Intra- and Inter-Class Induced Discriminative Deep Dictionary Learning for Visual Recognition

Deep dictionary learning (DDL) aims to learn dictionaries at different levels and the deepest level representations. However, existing DDL algorithms impose a
$l_{1}$
-norm constraint on the deepest level representations, ignoring the constraints on different level representations. Meanwhile, they fail to discover effectively the essential discrimination information. Therefore, the obtained representations are less discriminative, which degrades model performance. To tackle those issues, we propose an intra- and inter-class induced discriminative deep dictionary learning (DDDL). Specifically, both intra-class compactness and inter-class separability of layer-wise data representations are newly devised as two discriminative constraints on deep dictionary learning. In a hierarchical structure, we obtain a more informative dictionary and the class-specific representations are thus more discriminative at each layer. Due to the
$l_{2}$
-norm intra- and inter-class constraints of layer-wise data representation, we devise a layer-wise optimization strategy to efficiently learn the closed-form solution of the deepest representation for classification. Comprehensive experiments and analyses on several visual recognition tasks show that our DDDL model surpasses recent shallow and deep representation learning approaches.