Spatial and Cluster Structural Prior-Guided Subspace Clustering for Hyperspectral Image

Subspace clustering has achieved remarkable performance for hyperspectral image (HSI). However, existing methods are often computationally expensive and have limited ability to capture the intrinsic structural information of HSI. In this article, we propose a structural prior-guided subspace clustering method, which simultaneously incorporates the local and nonlocal spatial information and the cluster prior information. Accordingly, three efficient regularizations are developed. Considering the local connectivity of pixels, we propose an
$\ell _{2,1}$
norm-based constraint on the representation difference matrix to improve the homogeneity of clustering result. Next, to capture the nonlocal geometric structure of HSI, we propose a manifold-based regularization with an adaptively learned landmark graph. Furthermore, we explore the block-diagonal cluster structure of HSI and develop a landmark-based clustering constraint, which makes the representations more favorable for clustering. Our local constraint is imposed on all the data points due to its efficiency and the latter two are solely imposed on landmarks, leading to computationally efficient regularizations. Due to the local constraint, the manifold and cluster structure of the landmarks can be effectively propagated to all the data points. To make our model scalable to large-scale data, we learn a compact dictionary with an orthogonal constraint, significantly reducing the number of parameters. In addition, we propose a novel landmark selection method to support our landmark-based constraints using multiscale super-pixel segmentation and clustering, which improves the uniformity and diversity of landmarks. We also develop an efficient algorithm to solve the proposed model. Experimental results demonstrate that our model outperforms the state-of-the-art.