Feature Dimensionality Reduction with L 2,p -Norm-Based Robust Embedding Regression for Classification of Hyperspectral Images

The curse of dimensionality and noise corruption are two tough problems that need to be solved in hyperspectral image (HSI) classification. However, the current feature dimensionality reduction methods, including both feature extraction and feature selection ones, cannot simultaneously solve the above two problems well. To address this issue, this paper proposes a novel method called L _2,p -norm-based robust embedding regression ( L _2,p -RER) for robust feature dimensionality reduction of HSI, which can effectively suppress the impact of noises and reduce the feature dimensions. Specifically, L _2,p -RER first integrates projection learning with robust principle component analysis (RPCA) to remove noise in a low-dimensional space. Secondly, an embedding regression regularization is proposed to improve the discriminability of the extracted low-dimensional features. Thirdly, a L _2,1 -norm constraint is imposed to improve the interpretability of the learned projection matrix, which can jointly extract the key features from all bands with their physical meanings certainly preserved. Last but most important, the L _2,p -norm that can adaptively balance the sparsity and the convexity is employed to model the noise and regression residual in the embedded low-dimensional space, which can further enhance the robustness and generalization of the proposed method. In addition, extensive experiments conducted on three benchmark HSI datasets validated the effectiveness of the proposed method.