Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond

Understand

In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks.

• Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on simplicial complexes and hypergraphs, two common higher-order network abstractions that can incorporate polyadic relationships.
• We provide brief introductions to simplicial complexes and hypergraphs, with a special emphasis on the concepts needed for the processing of signals supported on these structures.
• Specifically, we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and nonlinear processing through neural networks, using these two higher-order network models.