Empirically Driven Orthonormal Bases for Functional Data Analysis

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

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 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
PublisherSpringer Science and Business Media B.V.
Pages773-783
Number of pages11
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)9783030558734
DOIs
Publication statusPublished - 2021
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands
Duration: 2019 Sept 302019 Oct 4

Publication series

NameLecture Notes in Computational Science and Engineering
Volume139
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Country/TerritoryNetherlands
CityEgmond aan Zee
Period2019/09/302019/10/04

Subject classification (UKÄ)

  • Control Engineering

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