Empirically driven orthonormal bases for functional data analysis

Hiba Nassar, Krzysztof Podgorski

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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 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.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2019
Editors Fred J. Vermolen, ornelis Vuik
PublisherSpringer
Publication date2021
ISBN (Print)978-3-030-55873-4
ISBN (Electronic)978-3-030-55874-1
DOIs
Publication statusPublished - 2021
EventEuropean Numerical Mathematics and
Advanced Applications Conference 2019
- Hotel Zuiderduin, Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019
https://www.enumath2019.eu/

Conference

ConferenceEuropean Numerical Mathematics and
Advanced Applications Conference 2019
LocationHotel Zuiderduin
CountryNetherlands
CityEgmond aan Zee
Period30/09/201904/10/2019
Internet address
SeriesLecture Notes in Computational Science and Engineering
ISSN1439-7358

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