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

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Computer Science > Machine Learning

arXiv:2606.25112 (cs)
[Submitted on 23 Jun 2026]

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

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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.
Comments: 4 pages, 6 figures. Presented as an oral presentation at the 9th Graph Signal Processing Workshop (GSP 2026), June 8-10, 2026, Madrid, Spain
Subjects: Machine Learning (cs.LG); Signal Processing (eess.SP)
Cite as: arXiv:2606.25112 [cs.LG]
  (or arXiv:2606.25112v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2606.25112
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Carlos Mundo-Levano [view email]
[v1] Tue, 23 Jun 2026 19:40:32 UTC (6,241 KB)
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