# Hypergraph p-Laplacian equations for data interpolation and semi-supervised learning

arXiv: https://arxiv.org/abs/2411.12601 · HTML: https://mlsanity.com/paper/2411.12601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 19 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Analysis of p-Laplacian Regularization in Semi-Supervised Learning](https://mlsanity.com/paper/1707.06213/) (2017)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications](https://mlsanity.com/paper/1706.04957/) (2017)
- [Asymptotic behavior of ℓp-based Laplacian regularization in semi-supervised learning](https://mlsanity.com/paper/1603.00564/) (2016)
- [Analysis and algorithms for ℓp-based semi-supervised learning on graphs](https://mlsanity.com/paper/1901.05031/) (2019)
- [Continuum limit of p-biharmonic equations on graphs](https://mlsanity.com/paper/2404.19689/) (2024)
- [Hypergraph p-Laplacian regularization on point clouds for data interpolation](https://mlsanity.com/paper/2405.01109/) (2024)

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

- [Higher-Order Regularization Learning on Hypergraphs](https://mlsanity.com/paper/2510.26533/) (2025)

## Abstract (arXiv)

Hypergraph learning with p-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph p-Laplacian equation from the subdifferential of the p-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified p-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications.