mlsanityData to 7 Oct 2026

A nonlinear diffusion method for semi-supervised learning on hypergraphs

arXiv 2103.14867 ↗First posted 27 Mar 2021cs.LG cs.SI physics.data-ancited by 11

Not on the map. Why?

Abstract (arXiv)

Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are classical techniques for semi-supervised learning in the graph setting, and there are some standard ways to extend them to hypergraphs. However, these methods are linear models, and do not offer an obvious way of incorporating node features for making predictions. Here, we develop a nonlinear diffusion process on hypergraphs that spreads both features and labels following the hypergraph structure, which can be interpreted as a hypergraph equilibrium network. Even though the process is nonlinear, we show global convergence to a unique limiting point for a broad class of nonlinearities, which is the global optimum of a interpretable, regularized semi-supervised learning loss function. The limiting point serves as a node embedding from which we make predictions with a linear model. Our approach is much more accurate than several hypergraph neural networks, and also takes less time to train.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 31 of its 59 references that are in the map. First posted on arXiv 27 Mar 2021.

Builds on

31 of 59 references.

References · 31

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
  3. 2019Simplifying Graph Convolutional Networkscited by 1,470
  4. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  5. 2019When Does Label Smoothing Help?cited by 985
  6. 2019Deep Equilibrium Modelscited by 603
  7. 2018Hypergraph Neural Networkscited by 482
  8. 2020Combining Label Propagation and Simple Models Out-performs Graph Neural Networkscited by 199
  9. 2020Networks beyond pairwise interactions: structure and dynamicscited by 127
  10. 2016Higher-order organization of complex networkscited by 109
  11. 2020HNHN: Hypergraph Networks with Hyperedge Neuronscited by 104
  12. 2020Monotone operator equilibrium networkscited by 100
19 more
  1. 2018Simplicial Closure and higher-order link predictioncited by 92
  2. 2013The Total Variation on Hypergraphs - Learning on Hypergraphs Revisitedcited by 35
  3. 2017Inhomogeneous Hypergraph Clustering with Applicationscited by 31
  4. 2018Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clusteringcited by 25
  5. 2020The why, how, and when of representations for complex systemscited by 23
  6. 2020Nonlinear Higher-Order Label Spreadingcited by 19
  7. 2021A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinationscited by 18
  8. 2015Algorithms for Lipschitz Learning on Graphscited by 16
  9. 2021Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Taskscited by 13
  10. 2020SCE: Scalable Network Embedding from Sparsest Cutcited by 12
  11. 2020Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learningcited by 12
  12. 2017Hypergraph p-Laplacian: A Differential Geometry Viewcited by 11
  13. 2014Hypergraph Markov Operators, Eigenvalues and Approximation Algorithmscited by 9
  14. 2021Node and Edge Nonlinear Eigenvector Centrality for Hypergraphscited by 8
  15. 2019Quadratic Decomposable Submodular Function Minimization: Theory and Practice (Computation and Analysis of PageRank over Hypergraphs)cited by 7
  16. 2016Graph partitions and cluster synchronization in networks of oscillatorscited by 5
  17. 2019Explosive higher-order Kuramoto dynamics on simplicial complexescited by 5
  18. 2015A network dynamics approach to chemical reaction networkscited by 2
  19. 2019A framework for second order eigenvector centralities and clustering coefficientscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 3; 2024: 1; 2025: 1; 2026: 1.

11 papers.

  1. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 124
  2. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  3. 2022A Survey on Hyperlink Predictioncited by 9
  4. 2022A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddingscited by 9
  5. 2023Self-supervised Hypergraphs for Learning Multiple World Interpretationscited by 8
  6. 2023Hypergraph Transformer for Semi-Supervised Classificationcited by 7
  7. 2023Multi-Task Hypergraphs for Semi-supervised Learning using Earth Observationscited by 6
  8. 2024Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusioncited by 2
  9. 2026Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passingcited by 2
  10. 2022A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddingscited by 0
  11. 2025HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networkscited by 0