Mathematical Geosciences

, Volume 45, Issue 4, pp 487–498 | Cite as

Covariance-Based Variable Selection for Compositional Data

  • Karel HronEmail author
  • Peter Filzmoser
  • Sandra Donevska
  • Eva Fišerová


Omitting variables in compositional data analysis may lead to a substantial change in results from that of multivariate statistical analysis. In particular, this is the case for principal component analysis and the compositional biplot, where both the interpretation of loadings and scores of the remaining subcomposition are affected. A stepwise procedure is introduced that allows for a reduction of the original composition to a subcomposition by avoiding a substantial change of the information, like those carried by the compositional biplot. The subcomposition is easier to handle and interpret. Numerical results give evidence of the usefulness of the procedure.


Aitchison geometry on the simplex Centered log-ratio transformation Isometric log-ratio transformation Variable selection 



The authors are grateful to the referee for helpful comments and suggestions. The authors also gratefully acknowledge the support by the Operational Program Education for Competitiveness—European Social Fund (project CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth, and Sports of the Czech Republic) and the Grant No. PrF-2012-017 of the Internal Grant Agency of the Palacký University in Olomouc.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Karel Hron
    • 1
    • 2
    Email author
  • Peter Filzmoser
    • 3
  • Sandra Donevska
    • 1
    • 2
  • Eva Fišerová
    • 1
    • 2
  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzech Republic
  2. 2.Department of Geoinformatics, Faculty of SciencePalacký UniversityOlomoucCzech Republic
  3. 3.Department of Statistics and Probability TheoryVienna University of TechnologyViennaAustria

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