Extending compositional data analysis from a graph signal processing perspective

Traditional methods for the analysis of compositional data consider log-ratios between all different pairs variables with equal weight, typically in form aggregated contributions. This is not meaningful contexts where it known that a relationship only exists very specific (e.g. metabolomic pathways), while other does exist. Modeling absence or presence relationships done graph theory, vertices represent variables, and connections refer to relations. paper links signal processing, extends Aitchison geometry setting selected can be considered. The presented framework retains desirable properties scale invariance coherence. A real example from bioinformatics underlines usefulness this approach.