Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73635111" target="_blank" >RIV/61989592:15310/25:73635111 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-031-92383-8_18" target="_blank" >http://dx.doi.org/10.1007/978-3-031-92383-8_18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-92383-8_18" target="_blank" >10.1007/978-3-031-92383-8_18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition

Popis výsledku v původním jazyce

Embedding bivariate probability density functions in Bayes spaces enables their orthogonal decomposition into independent and interactive parts, the former can be further decomposed into orthogonal geometric marginals. After performing the clr (centered logratio) transformation, densities can be analysed as functional data in L^2_0 space. In this paper, we focus on functional principal component analysis (FPCA) and its use for bivariate densities as well as for the vector of orthogonal densities from their decomposition. We show that performing FPCA on the original bivariate densities is equivalent to performing multivariate FPCA on the decomposed densities (the vector of the interactive part and geometric marginals). Moreover, eigenfunctions and scores decompose accordingly, and this allows to identify which parts of the decomposition contribute the most to the variation of the densities.The theoretical results are complemented by an illustration on an empirical data set.

Název v anglickém jazyce

Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition

Popis výsledku anglicky

Embedding bivariate probability density functions in Bayes spaces enables their orthogonal decomposition into independent and interactive parts, the former can be further decomposed into orthogonal geometric marginals. After performing the clr (centered logratio) transformation, densities can be analysed as functional data in L^2_0 space. In this paper, we focus on functional principal component analysis (FPCA) and its use for bivariate densities as well as for the vector of orthogonal densities from their decomposition. We show that performing FPCA on the original bivariate densities is equivalent to performing multivariate FPCA on the decomposed densities (the vector of the interactive part and geometric marginals). Moreover, eigenfunctions and scores decompose accordingly, and this allows to identify which parts of the decomposition contribute the most to the variation of the densities.The theoretical results are complemented by an illustration on an empirical data set.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

New Trends in Functional Statistics and Related Fields

ISBN

978-3-031-92382-1

ISSN

1431-1968

e-ISSN

2628-8966

Počet stran výsledku

8

Strana od-do

143-150

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Novara, Itálie

Datum konání akce

25. 6. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001545850800018