Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Functional Principal Component Analysis for Bivariate Densities and their Orthogonal Decomposition
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
New Trends in Functional Statistics and Related Fields
ISBN
978-3-031-92382-1
ISSN
1431-1968
e-ISSN
2628-8966
Number of pages
8
Pages from-to
143-150
Publisher name
Springer
Place of publication
Cham
Event location
Novara, Itálie
Event date
Jun 25, 2025
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001545850800018