Ensemble p-Laplacian Regularization for Scene Image Recognition

Abstract

Recently, manifold regularized semi-supervised learning (MRSSL) received considerable attention, because it successfully exploits the geometry of the intrinsic data probability distribution to leverage the performance of a learning model. As a natural nonlinear generalization of graph Laplacian, p-Laplacian has been proved having the rich theoretical foundations to better preserve the local structure. However, it is difficult to determine the fitting graph p-Lapalcian, i.e., the parameter p, which is a critical factor for the performance of graph p-Laplacian. Therefore, we develop an ensemble p-Laplacian regularization (EpLapR) to fully approximate the intrinsic manifold of the data distribution. EpLapR incorporates multiple graphs into a regularization term in order to sufficiently explore the complementation of graph p-Laplacian. Specifically, we construct a fused graph by introducing an optimization approach to assign suitable weights on different p value graphs. And then, we conduct semi-supervised learning framework on the fused graph. Extensive experiments on UC-Merced dataset and Scene 15 dataset demonstrate the effectiveness and efficiency of the proposed method.