Community-Driven Signal Processing On Directed Brain Graphs

Graphs have become a predominant way of representing structured information. Pioneering frameworks such as graph signal processing (GSP) have been developed for the analysis of data within such representations (e.g. brain graphs). Notably, by integrating community structures, community-aware GSP emphasizes on the importance of capturing the intrinsic organization of the graph, by bringing forth the notion of modularity in the signal analysis. Here, we leverage recent work on community detection for directed graphs and propose a community-driven signal processing approach. Graphs signals are projected through regression onto a dictionary defined by the directed communities, termed bicommunities, to later obtain a decomposition of the original signal. We then apply the proposed framework to brain graphs and signals obtained with magnetic resonance imaging. Our findings provide relevant insights into known functional brain networks and open new avenues for the study of their interaction.