t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions
| Author(s) | Pena-Pena, Karelia | |
| Author(s) | Lau, Daniel L. | |
| Author(s) | Arce, Gonzalo R. | |
| Date Accessioned | 2023-08-08T19:57:36Z | |
| Date Available | 2023-08-08T19:57:36Z | |
| Publication Date | 2023-05-16 | |
| Description | This article was originally published in IEEE Transactions on Signal and Information Processing over Networks. The version of record is available at: https://doi.org/10.1109/TSIPN.2023.3276687. © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This article will be embargoed until 05/16/2025. | |
| Abstract | 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. | |
| Sponsor | This work was supported in part by the National Science Foundation under grants CCF 2230161 and 2230162, by the AFOSR award FA9550-22-1-0362, and by the Institute of Financial Services Analytics at the University of Delaware. | |
| Citation | K. Pena-Pena, D. L. Lau and G. R. Arce, "t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions," in IEEE Transactions on Signal and Information Processing over Networks, vol. 9, pp. 329-345, 2023, doi: 10.1109/TSIPN.2023.3276687. | |
| ISSN | 2373-776X | |
| URL | https://udspace.udel.edu/handle/19716/33059 | |
| Language | en_US | |
| Publisher | IEEE Transactions on Signal and Information Processing over Networks | |
| Keywords | graph | |
| Keywords | signal processing | |
| Keywords | tensor | |
| Keywords | data analysis | |
| Title | t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions | |
| Type | Article |