L₂,₁-Norm Regularized Robust and Sparse Linear Discriminant Analysis via an Alternating Direction Method of Multipliers

Abstract

Recently, an absolute value inequalities discriminant analysis criterion with robustness and sparseness for supervised dimensionality reduction was studied. However, it obtains discriminant directions one by one through greedy search, which makes the sparseness of multiple discriminant directions unexplainable. In addition, it relaxes the original problem into a series of linear programming problems which makes it time consuming. In this paper, we construct a novel linear discriminant analysis with robustness and sparseness jointly through the $L_{1}$ -norm and $L_{2,1}$ -norm. The proposed approach obtains all the discriminant directions simultaneously, and rather than solving linear programming problems, it is solved by a more effective alternating direction method of multipliers. The effectiveness of the proposed method is supported by preliminary experimental results on two artificial datasets, some benchmark datasests and two face image datasets.

Keywords

• Dimensionality reduction
• linear discriminant analysis
• robust linear discriminant analysis
• sparse linear discriminant analysis