Dimensionality reduction is an essential and important issue in hyperspectral image processing. With the advantages of preserving the spatial neighborhood information and the global structure information, tensor analysis and low rank representation have been widely considered in this field and yielded satisfactory performance. In available tensor- and low rank-based methods, how to construct appropriate tensor samples and determine the optimal rank of hyperspectral images along each mode are still challenging issues. To address these drawbacks, an unsupervised tensor-based multiscale low rank decomposition (T-MLRD) method for hyperspectral images dimensionality reduction is proposed in this paper. By regarding the raw cube hyperspectral image as the only tensor sample, T-MLRD needs no labeled samples and avoids the processing of constructing tensor samples. In addition, a novel multiscale low rank estimating method is proposed to obtain the optimal rank along each mode of hyperspectral image which avoids the complicated rank computing. Finally, the multiscale low rank feature representation is fused to achieve dimensionality reduction. Experimental results on real hyperspectral datasets demonstrate the superiority of the proposed method over several state-of-the-art approaches.

Recently, Transformer-based approaches have emerged as powerful tools for hyperspectral image (HSI) classification. HSI inherently exhibits low-rank and sparse properties due to spatial continuity and spectral redundancy. However, most existing methods directly adopt standard Transformer architectures, overlooking the distinctive priors inherent in HSI, which limits the classification performance and modeling efficiency. To address these challenges, this paper proposes a Multi-scale Low-rank and Sparse Transformer (MLSFormer) that effectively integrates both low-rank and sparse priors. Specifically, we leverage tensor low-rank decomposition (TLRD) to factorize the query, key, and value matrices into low-rank tensor products, capturing dominant low-rank structures. In parallel, we introduce a sparse attention mechanism to retain only the most important connections. Furthermore, a multi-scale attention mechanism is designed to hierarchically partition attention heads into global, medium, and local groups, each assigned tailored decomposition ranks and sparsity ratios, enabling comprehensive multi-scale feature extraction. Extensive experiments on three benchmark datasets demonstrate that MLSFormer achieves superior classification performance compared to state-of-the-art methods.

Dimensionality reduction is of great importance which aims at reducing the spectral dimensionality while keeping the desirable intrinsic structure information of hyperspectral images. Tensor analysis which can retain both spatial and spectral information of hyperspectral images has caused more and more concern in the field of hyperspectral images processing. In general, a desirable low dimensionality feature representation should be discriminative and compact. To achieve this, a tensor discriminant analysis model via compact feature representation (TDA-CFR) was proposed in this paper. In TDA-CFR, the traditional linear discriminant analysis was extended to tensor space to make the resulting feature representation more informative and discriminative. Furthermore, TDA-CFR redefines the feature representation of each spectral band by employing the tensor low rank decomposition framework which leads to a more compact representation.

With the integration of graph structure representation and self-attention mechanism, the graph Transformer (GT) demonstrates remarkable effectiveness in hyperspectral image (HSI) classification by simultaneously modeling complex topological structures and capturing long-range spectral–spatial dependencies. Current GT models struggle to effectively integrate node features with position information while balancing global positional context and local structural relationships. To address these challenges, this article proposes a structure perception GT (SPGFormer) with Laplacian position encoding (PE) for HSI classification. Specifically, SPGFormer introduces a dual-branch interactive Transformer (DBIT) module that processes node spectral features and Laplacian position information in parallel by the node feature Transformer (NFT) branch and the structure perception position Transformer (SPPT) branch, respectively. The NFT branch employs a Transformer encoder to model spectral characteristics, while the SPPT branch leverages graph Laplacian eigenvectors to capture global position information. In addition, a structure perception multihead self-attention (SPMHSA) mechanism is proposed to integrate the local topological structural information into the SPPT branch. Moreover, to facilitate effective interaction between these complementary feature spaces, a bidirectional cross-attention module (BCAM) is proposed to enable bidirectional communication between these two branches. Comprehensive experimental results demonstrate that SPGFormer outperforms existing state-of-the-art (SOTA) methods in multiple metrics, including overall accuracy (OA), average accuracy (AA), and Kappa coefficient, with improvements in OA of 2.04%, 2.39%, 1.10%, and 2.27%, respectively, on four benchmark HSI datasets.