Edgewise outliers of network indexed signals

We consider models for network indexed multivariate data involving a dependence between variables as well as across graph nodes. In the framework of these models, we focus on outliers detection and introduce the concept of edgewise outliers. For this purpose, we first derive the distribution of some sums of squares, in particular squared Mahalanobis distances that can be used to fix detection rules and thresholds for outlier detection. We then propose a robust version of the deterministic MCD algorithm that we call edgewise MCD. An application on simulated data shows the interest of taking the dependence structure into account. We also illustrate the utility of the proposed method with a real data set.

Extending compositional data analysis from a graph signal processing perspective

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 absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. This paper links compositional data analysis with graph signal processing, and it extends the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance and compositional coherence. An additional extension to include absolute information is readily made. Examples from bioinformatics and geochemistry underline the usefulness of thisapproach in comparison to standard methods for compositional data analysis.