Robust collaborative representation-based classification via regularization of truncated total least squares

Collaborative representation-based classification has shown promising results on cognitive vision tasks like face recognition. It solves a linear problem with l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_1$$\end{document} or 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} norm regularization to obtain a stable sparse representation. Previous studies showed that the collaboration representation assisted the output of optimum sparsity constraint, but the choice of regularization also played a crucial role in stable representation. In this paper, we proposed a novel discriminative collaborative representation-based classification method via regularization implemented by truncated total least squares algorithm. The key idea of the proposed method is combining two coefficients obtained by 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} regularization and truncated TLS-based regularization. After evaluated by extensive experiments conducted on several benchmark facial databases, the proposed method is demonstrated to outperform the naive collaborative representation-based method, as well as some other state-of-the-art methods for face recognition. The regularization by truncation effectively and dramatically enhances sparsity constraint on coding coefficients in collaborative representation and increases robustness for face recognition.