Structured analysis dictionary learning based on discriminative Fisher pair

In analysis dictionary learning (ADL) algorithms, the row vectors (profiles) of the analysis coefficient matrix and analysis atoms are always one-to-one correspondence, and the analysis information of atoms could be represented by their corresponding profiles. However, the analysis atoms and their corresponding profiles are seldom jointly explored to formulate a discrimination term. In this paper, we exploit the analysis atoms and profiles to design a structured discriminative ADL algorithm for image classification, called structured analysis dictionary learning based on discriminative Fisher pair (SADL-DFP). Specifically, we explicitly provide the definitions of the profile and the newly defined profile block, which are used to illustrate the analysis mechanism of the ADL model. Then, the discriminative Fisher pair (DFP) model is designed by using the Fisher criterion of analysis atoms and profiles, which can enhance the inter-class separability and intra-class compactness of the analysis atoms and profiles. Since the profiles and analysis atoms can be updated alternatively and interactively, our DFP model can further encourage the analysis atoms to analyze the same-class training samples as much as possible. In addition, a robust multiclass classifier is simultaneously learned by utilizing the label information of the training samples and analysis atoms in our SADL-DFP algorithm. The experimental results show that the proposed SADL-DFP algorithm can outperform many state-of-the-art dictionary learning algorithms on multiple datasets with both deep learning-based features and hand-crafted features.