Discriminative low-rank graph preserving dictionary learning with Schatten-p quasi-norm regularization for image recognition

The dictionary used in sparse coding plays a key role in sparse representation-based classification. A desired dictionary should have powerful representational and discriminative capability. In this paper, we propose a discriminative low-rank graph preserving dictionary learning (DLRGP_DL) method to learn a discriminative structured dictionary for sparse representation-based image recognition, in which training samples might be corrupted with relatively large noise. Specifically, we impose the Schatten-p quasi-norm regularization on sub-dictionaries to make them to be of low-rank, which can effectively reduce the negative effect of noise contained in training samples and make the learned dictionary pure and compact. To improve the discriminative capability of the learned dictionary, we apply a discriminative graph preserving criterion to coding coefficients during the dictionary learning process with the goal that the similar training samples from the same class have similar coding coefficients. The learned dictionary is first used for sparse coding, and then both the learned coding coefficients of training samples and the class-specific reconstruction errors are used for classification. The experimental results on four image datasets demonstrate the effectiveness and robustness of DLRGP_DL.