Discriminative Local Sparse Representation by Robust Adaptive Dictionary Pair Learning

In this article, we propose a structured robust adaptive dictionary pair learning (RA-DPL) framework for the discriminative sparse representation (SR) learning. To achieve powerful representation ability of the available samples, the setting of RA-DPL seamlessly integrates the robust projective DPL, locality-adaptive SRs, and discriminative coding coefficients learning into a unified learning framework. Specifically, RA-DPL improves existing projective DPL in four perspectives. First, it applies a sparse <inline-formula> <tex-math notation="LaTeX">$l_{2,1}$ </tex-math></inline-formula>-norm-based metric to encode the reconstruction error to deliver the robust projective dictionary pairs, and the <inline-formula> <tex-math notation="LaTeX">$l_{2,1}$ </tex-math></inline-formula>-norm has the potential to minimize the error. Second, it imposes the robust <inline-formula> <tex-math notation="LaTeX">$l_{2,1}$ </tex-math></inline-formula>-norm clearly on the analysis dictionary to ensure the sparse property of the coding coefficients rather than using the costly <inline-formula> <tex-math notation="LaTeX">$l_{0}/l_{1}$ </tex-math></inline-formula>-norm. As such, the robustness of the data representation and the efficiency of the learning process are jointly considered to guarantee the efficacy of our RA-DPL. Third, RA-DPL conceives a structured reconstruction weight learning paradigm to preserve the local structures of the coding coefficients within each class clearly in an adaptive manner, which encourages to produce the locality preserving representations. Fourth, it also considers improving the discriminating ability of coding coefficients and dictionary by incorporating a discriminating function, which can ensure high intraclass compactness and interclass separation in the code space. Extensive experiments show that our RA-DPL can obtain superior performance over other state of the arts.