A tree-structured discriminative dictionary learning for classification

Abstract

This paper proposes a dictionary learning algorithm in which the atoms of the dictionary have a tree-structured hierarchy such that atoms of the parent node are tunned in representing patterns common across images belonging to all classes that the atoms of its child nodes are tunned to represent. Thus, the atoms at the root are tunned to represent patterns common to all images, while the atoms at the leaves are tunned to represent image patterns exclusive to a class. An image feature is assumed to be represented by atoms in the dictionary along a unique path from the root to a leaf. The learned dictionary is efficient in its use of the atoms, and leads to a more discriminative representation than that led by previous dictionaries which is devoid of any structure and contains redundant atoms : previously proposed dictionaries are a collection of independently constructed class dictionaries. The dictionary is learned by solving a constraint optimization problem that minimizes the reconstruction error of a given set of images while using the atoms along a particular path from the root to the leaf exclusive to each class. For a given "tree-structured dictionary", sparse representation is pursued to improve generalization. The proposed algorithm is extensively evaluated on benchmark image dataatoms in comparison with existing sparse representation and DL based classification methods.