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  • 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, standard statistical 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 this paper 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.
  • 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, standard statistical 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 this paper 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. (en)
Title
  • On interpretation of orthonormal coordinates for compositional data
  • On interpretation of orthonormal coordinates for compositional data (en)
skos:prefLabel
  • On interpretation of orthonormal coordinates for compositional data
  • On interpretation of orthonormal coordinates for compositional data (en)
skos:notation
  • RIV/61989592:15310/11:10223741!RIV12-MSM-15310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika
  • 4
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http://linked.open...aciTvurceVysledku
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  • 218053
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  • RIV/61989592:15310/11:10223741
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  • Aitchison geometry on the simplex, Isometric log-ratio transformation, Orthonormal coordinates, Covariance structure (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [9D6E17E67C9B]
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  • Mathematical Geosciences
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http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 43
http://linked.open...iv/tvurceVysledku
  • Hron, Karel
  • Fišerová, Eva
http://linked.open...ain/vavai/riv/wos
  • 000290544600004
http://linked.open...n/vavai/riv/zamer
issn
  • 1874-8961
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http://localhost/t...ganizacniJednotka
  • 15310
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