Deep discriminative dictionary pair learning for image classification

Discriminative dictionary learning has been extensively used for pattern classification tasks. By incorporating different kinds of label information into the dictionary learning framework, a dictionary can be attained that represents the original signal with discriminative reconstruction. The previous works learn the dictionary in the original space which limits the dictionary learning performance. In this paper, we propose an approach, namely Deep Discriminative Dictionary Pair Learning (D3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}PL) for image classification. The input of D3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}PL is not the matrix collected by original gray images or hand-crafted features but the relatively deeper features derived from autoencoders. Then, a structured dictionary is designed based on the discriminative contributions across different classes to reconstruct the deep feature. In addition, the associated structured projective dictionary is learned as well to guarantee the decoders updating towards the minimal error of deconvolution operator. By leveraging the discriminative-dictionary-learning-based loss function and the autoencoder loss function, D3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}PL can simultaneously learn the deep potential feature and the corresponding dictionary pair. In the testing phase of D3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}PL, the minimum error between the deep feature and the structured projective component with regard to different classes can directly indicate the label by a basic matrix multiplication operation. Experimental results on challenging Extended Yale B, AR, UMIST, COIL20, Scene 15, and Caltech101 datasets demonstrate that the proposed D3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}PL outperforms the prominent dictionary learning methods.