# Scalable Hypergraph Structure Learning with Diverse Smoothness Priors

arXiv: https://arxiv.org/abs/2504.03583 · HTML: https://mlsanity.com/paper/2504.03583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 65 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Graph Convolutional Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2008.02457/) (2020)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [Hypernetwork Science via High-Order Hypergraph Walks](https://mlsanity.com/paper/1906.11295/) (2019)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [Hypergraph Random Walks, Laplacians, and Clustering](https://mlsanity.com/paper/2006.16377/) (2020)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [Learning on Hypergraphs with Sparsity](https://mlsanity.com/paper/1804.00836/) (2018)
- [Hypergraph Convolutional Networks for Weakly-Supervised Semantic Segmentation](https://mlsanity.com/paper/2210.05564/) (2022)
- [Planted Hitting Set Recovery in Hypergraphs](https://mlsanity.com/paper/1905.05839/) (2019)
- [Learning graphs and simplicial complexes from data](https://mlsanity.com/paper/2312.10545/) (2023)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Learning the Topology of a Simplicial Complex Using Simplicial Signals: A Greedy Approach](https://mlsanity.com/paper/2502.20159/) (2025)

## Built on by (most cited first, 1 of 1)

- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph Laplacian on which the observed signals are smooth. With the extension of graphs to hypergraphs - where edges can connect more than two nodes - graph learning methods have similarly been generalized to hypergraphs. However, the absence of a unified framework for calculating total variation has led to divergent definitions of smoothness and, consequently, differing approaches to hyperedge recovery. We confront this challenge through generalization of several previously proposed hypergraph total variations, subsequently allowing ease of substitution into a vector based optimization. To this end, we propose a novel hypergraph learning method that recovers a hypergraph topology from time-series signals based on a smoothness prior. Our approach, designated as Hypergraph Structure Learning with Smoothness (HSLS), addresses key limitations in prior works, such as hyperedge selection and convergence issues, by formulating the problem as a convex optimization solved via a forward-backward-forward algorithm, ensuring guaranteed convergence. Additionally, we introduce a process that simultaneously limits the span of the hyperedge search and maintains a valid hyperedge selection set. In doing so, our method becomes scalable in increasingly complex network structures. The experimental results demonstrate improved performance, in terms of accuracy, over other state-of-the-art hypergraph inference methods; furthermore, we empirically show our method to be robust to total variation terms, biased towards global smoothness, and scalable to larger hypergraphs.