Simultaneous Sparse Graph Embedding for Hyperspectral Image Classification

Sparse graph embedding (SGE) is a promising technique useful for the nonlinear feature extraction (FE) of hyperspectral images (HSIs). However, such images exhibit spatial variability and spectral multimodality, presenting challenges to existing FE methods, including SGE. To address this issue, this paper presents two novel SGE methods for HSI classification. One method, which is termed simultaneous SGE (SSGE), is designed to consider the spatial variability of spectral signatures by using a simultaneous sparse representation (SSR) model integrated with a shape-adaptive neighborhood building approach. In addition, a sparse graph is constructed via matrix computation based on sparse codes. Then, low-dimensional features are produced by employing linear graph embedding (LGE) based on the constructed sparse graph. The other method, which is termed simultaneous sparse multimanifold learning (SSMML), is proposed to handle the multimodality of an HSI. In SSMML, multiple views are generated to represent different modalities. Then, multiview-oriented submanifolds are produced by adopting SSGE, and they are further integrated via coregularization. SSGE is capable of modeling both local and global data structures. Furthermore, SSMML serves as a prototype that can model multimodal data structures. The proposed methods are evaluated by using sparse multinomial logistic regression for HSI classification. Experimental results with two popular hyperspectral data sets validate the good performance of the two methods in producing more representative low-dimensional features and yielding superior classification results compared with other related approaches.