A new discriminative collaborative representation-based classification method via l2 regularizations

Collaborative representation-based classification (CRC) is one of the famous representation-based classification methods in pattern recognition. However, a testing sample in most of the CRC variants is collaboratively reconstructed by a linear combination of all the training samples from all the classes, the training samples from the class that the testing sample belongs to have no advantage in discriminatively and competitively representing and classifying the testing sample. Moreover, the incorrect classification can easily come into being when the training samples from the different classes are very similar. To address the issues, we propose a novel discriminative collaborative representation-based classification (DCRC) method via l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document} regularizations to enhance the power of pattern discrimination. In the proposed model, we consider not only the discriminative decorrelations among all the classes, but also the similarities between the reconstructed representation of all the classes and the class-specific reconstructed representations in the l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document} regularizations. The experiments on several public face databases have demonstrated that the proposed DCRC effectively and robustly outperforms the state-of-the-art representation-based classification methods.