# Hypergraph p-Laplacian Regularization for Remote Sensing Image Recognition

arXiv: https://arxiv.org/abs/1806.08104 · HTML: https://mlsanity.com/paper/1806.08104/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Unsupervised Hyperspectral and Multispectral Image Blind Fusion Based on Deep Tucker Decomposition Network with Spatial-Spectral Manifold Learning](https://mlsanity.com/paper/2409.09670/) (2024)
- [Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation](https://mlsanity.com/paper/2503.06066/) (2025)
- [SSDL: Self-Supervised Dictionary Learning](https://mlsanity.com/paper/2112.01790/) (2021)
- [A Transformer-in-Transformer Network Utilizing Knowledge Distillation for Image Recognition](https://mlsanity.com/paper/2502.16762/) (2025)

## Abstract (arXiv)

It is of great importance to preserve locality and similarity information in semi-supervised learning (SSL) based applications. Graph based SSL and manifold regularization based SSL including Laplacian regularization (LapR) and Hypergraph Laplacian regularization (HLapR) are representative SSL methods and have achieved prominent performance by exploiting the relationship of sample distribution. However, it is still a great challenge to exactly explore and exploit the local structure of the data distribution. In this paper, we present an effect and effective approximation algorithm of Hypergraph p-Laplacian and then propose Hypergraph p-Laplacian regularization (HpLapR) to preserve the geometry of the probability distribution. In particular, p-Laplacian is a nonlinear generalization of the standard graph Laplacian and Hypergraph is a generalization of a standard graph. Therefore, the proposed HpLapR provides more potential to exploiting the local structure preserving. We apply HpLapR to logistic regression and conduct the implementations for remote sensing image recognition. We compare the proposed HpLapR to several popular manifold regularization based SSL methods including LapR, HLapR and HpLapR on UC-Merced dataset. The experimental results demonstrate the superiority of the proposed HpLapR.