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Traditional methods for the analysis of compositional data consider thelog-ratios between all different pairs of variables with equal weight,typically in the form of aggregated contributions. This is not meaningful incontexts where it is known that a relationship only exists between veryspecific variables (e.g.~for metabolomic pathways), while for other pairs arelationship does not exist. Modeling absence or presence of relationships isdone in graph theory, where the vertices represent the variables, and theconnections refer to relations. This paper links compositional data analysiswith graph signal processing, and it extends the Aitchison geometry to asetting where only selected log-ratios can be considered. The presentedframework retains the desirable properties of scale invariance andcompositional coherence. An additional extension to include absoluteinformation is readily made. Examples from bioinformatics and geochemistryunderline the usefulness of thisapproach in comparison to standard methods forcompositional data analysis.

Extending compositional data analysis from a graph signal processing perspective