Graphon Filters: Graph Signal Processing in the Limit

Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. works have heretofore assumed knowledge graph shift operator. Our approach investigate question filtering about we only know model. To do leverage theory graphons proposed by L. Lovasz B. Szegedy. We make three key contributions processing. show first filters defined scaled adjacency matrix random drawn from graphon converge Fredholm integral operator with as its kernel. Second, leveraging classical findings numerical solution equations, define Fourier-Galerkin Lastly, using operator, derive filter design algorithm depends graphon, thus probabilistic structure instead particular itself. The derived verified simulations variety models.