Weighting of parts in compositional data analysis: Advances and applications

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73615127" target="_blank" >RIV/61989592:15310/22:73615127 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s11004-021-09952-y" target="_blank" >https://link.springer.com/article/10.1007/s11004-021-09952-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11004-021-09952-y" target="_blank" >10.1007/s11004-021-09952-y</a>

Result language

angličtina

Original language name

Weighting of parts in compositional data analysis: Advances and applications

Original language description

It often occurs in practice that it is sensible to give different weights to the variables involved in a multivariate data analysis and the same holds for compositional data as multivariate observations carrying relative information. It can be convenient to apply weights to better accommodate differences in the quality of the measurements, the occurrence of zeros and missing values, or generally to highlight some specific features of compositional parts. The characterisation of compositional data as elements of a Bayes space, which is as a natural generalisation of the ordinary Aitchison geometry, enables the definition of a formal framework to implement weighting schemes for the parts of a composition. This is formally achieved by considering a reference measure in the Bayes space alternative to the common uniform measure via the well-known chain rule. Unweighted centred logratio (clr) coefficients and isometric logratio (ilr) coordinates then allow to express compositions in the real space equipped with the (unweighted) Euclidean geometry. The resulting elements of the real space generated by the clr coefficients or ilr coordinates are invariant to the scale of the original compositions, but the actual scale of the weights matters. In this work these formal developments are presented and used to introduce a general approach for weighting parts in compositional data analysis. The practical use is demonstrated on simulated and real-world data sets in the context of the earth sciences.

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

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GA19-01768S" target="_blank" >GA19-01768S: Separation of geochemical signals in sediments: application of advanced statistical methods on large geochemical datasets</a><br>

Continuities

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

Publication year

2022

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

54

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

23

Pages from-to

71-93

UT code for WoS article

000669833300001

EID of the result in the Scopus database

2-s2.0-85109318084