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Data driven orthogonal basis selection for functional data analysis

Basna, Rani LU orcid ; Nassar, Hiba LU and Podgórski, Krzysztof LU (2022) In Journal of Multivariate Analysis 189. p.104868-104868
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... (More)

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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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Functional data analysis, Machine learning, Splines
in
Journal of Multivariate Analysis
volume
189
pages
104868 - 104868
publisher
Academic Press
external identifiers
  • scopus:85118983472
ISSN
0047-259X
DOI
10.1016/j.jmva.2021.104868
language
English
LU publication?
yes
id
95168326-1b6b-4149-b282-7ea7e4afe74c
date added to LUP
2021-12-23 09:49:56
date last changed
2024-05-30 10:08:35
@article{95168326-1b6b-4149-b282-7ea7e4afe74c,
  abstract     = {{<p>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.</p>}},
  author       = {{Basna, Rani and Nassar, Hiba and Podgórski, Krzysztof}},
  issn         = {{0047-259X}},
  keywords     = {{Functional data analysis; Machine learning; Splines}},
  language     = {{eng}},
  pages        = {{104868--104868}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Multivariate Analysis}},
  title        = {{Data driven orthogonal basis selection for functional data analysis}},
  url          = {{http://dx.doi.org/10.1016/j.jmva.2021.104868}},
  doi          = {{10.1016/j.jmva.2021.104868}},
  volume       = {{189}},
  year         = {{2022}},
}