Multiscale Hodge Scattering Networks for Data Analysis

arXiv:2311.10270v2 Announce Type: replace
Abstract: We propose new scattering networks for signals measured on simplicial complexes, which we call \emph{Multiscale Hodge Scattering Networks} (MHSNs). Our construction is based on multiscale basis dictionaries on simplicial complexes, i.e., the $\kappa$-GHWT and $\kappa$-HGLET, which we recently developed for simplices of dimension $\kappa \in \mathbb{N}$ in a given simplicial complex by generalizing the node-based Generalized Haar-Walsh Transform (GHWT) and Hierarchical Graph Laplacian Eigen Transform (HGLET). The $\kappa$-GHWT and the $\kappa$-HGLET both form redundant sets …

abstract analysis arxiv call construction cs.lg cs.na cs.si data data analysis eess.sp math.na networks stat.ml type