  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.
