We propose a joint subspace recovery and enhanced locality based robust flexible label consistent dictionary learning method called Robust Flexible Discriminative Dictionary Learning (RFDDL). RFDDL mainly improves the data representation and classification abilities by enhancing the robust property to sparse errors and encoding the locality, reconstruction error and label consistency more accurately. First, for the robustness to noise and sparse errors in data and atoms, RFDDL aims at recovering the underlying clean data and clean atom subspaces jointly, and then performs DL and encodes the locality in the recovered subspaces. Second, to enable the data sampled from a nonlinear manifold to be handled potentially and obtain the accurate reconstruction by avoiding the overfitting, RFDDL minimizes the reconstruction error in a flexible manner. Third, to encode the label consistency accurately, RFDDL involves a discriminative flexible sparse code error to encourage the coefficients to be soft. Fourth, to encode the locality well, RFDDL defines the Laplacian matrix over recovered atoms, includes label information of atoms in terms of intra-class compactness and inter-class separation, and associates with group sparse codes and classifier to obtain the accurate discriminative locality-constrained coefficients and classifier. Extensive results on public databases show the effectiveness of our RFDDL. Index Terms -Robust flexible discriminative dictionary learning; joint subspace recovery; enhanced locality; classificationS ----------------

We propose a novel and unsupervised representation learning model, i.e., Robust Block-Diagonal Adaptive Locality-constrained Latent Representation (rBDLR). rBDLR is able to recover multisubspace structures and extract the adaptive locality-preserving salient features jointly. Leveraging on the Frobenius-norm based latent low-rank representation model, rBDLR jointly learns the coding coefficients and salient features, and improves the results by enhancing the robustness to outliers and errors in given data, preserving local information of salient features adaptively and ensuring the block-diagonal structures of the coefficients. To improve the robustness, we perform the latent representation and adaptive weighting in a recovered clean data space. To force the coefficients to be block-diagonal, we perform auto-weighting by minimizing the reconstruction error based on salient features, constrained using a block-diagonal regularizer. This ensures that a strict block-diagonal weight matrix can be obtained and salient features will possess the adaptive locality preserving ability. By minimizing the difference between the coefficient and weights matrices, we can obtain a block-diagonal coefficients matrix and it can also propagate and exchange useful information between salient features and coefficients. Extensive results demonstrate the superiority of rBDLR over other state-of-the-art methods.

In this paper, we investigate the robust dictionary learning (DL) to discover the hybrid salient low-rank and sparse representation in a factorized compressed space. A Joint Robust Factorization and Projective Dictionary Learning (J-RFDL) model is presented. The setting of J-RFDL aims at improving the data representations by enhancing the robustness to outliers and noise in data, encoding the reconstruction error more accurately and obtaining hybrid salient coefficients with accurate reconstruction ability. Specifically, J-RFDL performs the robust representation by DL in a factorized compressed space to eliminate the negative effects of noise and outliers on the results, which can also make the DL process efficient. To make the encoding process robust to noise in data, J-RFDL clearly uses sparse L2, 1-norm that can potentially minimize the factorization and reconstruction errors jointly by forcing rows of the reconstruction errors to be zeros. To deliver salient coefficients with good structures to reconstruct given data well, J-RFDL imposes the joint low-rank and sparse constraints on the embedded coefficients with a synthesis dictionary. Based on the hybrid salient coefficients, we also extend J-RFDL for the joint classification and propose a discriminative J-RFDL model, which can improve the discriminating abilities of learnt coefficients by minimizing the classification error jointly. Extensive experiments on public datasets demonstrate that our formulations can deliver superior performance over other state-of-the-art methods. Index Terms-Hybrid salient representation, robust factorized compression, robust projective dictionary learning, classificationW ---------------- J. Ren is with the

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Low-rank coding-based representation learning is powerful for discovering and recovering the subspace structures in data, which has obtained an impressive performance; however, it still cannot obtain deep hidden information due to the essence of single-layer structures. In this article, we investigate the deep low-rank representation of images in a progressive way by presenting a novel strategy that can extend existing single-layer latent low-rank models into multiple layers. Technically, we propose a new progressive Deep Latent Low-Rank Fusion Network (DLRF-Net) to uncover deep features and the clustering structures embedded in latent subspaces. The basic idea of DLRF-Net is to progressively refine the principal and salient features in each layer from previous layers by fusing the clustering and projective subspaces, respectively, which can potentially learn more accurate features and subspaces. To obtain deep hidden information, DLRF-Net inputs shallow features from the last layer into subsequent layers. Then, it aims at recovering the hierarchical information and deeper features by respectively congregating the subspaces in each layer of the network. As such, one can also ensure the representation learning of deeper layers to remove the noise and discover the underlying clean subspaces, which will be verified by simulations. It is noteworthy that the framework of our DLRF-Net is general and is applicable to most existing latent low-rank representation models, i.e., existing latent low-rank models can be easily extended to the multilayer scenario using DLRF-Net. Extensive results on real databases show that our framework can deliver enhanced performance over other related techniques.