Learning Robust Discriminant Projections via Double Capped L p -Norm Distance Metrics With “Min” Constraints

Recently, there has been a surge in the development of robust norm distance-based linear discriminant analysis (LDA) techniques, which have garnered significant attention in the field of feature extraction. However, a persistent issue that has yet to be resolved is that the successful suppression of outliers may inadvertently impede the accurate discrimination of normal points. To solve this problem, we, in this article, study a novel robust LDA measured by double capped $L_{p}$ -norm distance (CLD) metrics with min constraints (DCLDA) to learn robust discriminant projections, in which normal points and outliers are separately treated. To be specific, it takes a double capped $L_{p}$ -norm with "Min" constraints in the proposed model to measure the distances for between- and within-class dispersions. The proposed model effectively ensures accurate discrimination of normal points by $L_{p}$ -norm, while also eliminating the exaggerated effect of outliers that may arise from larger $p$ values. The resulted objective is not trivial because of its nonconvexity and nonsmoothness. As one of the major contributions of this article, we introduce a new reformulation that provides an objective problem theoretically equivalent to the original. By this reformulation, we develop an effective iterative algorithm to solve the proposed model. The algorithm is proven to be convergent through rigorous theoretical analysis. Extensive experiments were conducted on several real-world datasets across different image classification tasks to showcase the effectiveness of the proposed method.