Hypergraph p-Laplacian Regularization for Remote Sensing Image Recognition

TL;DR

This paper introduces a novel Hypergraph p-Laplacian regularization method that better preserves local data structures, improving semi-supervised learning for remote sensing image recognition.

Contribution

It proposes an effective approximation algorithm for Hypergraph p-Laplacian and applies it to enhance semi-supervised logistic regression for remote sensing images.

Findings

HpLapR outperforms LapR, HLapR, and HpLapR on UC-Merced dataset.

The method effectively preserves local data geometry.

Experimental results demonstrate superior recognition accuracy.

Abstract

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.