Feature Selective Projection Learning via Low-Rank Embedding Regression for Feature Dimensionality Reduction of Hyperspectral Images

Dimensionality reduction (DR) is an effective approach to improve the speed and efficiency of hyperspectral image (HSI) processing. However, the existing DR methods, including both feature extraction and feature selection, struggle to address the combined challenges of the “curse of dimensionality” and spectral variation in HSI. To this end, we developed a novel method called low-rank preserved selective projection with embedding regression regularization (LPSPER). This method effectively addresses DR challenges in HSIs by simultaneously performing feature selection and feature extraction, thereby enhancing robustness in handling noise pollutions and improving the discriminative power of low-dimensional features. In particular, low-rank representation (LRR) and projection learning are incorporated to maintain the global structure of data within a low-dimensional subspace. To further enhance the discriminant capability of features in the subspace, a robust L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub>-norm-constrained embedding regression is employed. Additionally, an alternating minimization (AM) algorithm was developed to solve the resulting optimization problem. An efficient and convergent alternating direction method of multipliers (ADMM) was introduced to solve the subproblem. Experiments conducted on four publicly available hyperspectral datasets demonstrate the superiority of the proposed method in improving classification accuracy compared to state-of-the-art methods. The code for this work is publicly available at https://github.com/SilenceAct/LPSPER.