Graph Regularized Nonlinear Ridge Regression for Remote Sensing Data Analysis

In this paper, a graph regularized nonlinear ridge regression (RR) model is proposed for remote sensing data analysis, including hyper-spectral image classification and atmospheric aerosol retrieval. The RR is an efficient linear regression method, especially in handling cases with a small number of training samples or with correlated features. However, large amounts of unlabeled samples exist in remote sensing data analysis. To sufficiently explore the information in unlabeled samples, we propose a graph regularized RR (GRR) method, where the vertices denote labeled or unlabeled samples and the edges represent the similarities among different samples. A natural assumption is that the predict values of neighboring samples are close to each other. To further address the nonlinearly separable problem in remote sensing data caused by the complex acquisition process as well as the impacts of atmospheric and geometric distortions, we extend the proposed GRR into a kernelized nonlinear regression method, namely KGRR. To evaluate the proposed method, we apply it to both classification and regression tasks and compare with representative methods. The experimental results show that KGRR can achieve favorable performance in terms of predictability and computation time.