Joint Sparse Local Linear Discriminant Analysis for Feature Dimensionality Reduction of Hyperspectral Images

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 L2,1-norm constraint. The L2,1-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.