# Learning on Hypergraphs with Sparsity

arXiv: https://arxiv.org/abs/1804.00836 · HTML: https://mlsanity.com/paper/1804.00836/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 6 of 6)

- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [On Convex Clustering Solutions](https://mlsanity.com/paper/2105.08348/) (2021)
- [Scalable Hypergraph Structure Learning with Diverse Smoothness Priors](https://mlsanity.com/paper/2504.03583/) (2025)
- [Regularized Recovery by Multi-order Partial Hypergraph Total Variation](https://mlsanity.com/paper/2102.09771/) (2021)
- [Central-Smoothing Hypergraph Neural Networks for Predicting Drug-Drug Interactions](https://mlsanity.com/paper/2112.07837/) (2021)
- [Uniform tensor clustering by jointly exploring sample affinities of various orders](https://mlsanity.com/paper/2302.01569/) (2023)

## Abstract (arXiv)

Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, one wishes to learn a smooth function with respect to its topology. A fundamental issue is to find suitable smoothness measures of functions on the nodes of a graph/hypergraph. We show a general framework that generalizes previously proposed smoothness measures and also gives rise to new ones. To address the problem of irrelevant or noisy data, we wish to incorporate sparse learning framework into learning on hypergraphs. We propose sparsely smooth formulations that learn smooth functions and induce sparsity on hypergraphs at both hyperedge and node levels. We show their properties and sparse support recovery results. We conduct experiments to show that our sparsely smooth models have benefits to irrelevant and noisy data, and usually give similar or improved performances compared to dense models.