Graph Signal Processing for Compositional Data

The field of graph signal processing (GSP) offers numerous methodologies for handling data whose domain is captured by graphs. In this work, we introduce novel GSP concepts that are tailored to compositional data, a type of data that represents parts of a whole and features an inherently non-Euclidean geometry. To construct signature graphs (multilayer signed graphs) for this kind of data, we formulate novel involutions (self-inverse mappings) and we introduce appropriate distance metrics. We further describe how to identify the pertinent involutions from given datasets in semi-supervised and unsupervised scenarios. The usefulness of our framework is illustrated experimentally in the context of data clustering problems.