Structured Joint Sparse Discriminative Dictionary Learning for Image Classification

In order to improve the image classification performance of dictionary learning, this article develops a structured joint sparse discriminative dictionary learning (SJSDDL). In contrast to the Fisher Discriminative Dictionary Learning (FDDL), we propose introducing an additional low-rank shared subspace in the original dictionary and conducting the joint sparse coding for dictionary coefficients. Overall, the introduced low-rank atoms are beneficial for alleviating the entanglement relationship in similar samples from different classes, which facilitates the coefficient discrimination term to distinguish the data categories. Extraordinarily, by imposing the joint constraints of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{2,0^{-}}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_1$</tex>-norms on the coefficients, the resulting joint sparse coding allows the associated dictionary subspaces to overlap partially, thereby constructing the class-specific sub-dictionaries with appropriate dimensions. The structured sparse coding and the flexible dictionary construction strategy endow the proposed method with better discriminability. The utilized optimization techniques involve the FISTA for sparse coding and the ADMM for dictionary update. The improved classification performance of SJSDDL is illustrated by the experimental results on widely used image datasets.