Learning Hypergraphs Tensor Representations from Data via t-HGSP

Karelia Pena-Pena, Lucas Taipe, Fuli Wang, Daniel L. Lau, Gonzalo R. Arce

Research output: Contribution to journalArticlepeer-review

Abstract

Representation learning considering high-order relationships in data has recently shown to be advantageous in many applications. The construction of a meaningful hypergraph plays a crucial role in the success of hypergraph-based representation learning methods, which is particularly useful in hypergraph neural networks and hypergraph signal processing. However, a meaningful hypergraph may only be available in specific cases. This paper addresses the challenge of learning the underlying hypergraph topology from the data itself. As in graph signal processing applications, we consider the case in which the data possesses certain regularity or smoothness on the hypergraph. To this end, our method builds on the novel tensor-based hypergraph signal processing framework (t-HGSP) that has recently emerged as a powerful tool for preserving the intrinsic high-order structure of data on hypergraphs. Given the hypergraph spectrum and frequency coefficient definitions within the t-HGSP framework, we propose a method to learn the hypergraph Laplacian from data by minimizing the total variation on the hypergraph (TVL-HGSP). Additionally, we introduce an alternative approach (PDL-HGSP) that improves the connectivity of the learned hypergraph without compromising sparsity and use primal-dual-based algorithms to reduce the computational complexity. Finally, we combine the proposed learning algorithms with novel tensor-based hypergraph convolutional neural networks to propose hypergraph learning-convolutional neural networks (t-HyperGLNN).

Original languageEnglish
Pages (from-to)17-31
Number of pages15
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume10
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

  • Hypergraph topology learning
  • hypergraph neural networks

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Computer Networks and Communications

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