Robust Adaptive Linear Discriminant Analysis with Bidirectional Reconstruction Constraint

Linear discriminant analysis (LDA) is a well-known supervised method for dimensionality reduction in which the global structure of data can be preserved. The classical LDA is sensitive to the noises, and the projection direction of LDA cannot preserve the main energy. This article proposes a novel feature extraction model with l 2,1 norm constraint based on LDA, termed as RALDA. This model preserves within-class local structure in the latent subspace according to the label information. To reduce information loss, it learns a projection matrix and an inverse projection matrix simultaneously. By introducing an implicit variable and matrix norm transformation, the alternating direction multiple method with updating variables is designed to solve the RALDA model. Moreover, both computational complexity and weak convergence property of the proposed algorithm are investigated. The experimental results on several public databases have demonstrated the effectiveness of our proposed method.