Empirically Driven Orthonormal Bases for Functional Data Analysis
(2021) European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 In Lecture Notes in Computational Science and Engineering 139. p.773-783- Abstract
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not been properly studied. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered to transform observed functional data and a choice is made without any formal criteria indicating which of the bases is preferable for the initial transformation of the data. In an attempt to address this issue, we propose a strictly data-driven method of orthonormal basis selection. The method uses B-splines and utilizes recently introduced efficient orthornormal bases called the splinets. The algorithm learns from the data in the machine learning style to efficiently place knots. The optimality criterion is... (More)
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not been properly studied. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered to transform observed functional data and a choice is made without any formal criteria indicating which of the bases is preferable for the initial transformation of the data. In an attempt to address this issue, we propose a strictly data-driven method of orthonormal basis selection. The method uses B-splines and utilizes recently introduced efficient orthornormal bases called the splinets. The algorithm learns from the data in the machine learning style to efficiently place knots. The optimality criterion is based on the average (per functional data point) mean square error and is utilized both in the learning algorithms and in comparison studies. The latter indicate efficiency that could be used to analyze responses to a complex physical system.
(Less)
- author
- Nassar, Hiba LU and Podgórski, Krzysztof LU
- organization
- publishing date
- 2021
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
- series title
- Lecture Notes in Computational Science and Engineering
- editor
- Vermolen, Fred J. and Vuik, Cornelis
- volume
- 139
- pages
- 11 pages
- publisher
- Springer Science and Business Media B.V.
- conference name
- European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
- conference location
- Egmond aan Zee, Netherlands
- conference dates
- 2019-09-30 - 2019-10-04
- external identifiers
-
- scopus:85104220125
- ISSN
- 1439-7358
- 2197-7100
- ISBN
- 978-3-030-55874-1
- 9783030558734
- DOI
- 10.1007/978-3-030-55874-1_76
- language
- English
- LU publication?
- yes
- id
- fd88824f-6c0c-4f32-9e30-136bdc8f78ec
- date added to LUP
- 2021-12-10 10:29:45
- date last changed
- 2024-06-15 22:28:44
@inproceedings{fd88824f-6c0c-4f32-9e30-136bdc8f78ec,
abstract = {{<p>In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not been properly studied. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered to transform observed functional data and a choice is made without any formal criteria indicating which of the bases is preferable for the initial transformation of the data. In an attempt to address this issue, we propose a strictly data-driven method of orthonormal basis selection. The method uses B-splines and utilizes recently introduced efficient orthornormal bases called the splinets. The algorithm learns from the data in the machine learning style to efficiently place knots. The optimality criterion is based on the average (per functional data point) mean square error and is utilized both in the learning algorithms and in comparison studies. The latter indicate efficiency that could be used to analyze responses to a complex physical system.</p>}},
author = {{Nassar, Hiba and Podgórski, Krzysztof}},
booktitle = {{Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference}},
editor = {{Vermolen, Fred J. and Vuik, Cornelis}},
isbn = {{978-3-030-55874-1}},
issn = {{1439-7358}},
language = {{eng}},
pages = {{773--783}},
publisher = {{Springer Science and Business Media B.V.}},
series = {{Lecture Notes in Computational Science and Engineering}},
title = {{Empirically Driven Orthonormal Bases for Functional Data Analysis}},
url = {{http://dx.doi.org/10.1007/978-3-030-55874-1_76}},
doi = {{10.1007/978-3-030-55874-1_76}},
volume = {{139}},
year = {{2021}},
}