Robust bilateral Lp-norm two-dimensional linear discriminant analysis

Abstract

Traditional linear discriminant analysis (LDA) may suffer from a sensitivity to outliers and the small sample size (SSS) problem, while the Lp-norm measure for 0 < p ≤ 1 is robust in a sense. In this paper, based on the criterion of the Bayes optimality, we propose a matrix-based bilateral Lp-norm two-dimensional linear discriminant analysis (BLp2DLDA) with robust performance, where 0 < p ≤ 1. We prove that the BLp2DLDA criterion is equivalent to an upper bound of the theoretical framework of the Bayes optimality. Compared with the L2-norm 2-directional 2-dimensional LDA ((2D)2LDA), our BLp2DLDA is more robust to outliers and noise. Moreover, unilateral Lp2DLDA can also be easily derived from BLp2DLDA. In addition, a simple but effective iterative technique is introduced to solve BLp2DLDA and the unilateral Lp2DLDA. Experimental results on different types of contaminated human face databases show that the proposed BLp2DLDA outperforms (2D)2LDA.