mlsanityData to 7 Oct 2026

The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited

arXiv 1312.5179 ↗First posted 18 Dec 2013stat.ML cs.LG math.OCcited by 35

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Abstract (arXiv)

Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions. In this paper, we present a new learning framework on hypergraphs which fully uses the hypergraph structure. The key element is a family of regularization functionals based on the total variation on hypergraphs.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Dec 2013.

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Citing papers per year: 2021: 6; 2022: 8; 2023: 8; 2024: 9; 2025: 3; 2026: 1.

35 papers.

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  1. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 124
  2. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  3. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  4. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  5. 2022Hypergraph Transformer for Skeleton-based Action Recognitioncited by 36
  6. 2023Sheaf Hypergraph Networkscited by 33
  7. 2022I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphscited by 20
  8. 2022Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphscited by 15
  9. 2023Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Designcited by 13
  10. 2021A nonlinear diffusion method for semi-supervised learning on hypergraphscited by 11
  11. 2021Adaptive Neural Message Passing for Inductive Learning on Hypergraphscited by 10
  12. 2022Multi-Modal Hypergraph Diffusion Network with Dual Prior for Alzheimer Classificationcited by 9
23 more
  1. 2021Local Hyper-Flow Diffusioncited by 8
  2. 2022Nothing Stands Alone: Relational Fake News Detection with Hypergraph Neural Networkscited by 6
  3. 2023CAT-Walk: Inductive Hypergraph Learning via Set Walkscited by 6
  4. 2024Hypergraph Self-supervised Learning with Sampling-efficient Signalscited by 6
  5. 2024A Versatile Framework for Attributed Network Clustering via K-Nearest Neighbor Augmentationcited by 6
  6. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  7. 2024Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequalitycited by 4
  8. 2023Multi-class Graph Clustering via Approximated Effective p-Resistancecited by 2
  9. 2024Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusioncited by 2
  10. 2026Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passingcited by 2
  11. 2022Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel k-means, and Heat Kernelcited by 1
  12. 2022Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clusteringcited by 1
  13. 2023Hypergraphs with Edge-Dependent Vertex Weights: Spectral Clustering based on the 1-Laplaciancited by 1
  14. 2024Continuum limit of p-biharmonic equations on graphscited by 1
  15. 2024Hypergraph p-Laplacian regularization on point clouds for data interpolationcited by 1
  16. 2024Hypergraph p-Laplacian equations for data interpolation and semi-supervised learningcited by 1
  17. 2024Hypergraph clustering using Ricci curvature: an edge transport perspectivecited by 1
  18. 2025Scalable Hypergraph Structure Learning with Diverse Smoothness Priorscited by 1
  19. 2025Parameter-Free Hypergraph Neural Network for Few-Shot Node Classificationcited by 1
  20. 2025Higher-Order Regularization Learning on Hypergraphscited by 1
  21. 2021Regularized Recovery by Multi-order Partial Hypergraph Total Variationcited by 0
  22. 2023Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descentcited by 0
  23. 2023Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for Semi-Supervised Learning on Multilayer Graphscited by 0