Sparse L1-norm two dimensional linear discriminant analysis via the generalized elastic net regularization

摘要

Linear discriminant analysis (LDA) and two dimensional LDA (2DLDA) are widely applied methods for dimensionality reduction. However, both of them lack of robustness and sparseness. Recent studies show that the elastic net and the L1-norm would improve the learning ability of dimensionality reduction. In this paper, we propose a generalized elastic net and apply it into the L1-norm based LDA and 2DLDA to extend LDA and 2DLDA with robustness and sparseness simultaneously (named LDAL1-S and 2DLDAL1-S, respectively). The generalized elastic net also helps LDAL1-S and 2DLDAL1-S avoiding the singularity problem. Moreover, the Lp-norm (0 p = 1) is used in the generalized elastic net, which makes LDAL1-S and 2DLDAL1-S realize the desired sparseness of the discriminant vectors by selecting proper p. Both LDAL1-S and 2DLDAL1-S are solved through a series of convex problems with equality constraints, with a closed solution for each single problem. Experimental results on three contaminated human face databases show the effectiveness of the proposed methods. (c) 2019 Elsevier B.V. All rights reserved.