Simplicial principal component analysis for density functions in Bayes spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33159835" target="_blank" >RIV/61989592:15310/16:33159835 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0167947315001644" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0167947315001644</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.csda.2015.07.007" target="_blank" >10.1016/j.csda.2015.07.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Simplicial principal component analysis for density functions in Bayes spaces

Popis výsledku v původním jazyce

Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria.

Název v anglickém jazyce

Simplicial principal component analysis for density functions in Bayes spaces

Popis výsledku anglicky

Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA15-06991S" target="_blank" >GA15-06991S: Analýza funkcionálních dat a související témata</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Computational Statistics and Data Analysis

ISSN

0167-9473

e-ISSN

—

Svazek periodika

94

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

330-350

Kód UT WoS článku

000364798200023

EID výsledku v databázi Scopus

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