1 research outputs found
Multiscale Transforms for Signals on Simplicial Complexes
Our previous multiscale graph basis dictionaries/graph signal transforms --
Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen
Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives
-- were developed for analyzing data recorded on nodes of a given graph. In
this article, we propose their generalization for analyzing data recorded on
edges, faces (i.e., triangles), or more generally -dimensional
simplices of a simplicial complex (e.g., a triangle mesh of a manifold). The
key idea is to use the Hodge Laplacians and their variants for hierarchical
partitioning of a set of -dimensional simplices in a given simplicial
complex, and then build localized basis functions on these partitioned subsets.
We demonstrate their usefulness for data representation on both illustrative
synthetic examples and real-world simplicial complexes generated from a
co-authorship/citation dataset and an ocean current/flow dataset.Comment: 19 Pages, Comments welcom