Sparse coding and dictionary learning with class-specific group sparsity

In recent years, sparse coding via dictionary learning has been widely used in many applications for exploiting sparsity patterns of data. For classification, useful sparsity patterns should have discrimination, which cannot be well achieved by standard sparse coding techniques. In this paper, we investigate structured sparse coding for obtaining discriminative class-specific group sparsity patterns in the context of classification. A structured dictionary learning approach for sparse coding is proposed by considering the ℓ2,0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,0}$$\end{document} norm on each class of data. An efficient numerical algorithm with global convergence is developed for solving the related challenging ℓ2,0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,0}$$\end{document} minimization problem. The learned dictionary is decomposed into class-specific dictionaries for the classification that is done according to the minimum reconstruction error among all the classes. For evaluation, the proposed method was applied to classifying both the synthetic data and real-world data. The experiments show the competitive performance of the proposed method in comparison with several existing discriminative sparse coding methods.