : Acad. Press, 1971, 189
Übergeordnetes Werk:	volume:189

DOI / URN:	10.1016/j.jmva.2021.104868

Katalog-ID:	ELV007458800

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520			\|a Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data.
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allfields	10.1016/j.jmva.2021.104868 doi (DE-627)ELV007458800 (ELSEVIER)S0047-259X(21)00146-9 DE-627 ger DE-627 rda eng 510 DE-600 31.73 bkl Basna, Rani verfasserin (orcid)0000-0001-7510-8460 aut Data driven orthogonal basis selection for functional data analysis 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data. Functional data analysis Machine learning Splines Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin aut Enthalten in Journal of multivariate analysis Orlando, Fla. : Acad. Press, 1971 189 Online-Ressource (DE-627)267328141 (DE-600)1469773-7 (DE-576)103373233 nnns volume:189 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.73 Mathematische Statistik AR 189
spelling	10.1016/j.jmva.2021.104868 doi (DE-627)ELV007458800 (ELSEVIER)S0047-259X(21)00146-9 DE-627 ger DE-627 rda eng 510 DE-600 31.73 bkl Basna, Rani verfasserin (orcid)0000-0001-7510-8460 aut Data driven orthogonal basis selection for functional data analysis 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data. Functional data analysis Machine learning Splines Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin aut Enthalten in Journal of multivariate analysis Orlando, Fla. : Acad. Press, 1971 189 Online-Ressource (DE-627)267328141 (DE-600)1469773-7 (DE-576)103373233 nnns volume:189 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.73 Mathematische Statistik AR 189
allfields_unstemmed	10.1016/j.jmva.2021.104868 doi (DE-627)ELV007458800 (ELSEVIER)S0047-259X(21)00146-9 DE-627 ger DE-627 rda eng 510 DE-600 31.73 bkl Basna, Rani verfasserin (orcid)0000-0001-7510-8460 aut Data driven orthogonal basis selection for functional data analysis 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data. Functional data analysis Machine learning Splines Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin aut Enthalten in Journal of multivariate analysis Orlando, Fla. : Acad. Press, 1971 189 Online-Ressource (DE-627)267328141 (DE-600)1469773-7 (DE-576)103373233 nnns volume:189 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.73 Mathematische Statistik AR 189
allfieldsGer	10.1016/j.jmva.2021.104868 doi (DE-627)ELV007458800 (ELSEVIER)S0047-259X(21)00146-9 DE-627 ger DE-627 rda eng 510 DE-600 31.73 bkl Basna, Rani verfasserin (orcid)0000-0001-7510-8460 aut Data driven orthogonal basis selection for functional data analysis 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data. Functional data analysis Machine learning Splines Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin aut Enthalten in Journal of multivariate analysis Orlando, Fla. : Acad. Press, 1971 189 Online-Ressource (DE-627)267328141 (DE-600)1469773-7 (DE-576)103373233 nnns volume:189 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.73 Mathematische Statistik AR 189
allfieldsSound	10.1016/j.jmva.2021.104868 doi (DE-627)ELV007458800 (ELSEVIER)S0047-259X(21)00146-9 DE-627 ger DE-627 rda eng 510 DE-600 31.73 bkl Basna, Rani verfasserin (orcid)0000-0001-7510-8460 aut Data driven orthogonal basis selection for functional data analysis 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data. Functional data analysis Machine learning Splines Nassar, Hiba verfasserin aut Podgórski, Krzysztof verfasserin aut Enthalten in Journal of multivariate analysis Orlando, Fla. : Acad. Press, 1971 189 Online-Ressource (DE-627)267328141 (DE-600)1469773-7 (DE-576)103373233 nnns volume:189 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.73 Mathematische Statistik AR 189
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title_sort	data driven orthogonal basis selection for functional data analysis
title_auth	Data driven orthogonal basis selection for functional data analysis
abstract	Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data.
abstractGer	Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data.
abstract_unstemmed	Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the functional principal component analysis, to the so-represented data. While the initial choice of a functional representation may have a significant impact on the second phase of the analysis, this issue has not gained much attention in the past. Typically, a rather ad hoc choice of some standard basis such as Fourier, wavelets, splines, etc. is used for the data transforming purpose. To address this important problem, we present its mathematical formulation, demonstrate its importance, and propose a data-driven method of functionally representing observations. The method chooses an initial functional basis by an efficient placement of the knots. A simple machine learning style algorithm is utilized for the knot selection and recently introduced orthogonal spline bases - splinets - are eventually taken to represent the data. The benefits are illustrated by examples of analyses of sparse functional data.
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title_short	Data driven orthogonal basis selection for functional data analysis
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author2	Nassar, Hiba Podgórski, Krzysztof
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doi_str	10.1016/j.jmva.2021.104868
up_date	2024-07-07T00:48:57.566Z
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