Multiway Graph Signal Processing on Tensors: Integrative Analysis of Irregular Geometries

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. Because acquired data are increasingly taking the form of multiway tensors, new signal processing tools are needed to maximally utilize the multiway structure within the data. In this article, we review modern signal processing frameworks that generalize GSP to multiway data, starting from graph signals coupled to familiar regular axes, such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multiway paradigm.