Patch Tensor-Based Sparse and Low-Rank Graph for Hyperspectral Images Dimensionality Reduction

Dimensionality reduction is an important aspect in hyperspectral images processing. Recently, graph-based dimensionality reduction methods have drawn much attention and achieved promising performance. In traditional graph methods, $k$-nearest neighbors and $\varepsilon$-ball neighborhood are the most commonly used methods for graph construction and the pairwise Euclidean distance is often chosen as the similarity between the corresponding data points. But these methods are sensitive to data noise, and their graph structures are unstable with additive noise. More recently, sparse graph and low-rank graph have been proposed to exploit local and global structures hidden in hyperspectral images. But these methods only consider part of the entire structural information and fail to capture the full intrinsic information of hyperspectral images. To overcome these drawbacks, a patch tensor-based sparse and low-rank graph (PT-SLG) is proposed for hyperspectral images dimensionality reduction in this paper. In PT-SLG, the sparsity and low-rankness properties are jointly considered to capture the local and global intrinsic structures hidden in hyperspectral data simultaneously. In addition, tensor analysis is utilized to preserve the spatial neighborhood information. A clustering strategy is used to exploit the nonlocal similarity information, which enhances the low-rank and sparse constraints and also reduces the computational cost. Moreover, a novel tensor-based graph construction method is presented, which considers the joint similarity along the two spatial domains across all the tensor samples and makes the resulting graph more informative. Experimental results on real hyperspectral datasets demonstrate the superiority of PT-SLG over the other state-of-the-art approaches.