Sparse Principal Component Analysis and Adaptive Multigraph Learning for Hyperspectral Band Selection

Band selection (BS) is an effective dimensionality reduction technique for hyperspectral images. Although many relevant methods have been proposed, they often only focus on the bandwise information and the correlation between the bands, and few of them pay attention to the manifold preservation in low-dimensional space, which may lead to the intrinsic structure of the data being damaged. In this article, we propose a novel method called sparse principal component analysis and adaptive multigraph learning (SPCA-AMGL) to address this issue. First, it applies SPCA to the BS task to learn the projection weight matrix, which utilizes the orthogonal constraint to remove redundant bands and uses the
$ {L}_{\text{2,1}}$
norm to impose a sparse regularization on the weight matrix to ensure the selection of effective bands. Then, to select the bands with manifold preserving capability, AMGL is proposed to capture the local neighbor structure of data by combining the benefit of multiple graphs, which can not only adaptively learn the graph structure but also obtain the analytical solution of the multigraph coefficients. Finally, an alternate iterative algorithm is designed to optimize the proposed method. Abundant experiments on three hyperspectral datasets prove the reliability and superiority of the proposed method.