An Improved Linear Discriminant Analysis with L1-Norm for Robust Feature Extraction

Feature extraction plays an important role in analyzing data with multivariate features. Linear discriminant analysis based on L1-norm (LDA-L1) is a recently developed technique for enhancing the robustness of the classic LDA against outliers. However, LDA-L1 employs a greedy strategy to find all the discriminant vectors, which may lead to suboptimal solution. To address this issue, we develop a novel algorithm termed as ILDA-L1 in this paper, which can optimize all the discriminant vectors simultaneously in a unified framework. Specifically, we introduce an orthonormal constraint on the discriminant vectors and convert the objective function of LDA-L1 into a difference formula. To solve the resulting nonconvex and nonsmooth problem, we first construct a successive concave approximation to the objective function at current solution and then use projected sub gradient method, thus leading to a convergent iterative algorithm. The experimental results on several benchmark datasets confirm the effectiveness of ILDA-L1 in extracting robust features.