A Framework for Directed Hypergraph Signal Processing via tensor t-SVD
For researchers in graph signal processing, this provides a novel method to process signals on directed hypergraphs, which are common in real-world networks.
The paper introduces Directed Hypergraph Signal Processing (DHGSP), a framework using tensor t-SVD to handle both higher-order and directional relationships. Experiments on traffic networks show DHGSP outperforms matrix-based and undirected tensor-based baselines in denoising tasks.
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.