Efficient Fisher Discrimination Dictionary Learning

Fisher Determination Dictionary Learning (FDDL) has shown to be effective in image classification. However, the Original FDDL (O-FDDL) method is time-consuming. To address this issue, a fast Simplified FDDL (S-FDDL) method was proposed. But S-FDDL ignores the role of collaborative reconstruction, thus having an unstable performance in classification tasks with unbalanced changes in different classes. This paper focuses on developing an Efficient FDDL (E-FDDL) method, which is more suitable for such classification problems. Precisely, instead of solving the original Fisher Discrimination based Sparse Representation (FDSR) problem, we propose to solve an Approximate FDSR (A-FDSR) problem whose objective function is an upper bound of that of FDSR. A-FDSR considers the role of both the discriminative reconstruction and the collaborative reconstruction. This makes E-FDDL stable when dealing with classification tasks with unbalanced changes in different classes. Furthermore, fast optimization strategies are applicable to A-FDSR, thus leading to the high efficiency of E-FDDL which can be explained by analysis on convergence rate and computational complexity. We also use E-FDDL to accelerate the Shared Domain-adapted Dictionary Learning (SDDL) algorithm which is a FDDL based new method for domain adaptation. Experimental results on face and object recognition demonstrate the stable and fast performance of E-FDDL.