Although linear discriminant analysis (LDA)-based subspace learning has been widely applied to hyperspectral image (HSI) classification, the existing LDA-based subspace learning methods exhibit several limitations: (1) They are often sensitive to noise and demonstrate weak robustness; (2) these methods ignore the local information inherent in data; and (3) the number of extracted features is restricted by the number of classes. To address these drawbacks, this paper proposes a novel joint sparse local linear discriminant analysis (JSLLDA) method by integrating embedding regression and locality-preserving regularization into the LDA model for feature dimensionality reduction of HSIs. In JSLLDA, a row-sparse projection matrix can be learned, to uncover the joint sparse structure information of data by imposing a $L_{2,1}$-norm constraint. The $L_{2,1}$-norm is also employed to measure the embedding regression reconstruction error, thereby mitigating the effects of noise and occlusions. A locality preservation term is incorporated to fully leverage the local geometric structural information of the data, enhancing the discriminability of the learned projection. Furthermore, an orthogonal matrix is introduced to alleviate the limitation on the number of acquired features. Finally, extensive experiments conducted on three hyperspectral image (HSI) datasets demonstrated that the performance of JSLLDA surpassed that of some related state-of-the-art dimensionality reduction methods.

Hyperspectral image (HSI) change detection (CD) is an important technology for identifying surface changes using multi-temporal HSIs. Nevertheless, the high dimensionality of HSIs presents significant challenges for CD tasks, including issues such as lack of robustness and high computational costs in existing methods. To address those issues, this paper proposes an unsupervised simple and effective HSI CD model termed $L_{2,1}$-norm regularized double non-negative matrix factorization ($L_{2,1}$-DNMF). Specifically, the proposed model employs a symmetric double non-negative matrix factorization (NMF) framework to jointly analyze multitemporal HSIs, capturing their common and invariant structural information to construct a shared feature basis. Meanwhile, two non-negative feature weight matrices are learned to generate a differential image matrix that directly reflects the change regions. To enhance robustness against noise, an $L_{2,1}$-norm constraint is imposed on the difference image matrix, ensuring that unchanged areas exhibit near-zero values while changed areas present nonzero values. Finally, comprehensive experiments performed on three benchmark hyperspectral datasets validated the efficacy of the proposed method, which is superior to some state-of-the-art ones regarding detection performance and computational cost.