Geodesic
Remark on properties of bases for additive logratio transformations of compositional data
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 77-82

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The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some applications from geosciences ([14]) or statistical aspects of multicriteria evaluation theory ([13]) it seems to be convenient to use another types of bases. This paper is devoted to describe its basic properties and illustrate the results on an example.
The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some applications from geosciences ([14]) or statistical aspects of multicriteria evaluation theory ([13]) it seems to be convenient to use another types of bases. This paper is devoted to describe its basic properties and illustrate the results on an example.
Classification : 15A03, 62H99
Keywords: Aitchison geometry on the simplex; bases on the simplex; additive logratio transformations 
Hron, Karel. Remark on properties of bases for additive logratio transformations of compositional data. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 77-82. http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a6/
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