Principal Component Analysis for Distributions Observed by Samples in Bayes Spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627773" target="_blank" >RIV/61989592:15310/24:73627773 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11004-024-10142-9" target="_blank" >https://link.springer.com/article/10.1007/s11004-024-10142-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11004-024-10142-9" target="_blank" >10.1007/s11004-024-10142-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Principal Component Analysis for Distributions Observed by Samples in Bayes Spaces

Popis výsledku v původním jazyce

Distributional data have recently become increasingly important for understanding processes in the geosciences, thanks to the establishment of cost-efficient analytical instruments capable of measuring properties over large numbers of particles, grains or crystals in a sample. Functional data analysis allows the direct application of multivariate methods, such as principal component analysis, to such distributions. However, these are often observed in the form of samples, and thus incur a sampling error. This additional sampling error changes the properties of the multivariate variance and thus the number of relevant principal components and their direction. The result of the principal component analysis becomes an artifact of the sampling error and can negatively affect the subsequent data analysis. This work presents a way of estimating this sampling error and how to confront it in the context of principal component analysis, where the principal components are obtained as a linear combination of elements of a newly constructed orthogonal spline basis. The effect of the sampling error and th effectiveness of the correction is demonstrated with a series of simulations. It is shown how the interpretability and reproducibility of the principal components improve and become independent of the selection of the basis. The proposed method is then applied on a dataset of grain size distributions in a geometallurgical dataset from Thaba mine in the Bushveld complex.

Název v anglickém jazyce

Principal Component Analysis for Distributions Observed by Samples in Bayes Spaces

Popis výsledku anglicky

Distributional data have recently become increasingly important for understanding processes in the geosciences, thanks to the establishment of cost-efficient analytical instruments capable of measuring properties over large numbers of particles, grains or crystals in a sample. Functional data analysis allows the direct application of multivariate methods, such as principal component analysis, to such distributions. However, these are often observed in the form of samples, and thus incur a sampling error. This additional sampling error changes the properties of the multivariate variance and thus the number of relevant principal components and their direction. The result of the principal component analysis becomes an artifact of the sampling error and can negatively affect the subsequent data analysis. This work presents a way of estimating this sampling error and how to confront it in the context of principal component analysis, where the principal components are obtained as a linear combination of elements of a newly constructed orthogonal spline basis. The effect of the sampling error and th effectiveness of the correction is demonstrated with a series of simulations. It is shown how the interpretability and reproducibility of the principal components improve and become independent of the selection of the basis. The proposed method is then applied on a dataset of grain size distributions in a geometallurgical dataset from Thaba mine in the Bushveld complex.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF22-15684L" target="_blank" >GF22-15684L: Zobecněná relativní data a robustnost v Bayesových prostorech</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematical Geosciences

ISSN

1874-8961

e-ISSN

1874-8953

Svazek periodika

56

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

29

Strana od-do

1641-1669

Kód UT WoS článku

001216033100001

EID výsledku v databázi Scopus

2-s2.0-85192019581