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Title: Connecting compositional data to graph signal processing Authors:  Christopher Rieser - TU Wien (Austria) [presenting]
Abstract: Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is known that a relationship only exists between very specific variables (e.g. for metabolomic pathways), while for other pairs a relationship does not exist. Modeling the absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. We show how to link compositional data analysis with graph signal processing and extend the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance. An example from bioinformatics is shown to demonstrate the usefulness of this approach.