A Framework for Directed Hypergraph Signal Processing via tensor t-SVD
Carlos Mundo-Levano, Nicolás Bello, Daniel L. Lau, Gonzalo R. Arce
Abstract
We introduce Directed Hypergraph Signal Processing (DHGSP), a unified framework that extends graph signal processing to accommodate both higher-order (polyadic) and asymmetric (directional) relationships simultaneously. Using the tensor singular value decomposition (t-SVD) within the t-product algebra, we define a novel adjacency tensor for directed hypergraphs, a topologically faithful shift operator, and a lossless Directed Hypergraph Fourier Transform (t-DHGFT). Experiments on real traffic networks demonstrate that DHGSP outperforms matrix-based (graph and digraph) and undirected tensor-based (hypergraph) baselines in denoising tasks.
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.