Laplacian-Regularized Low-Rank Subspace Clustering for Hyperspectral Image Band Selection

Band selection is an effective approach to mitigate the “Hughes phenomenon” of hyperspectral image (HSI) classification. Recently, sparse representation (SR) theory has been successfully introduced to HSI band selection, and many SR-based methods have been developed and shown great potential and superiority. However, due to the inherent limitations of the SR scheme, i.e., individually representing each band with only a few other bands from the same subspace, the SR-based methods cannot effectively capture the global structures of the data, which limit the band selection performance. In this paper, to overcome this obstacle, the novel Laplacian-regularized low-rank subspace clustering (LLRSC) algorithm is proposed for HSI band selection. On the one hand, the low-rank subspace clustering model is introduced to capture the global structure information for the learned representation coefficient matrix and deal with the HSI band selection task in the clustering framework. On the other hand, considering the high correlation between adjacent bands, 1-D Laplacian regularization is utilized to incorporate the neighboring band information and further reduce the representation bias. Lastly, an eigenvalue analysis algorithm based on band mutation information is utilized to estimate the appropriate size of the band subset. The experimental results indicate that the proposed LLRSC algorithm outperforms the other state-of-the-art methods and achieves a very competitive band selection performance for HSIs.