Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes

Explore multiscale basis dictionaries and scattering networks on simplicial complexes in this 34-minute lecture by Naoki Saito from UC Davis. Delve into the Hierarchical Graph Laplacian Eigen Transform (HGLET) and the Generalized Haar-Walsh Transform (GHWT), originally developed for analyzing signals on graph nodes and now extended to edges, triangles, and tetrahedra using Hodge Laplacians. Discover how these dictionaries provide redundant sets of multiscale basis vectors and expansion coefficients, allowing for optimal basis selection using the best-basis algorithm. Learn about the construction of scattering networks for simplicial complex signals using HGLET and GHWT, which offer robustness to input signal perturbations and invariance to node permutations. Examine practical applications of these techniques in coauthorship/citation complexes and Science News article classification, based on joint work with Stefan Schonsheck and Eugene Shvarts.