Functional Data Analysis: An Introduction and Recent Developments
ABSTRACT Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐...
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| Vydané v: | Biometrical journal Ročník 66; číslo 7; s. e202300363 - n/a |
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| Hlavní autori: | , , , |
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| Jazyk: | English |
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Germany
Wiley - VCH Verlag GmbH & Co. KGaA
01.10.2024
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| ISSN: | 0323-3847, 1521-4036, 1521-4036 |
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| Abstract | ABSTRACT
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub. |
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| AbstractList | Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub. ABSTRACT Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub. Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub . Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar-valued or multivariate data, but FDA brings additional challenges due to the high- and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands-on application, the code for these practical examples is made available through a code and data supplement and on GitHub.Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar-valued or multivariate data, but FDA brings additional challenges due to the high- and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands-on application, the code for these practical examples is made available through a code and data supplement and on GitHub. |
| Author | Gertheiss, Jan Rügamer, David Greven, Sonja Liew, Bernard X. W. |
| Author_xml | – sequence: 1 givenname: Jan orcidid: 0000-0001-6777-4746 surname: Gertheiss fullname: Gertheiss, Jan email: jan.gertheiss@hsu-hh.de organization: Helmut Schmidt University – sequence: 2 givenname: David surname: Rügamer fullname: Rügamer, David organization: Munich Center for Machine Learning – sequence: 3 givenname: Bernard X. W. surname: Liew fullname: Liew, Bernard X. W. organization: University of Essex – sequence: 4 givenname: Sonja surname: Greven fullname: Greven, Sonja organization: Humboldt‐Universität zu Berlin |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/39330918$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_3390_e27060552 crossref_primary_10_1007_s00180_025_01652_z crossref_primary_10_3390_math13050858 crossref_primary_10_1017_dce_2025_18 crossref_primary_10_1007_s00477_025_02986_2 crossref_primary_10_3390_jfmk10030330 crossref_primary_10_3390_axioms14080626 crossref_primary_10_1016_j_gaitpost_2024_09_010 crossref_primary_10_1038_s41598_024_61262_5 crossref_primary_10_3390_math13050853 crossref_primary_10_1080_14763141_2024_2398508 crossref_primary_10_1080_00224065_2025_2500554 crossref_primary_10_1002_wics_70026 crossref_primary_10_1016_j_jbiomech_2025_112585 crossref_primary_10_1016_j_ins_2025_122442 crossref_primary_10_15377_2409_5761_2025_12_4 crossref_primary_10_1007_s10182_025_00531_8 crossref_primary_10_1002_asmb_2879 crossref_primary_10_3390_s25123616 crossref_primary_10_54097_5jpvbv40 |
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Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains.... Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals... |
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| Title | Functional Data Analysis: An Introduction and Recent Developments |
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