2020/08/24 by Miljan Petrović, Miljan Petrovic, Raphaël Liégeois +3 · 1 citation
Computer Science · Engineering · Neuroscience · Physics and Astronomy · #Advanced Graph Neural Networks #Complex Network Analysis Techniques #Functional Brain Connectivity Studies #eess.SP
paper · pdf · doi:10.1109/msp.2020.3018087
21 pages, 4 figures, Accepted to Signal Processing Magazine: Special Issue on Graph Signal Processing: Foundations and Emerging Directions
arxiv created 2020/08/24 · arxiv updated 2020/08/25 · openalex publication_date 2020/11/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role to study graph properties and measure graph signal smoothness. Here instead, we propose the graph modularity matrix as the centerpiece of GSP, in order to incorporate knowledge about graph community structure when processing signals on the graph, but without the need for community detection. We study this approach in several generic settings such as filtering, optimal sampling and reconstruction, surrogate data generation, and denoising. Feasibility is illustrated by a small-scale example and a transportation network dataset, as well as one application in human neuroimaging where community-aware GSP reveals relationships between behavior and brain features that are not shown by Laplacian-based GSP. This work demonstrates how concepts from network science can lead to new meaningful operations on graph signals.