Linear Embedding by Joint Robust Discriminant Analysis and Inter-class Sparsity

Abstract

Feature extraction methods have been successfully applied to many real-world applications. The classical Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. Although they have been used for different classification tasks, these methods have some shortcomings. The main one is that the projection axes obtained are not informative about the relevance of original features. In this paper, we propose a linear embedding method that merges two interesting properties: Robust LDA and inter-class sparsity. Furthermore, the targeted projection transformation focuses on the most discriminant original features, The proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA FSIS). Two kinds of sparsity are explicitly included in the proposed model. The first kind is obtained by imposing the `2;1 constraint on the projection matrix in order to perform feature ranking. The second kind is obtained by imposing the inter-class sparsity constraint used for getting a common sparsity structure in each class. Comprehensive experiments on five real-world image datasets demonstrate the effectiveness and advantages of our framework over existing linear methods.