University of Delaware
Arce Research Group
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Hypergraph Signal Processing

Tensor-based hypergraph learning, directed hypergraphs, and neural networks for structured relational data.

Graphical abstract for Hypergraph Signal Processing

Overview

We build the mathematical and algorithmic foundations of hypergraph signal processing using t-product tensor decompositions. Where graphs capture pairwise relations, hypergraphs model higher-order interactions among many entities at once — a natural fit for complex relational and multi-way data.

Recent contributions include tensor hypergraph neural networks, directed and acyclic hypergraph frameworks, scalable structure learning, and connections between hypergraph convolution and signal denoising, with applications ranging from relational data to financial signals.

Hypergraph SP t-product tensors Hypergraph neural networks Directed hypergraphs Structure learning Graph signal processing
Publications

Papers in this direction

2026
A Framework for Directed Hypergraph Signal Processing via Tensor t-SVD
C. Mundo-Levano, N. Bello, D. L. Lau, G. R. Arce
arXiv preprint
2026
Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets
F. Wang, W. Qian, D. L. Lau, G. R. Arce
arXiv preprint
2025
Scalable Hypergraph Structure Learning with Diverse Smoothness Priors
B. T. Brown, H. Zhang, D. L. Lau, G. R. Arce
IEEE Transactions on Signal and Information Processing over Networks
2024
T-HyperGNNs: Hypergraph Neural Networks via Tensor Representations
F. Wang, K. Pena-Pena, W. Qian, G. R. Arce
IEEE Transactions on Neural Networks and Learning Systems
2023
T-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions
K. Pena-Pena, D. L. Lau, G. R. Arce
IEEE Transactions on Signal and Information Processing over Networks
2023
A Unified View Between Tensor Hypergraph Neural Networks and Signal Denoising
F. Wang, K. Pena-Pena, W. Qian, G. R. Arce
31st European Signal Processing Conference (EUSIPCO)