Double-constrained structured discriminant analysis-synthesis dictionary pair learning for pattern classification.

Existing discriminant analysis-synthesis dictionary pair learning (ASDPL) methods learn a structured analysis dictionary containing multiple class-specific analysis sub-dictionaries and a structured synthesis dictionary containing multiple class-specific synthesis sub-dictionaries. Although existing discriminant ASDPL methods achieve promising results in the field of pattern classification, most of them ignore the correlation between an analysis sub-dictionary and a synthesis sub-dictionary that belong to different classes, which may degrade the discriminative ability of their learned dictionary pairs. Moreover, most existing discriminant ASDPL methods do not give an explicit constraint to ensure that the reconstruction error of training samples under the joint action of a structured analysis dictionary and a structured synthesis dictionary is as small as possible, leading to insufficient representational ability of their learned dictionary pairs. To address these issues, we present a double-constrained structured discriminant analysis-synthesis dictionary pair learning (DCSDDPL) method. Specifically, we first design a class-specific analysis-synthesis sub-dictionary pair reconstruction constraint term to ensure that the reconstruction error of training samples of a class is as small as possible under the joint action of the analysis and synthesis sub-dictionaries belonging to the same class, which helps to improve the representational ability of the learned dictionary pair. Then, we design an analysis-synthesis sub-dictionary pair independence constraint term to eliminate the correlation between an analysis sub-dictionary and a synthesis sub-dictionary belonging to different classes so as to ensure the discriminative ability of the learned dictionary pair. Finally, we formulate the DCSDDPL model by integrating the two constraint terms into the basic discriminant analysis-synthesis dictionary pair learning model. Moreover, we design an optimization algorithm and use it to obtain the solution of the DCSDDPL model. We experimentally compare our method with five state-of-the-art dictionary learning methods, D-KSVD, LC-KSVD, FDDPL, DASDL and RA-DPL on the Extended Yale B, AR, PIE, CLD 22, Scene 15 and Caltech 101 datasets. The highest classification accuracy achieved by our method on these datasets is 99.13% and the highest F1-Score is 0.9906. The experimental results confirm that our method is effective for pattern classification. [ABSTRACT FROM AUTHOR]