Covariance Structure of Principal Components for Three-Part Compositional Data

Hrůzová, Klára, et al. "Covariance Structure of Principal Components for Three-Part Compositional Data." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.2 (2013): 61-69. <http://eudml.org/doc/260768>.

@article{Hrůzová2013,
abstract = {Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates. Theoretical results are applied to real-world data containing relative structure of landscape use in German regions.},
author = {Hrůzová, Klára, Hron, Karel, Rypka, Miroslav, Fišerová, Eva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {compositional data; covariance structure; principal components; log-contrasts; compositional data; covariance structure; principal components; log-contrasts},
language = {eng},
number = {2},
pages = {61-69},
publisher = {Palacký University Olomouc},
title = {Covariance Structure of Principal Components for Three-Part Compositional Data},
url = {http://eudml.org/doc/260768},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Hrůzová, Klára
AU - Hron, Karel
AU - Rypka, Miroslav
AU - Fišerová, Eva
TI - Covariance Structure of Principal Components for Three-Part Compositional Data
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 2
SP - 61
EP - 69
AB - Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates. Theoretical results are applied to real-world data containing relative structure of landscape use in German regions.
LA - eng
KW - compositional data; covariance structure; principal components; log-contrasts; compositional data; covariance structure; principal components; log-contrasts
UR - http://eudml.org/doc/260768
ER -