L1-Norm Distance Linear Discriminant Analysis Based on an Effective Iterative Algorithm

Qiaolin Ye, Jian Yang, Fan Liu, Chunxia Zhao, Ning Ye, Tongming Yin

Abstract: Recent works have proposed two L1-norm distance measure-based linear discriminant analysis (LDA) methods, L1-LD and LDA-L1, which aim to promote the robustness of the conventional LDA against outliers. In LDA-L1, a gradient ascending iterative algorithm is applied, which, however, suffers from the choice of stepwise. In L1-LDA, an alternating optimization strategy is proposed to overcome this problem. In this paper, however, we show that due to the use of this strategy, L1-LDA is accompanied with some serious problems that hinder the derivation of the optimal discrimination for data. Then, we propose an effective iterative framework to solve a general L1-norm minimization-maximization (minmax) problem. Based on the framework, we further develop a effective L1-norm distance-based LDA (called L1-ELDA) method. Theoretical insights into the convergence and effectiveness of our algorithm are provided and further verified by extensive experimental results on image databases.