Robust Principal Component Analysis for Compositional Tables

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73598524" target="_blank" >RIV/61989592:15310/20:73598524 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.tandfonline.com/doi/full/10.1080/02664763.2020.1722078" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/02664763.2020.1722078</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/02664763.2020.1722078" target="_blank" >10.1080/02664763.2020.1722078</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust Principal Component Analysis for Compositional Tables

Popis výsledku v původním jazyce

A data table arranged according to two factors can often be considered a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information consists of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (rPCA) is performed for dimension reduction, allowing to investigate relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply rPCA, which would otherwise suffer from the singularity of clr coefficients.

Název v anglickém jazyce

Robust Principal Component Analysis for Compositional Tables

Popis výsledku anglicky

A data table arranged according to two factors can often be considered a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information consists of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (rPCA) is performed for dimension reduction, allowing to investigate relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply rPCA, which would otherwise suffer from the singularity of clr coefficients.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF APPLIED STATISTICS

ISSN

0266-4763

e-ISSN

—

Svazek periodika

48

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

20

Strana od-do

214-233

Kód UT WoS článku

000512574700001

EID výsledku v databázi Scopus

2-s2.0-85078938090