Simplicial Convolutional Filters

arXiv:2201.11720v3 Announce Type: replace-cross
Abstract: We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces etc. To process such signals, we develop simplicial convolutional filters defined as matrix polynomials of the lower and upper Hodge Laplacians. First, we study the properties of these filters and show that they are linear and shift-invariant, as well as permutation and orientation equivariant. …

abstract arxiv cs.lg cs.si eess.sp etc filters graphs interpreted linear math.at math.sp matrix nodes process processing spaces study type