The Mathematics of Compositional Analysis

Authors

  • Carles Barcelo-Vidal University of Girona
  • Josep-Antoni Martín-Fernández University of Girona

DOI:

https://doi.org/10.17713/ajs.v45i4.142

Abstract

The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. The two principles are essential attributes of the corresponding quotient space. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. Using this structure, the statistical analysis of compositions consists of analysing logratio coordinates.

Published

2016-07-28

How to Cite

Barcelo-Vidal, C., & Martín-Fernández, J.-A. (2016). The Mathematics of Compositional Analysis. Austrian Journal of Statistics, 45(4), 57-71. https://doi.org/10.17713/ajs.v45i4.142

Issue

Section

Compositional Data Analysis