t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions

Karelia Pena-Pena, Daniel L. Lau, Gonzalo R. Arce

Research output: Contribution to journalArticlepeer-review


Graph signal processing (GSP) techniques are powerful tools that model complex relationships within large datasets, being now used in a myriad of applications in different areas including data science, communication networks, epidemiology, and sociology. Simple graphs can only model pairwise relationships among data which prevents their application in modeling networks with higher-order relationships. For this reason, some efforts have been made to generalize well-known graph signal processing techniques to more complex graphs such as hypergraphs, which allow capturing higher-order relationships among data. In this article, we provide a new hypergraph signal processing framework (t-HGSP) based on a novel tensor-tensor product algebra that has emerged as a powerful tool for preserving the intrinsic structures of tensors. The proposed framework allows the generalization of traditional GSP techniques while keeping the dimensionality characteristic of the complex systems represented by hypergraphs. To this end, the core elements of the t-HGSP framework are introduced, including the shifting operators and the hypergraph signal. The hypergraph Fourier space is also defined, followed by the concept of bandlimited signals and sampling. In our experiments, we demonstrate the benefits of our approach in applications such as clustering and denoising.

Original languageEnglish
Pages (from-to)329-345
Number of pages17
JournalIEEE Transactions on Signal and Information Processing over Networks
StatePublished - 2023

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation under Grants CCF 2230161 and 2230162, in part by AFOSR under Grant FA9550-22-1-0362, and in part by the Institute of Financial Services Analytics at the University of Delaware.

Publisher Copyright:
© 2015 IEEE.


  • Data Analysis
  • Graph
  • Signal Processing
  • Tensor

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Computer Networks and Communications


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