Learning low-rank and discriminative dictionary for image classification

• Learn a discriminative dictionary with low-rank regularization
• Fisher discriminant function is applied to the coding coefficients.
• IPM and ALM algorithms are adopted to solve our objective function.

Dictionary learning plays a crucial role in sparse representation based image classification. In this paper, we propose a novel approach to learn a discriminative dictionary with low-rank regularization on the dictionary. Specifically, we apply Fisher discriminant function to the coding coefficients to make the dictionary more discerning, that is, a small ratio of the within-class scatter to between-class scatter. In practice, noisy information in the training samples will undermine the discriminative ability of the dictionary. Inspired by the recent advances in low-rank matrix recovery theory, we apply low-rank regularization on the dictionary to tackle this problem. The iterative projection method (IPM) and inexact augmented Lagrange multiplier (ALM) algorithm are adopted to solve our objective function. The proposed discriminative dictionary learning with low-rank regularization (D2L2R2) approach is evaluated on four face and digit image datasets in comparison with existing representative dictionary learning and classification algorithms. The experimental results demonstrate the superiority of our approach.