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Community-Aware Graph Signal Processing

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Document pages: 21 pages

Abstract: The emerging field of graph signal processing (GSP) allows to transposeclassical signal processing operations (e.g., filtering) to signals on graphs.The GSP framework is generally built upon the graph Laplacian, which plays acrucial 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 whenprocessing signals on the graph, but without the need for community detection.We study this approach in several generic settings such as filtering, optimalsampling and reconstruction, surrogate data generation, and denoising.Feasibility is illustrated by a small-scale example and a transportationnetwork dataset, as well as one application in human neuroimaging wherecommunity-aware GSP reveals relationships between behavior and brain featuresthat are not shown by Laplacian-based GSP. This work demonstrates how conceptsfrom network science can lead to new meaningful operations on graph signals.

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