On interpretation of orthonormal coordinates for compositional data

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F11%3A10223741" target="_blank" >RIV/61989592:15310/11:10223741 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On interpretation of orthonormal coordinates for compositional data

Popis výsledku v původním jazyce

The simplex with the Aitchison geometry is a natural sample space for compositional data, that is, observations carrying only relative information (especially proportions, percentages, etc., often occurring in the geosciences). For this reason, standardstatistical methods that rely on Euclidean structure of the real space cannot be used directly for statistical analysis. At first, compositional data need to be expressed in coordinates of an orthonormal basis on the simplex (with respect to the Aitchison geometry). The mathematical interpretation of the orthonormal coordinates is derived from the procedure by which they are constructed (called sequential binary partition), and they act as balances between groups of compositional parts. The goal of thispaper is to describe the covariance structure of coordinates and, consequently, to provide a complementary interpretation based on log-ratios of parts of the original composition.

Název v anglickém jazyce

On interpretation of orthonormal coordinates for compositional data

Popis výsledku anglicky

The simplex with the Aitchison geometry is a natural sample space for compositional data, that is, observations carrying only relative information (especially proportions, percentages, etc., often occurring in the geosciences). For this reason, standardstatistical methods that rely on Euclidean structure of the real space cannot be used directly for statistical analysis. At first, compositional data need to be expressed in coordinates of an orthonormal basis on the simplex (with respect to the Aitchison geometry). The mathematical interpretation of the orthonormal coordinates is derived from the procedure by which they are constructed (called sequential binary partition), and they act as balances between groups of compositional parts. The goal of thispaper is to describe the covariance structure of coordinates and, consequently, to provide a complementary interpretation based on log-ratios of parts of the original composition.

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

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

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

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Svazek periodika

43

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

455-468

Kód UT WoS článku

000290544600004

EID výsledku v databázi Scopus

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