Signal Processing on Simplicial Complexes

Higher-order networks have so far been considered primarily in the context of studying structure complex systems, i.e., higher-order or multi-way relations connecting constituent entities. More recently, a number studies dynamical processes that explicitly account for such dependencies, e.g., epidemic spreading opinion formation. In this chapter, we focus on closely related, but distinct third perspective: how can use relationships to process signals and data supported network structures. particular, survey ideas from signal processing regular domains, as time series images, be extended graphs simplicial complexes. We discuss Fourier analysis, denoising, interpolation, nonlinear through neural based Key our developments is Hodge Laplacian matrix, multi-relational operator leverages special complexes generalizes desirable properties matrix graph processing.