Adaptive feature weighting for robust Lp-norm sparse representation with application to biometric image classification

Sparse representation has attracted much attention in the field of biometrics, such as face recognition and palmprint recognition. Although the lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{p}$$\end{document}-norm (0<p<1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0 < p < 1)$$\end{document} based sparse representation can obtain more sparse solution than the widely used 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}-norm based method, it needs to solve a non-convex optimization problem, which leads to poor robustness in real application. In this paper, we propose a robust lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{p}$$\end{document}-norm sparse representation method with adaptive feature weighting. We derive the adaptive feature weighting method by self-paced learning (SPL), and utilize it to guide the features of lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{p}$$\end{document}-norm sparse representation in the easy-to-hard learning process. Differing from existing SPL methods, feature weighted SPL in our method dynamically evaluates the learning difficulty of each feature rather than sample. For the advantages of the proposed method, it can avoid lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{p}$$\end{document}-norm sparse minimization failing into bad local minima and reduce the effects of noise feature in the early learning stage. Experiments on several biometric image datasets show that our proposed method is superior to conventional lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{p}$$\end{document}-norm based method and the state-of-the-art classification methods.