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The projective dictionary pair learning (DPL) model jointly seeks a synthesis dictionary and an analysis dictionary by extracting the block-diagonal coefficients with an incoherence-constrained analysis dictionary. However, DPL fails to discover the underlying subspaces and salient features at the same time, and it cannot encode the neighborhood information of the embedded coding coefficients, especially adaptively. In addition, although the data can be well reconstructed via the minimization of the reconstruction error, useful distinguishing salient feature information may be lost and incorporated into the noise term. In this article, we propose a novel self-expressive adaptive locality-preserving framework: twin-incoherent self-expressive latent DPL (SLatDPL). To capture the salient features from the samples, SLatDPL minimizes a latent reconstruction error by integrating the coefficient learning and salient feature extraction into a unified model, which can also be used to simultaneously discover the underlying subspaces and salient features. To make the coefficients block diagonal and ensure that the salient features are discriminative, our SLatDPL regularizes them by imposing a twin-incoherence constraint. Moreover, SLatDPL utilizes a self-expressive adaptive weighting strategy that uses normalized block-diagonal coefficients to preserve the locality of the codes and salient features. SLatDPL can use the class-specific reconstruction residual to handle new data directly. Extensive simulations on several public databases demonstrate the satisfactory performance of our SLatDPL compared with related methods. [ABSTRACT FROM AUTHOR]

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 l2,1-norm-based metric to encode the reconstruction error to deliver the robust projective dictionary pairs, and the l2,1-norm has the potential to minimize the error. Second, it imposes the robust l2,1-norm clearly on the analysis dictionary to ensure the sparse property of the coding coefficients rather than using the costly l0/l1-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. [ABSTRACT FROM AUTHOR]