Robust Two-Dimensional Linear Discriminant Analysis via Information Divergence

Due to the complexities of collected data that may contain outliers and noises, many variants of LDA and 2DLDA have been proposed to address this problem and have shown that the improved methods produce much better performance than classical LDA and 2DLDA. In this paper we propose a novel two-dimensional linear discriminant analysis method via information divergence. The proposed method applies the weighted L21 norm to learn a robust projection matrix in the image space. In the proposed model, we introduce the weights into the within-class scatter and the total scatter simultaneously, and learn the weights by imposing information divergence on the objective functions. To handle the proposed model, we resort to Dinkelbach’s extended algorithm to solve the proposed ratio minimization problem. Considering the characteristics of the subproblems, we exploit an equivalent representation of subproblems which can be solved by alternating optimization techniques where each block of variables has good optimization properties. The proposed model not only overcomes the small-sample-size problem, but also suppresses outliers by an adaptively weighted scheme with the guidance of information divergences. The experiments on several image data sets demonstrate that the classification performance of the proposed method is superior to that of some existing methods in the presence of outliers.