Robust Discriminant Regression for Feature Extraction

Ridge regression (RR) and its extended versions are widely used as an effective feature extraction method in pattern recognition. However, the RR-based methods are sensitive to the variations of data and can learn only limited number of projections for feature extraction and recognition. To address these problems, we propose a new method called robust discriminant regression (RDR) for feature extraction. In order to enhance the robustness, the
${L_{2,1}}$
-norm is used as the basic metric in the proposed RDR. The designed robust objective function in regression form can be solved by an iterative algorithm containing an eigenfunction, through which the optimal orthogonal projections of RDR can be obtained by eigen decomposition. The convergence analysis and computational complexity are presented. In addition, we also explore the intrinsic connections and differences between the RDR and some previous methods. Experiments on some well-known databases show that RDR is superior to the classical and very recent proposed methods reported in the literature, no matter the
${L_{2}}$
-norm or the
${L_{2,1}} $
-norm-based regression methods. The code of this paper can be downloaded from
http://www.scholat.com/laizhihui
.