Principal Component Analysis for Distributions Observed by Samples in Bayes Spaces

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Principal Component Analysis for Distributions Observed by Samples in Bayes Spaces

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GF22-15684L" target="_blank" >GF22-15684L: Generalized relative data and robustness in Bayes spaces</a><br>

Continuities

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

Publication year

2024

Confidentiality

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

Name of the periodical

Mathematical Geosciences

ISSN

1874-8961

e-ISSN

1874-8953

Volume of the periodical

56

Issue of the periodical within the volume

8

Country of publishing house

DE - GERMANY

Number of pages

29

Pages from-to

1641-1669

UT code for WoS article

001216033100001

EID of the result in the Scopus database

2-s2.0-85192019581