A Framework for Directed Hypergraph Signal Processing via tensor t-SVD

2026-06-23

AI Summary

Existing graph signal processing methods struggle to simultaneously capture high-order associations and directional relationships. To address this limitation, this work proposes a Directed Hypergraph Signal Processing (DHGSP) framework that unifies the modeling of high-order and directed interactions for the first time. Built upon tensor t-SVD and t-product algebra, the framework introduces an adjacency tensor, a topology-preserving shift operator, and a lossless Fourier transform. The proposed Directed Hypergraph Fourier Transform rigorously preserves the original topological structure without information loss. Experimental results on real-world traffic network denoising demonstrate that the method significantly outperforms conventional matrix-based graph and directed graph approaches, as well as undirected tensor-based hypergraph methods.

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.

Problem

• Directed Hypergraph
• Graph Signal Processing
• Higher-order Relationships
• Asymmetric Relationships
• Tensor t-SVD

Innovation

• Directed Hypergraph Signal Processing
• tensor t-SVD
• t-product algebra
• shift operator
• Directed Hypergraph Fourier Transform