Dictionary learning methods can be split into two categories: i) class specific dictionary learning ii) class shared dictionary learning. The difference between the two categories is how to use the discriminative information. With the first category, samples of different classes are mapped to different subspaces which leads to some redundancy in the base vectors. For the second category, the samples in each specific class can not be described well. Moreover, most class shared dictionary learning methods use the L0-norm regularization term as the sparse constraint. In this paper, we first propose a novel class shared dictionary learning method named label embedded dictionary learning (LEDL) by introducing the L1-norm sparse constraint to replace the conventional L0-norm regularization term in LC-KSVD method. Then we propose a novel network named hybrid dictionary learning network (HDLN) to combine the class specific dictionary learning with class shared dictionary learning together to fully describe the feature to boost the performance of classification. Extensive experimental results on six benchmark datasets illustrate that our methods are capable of achieving superior performance compared to several conventional classification algorithms.
Liu @cite_4 proposed CSDL-SRC to reduce the high residual error and instability of SRC. The authors consider the weight of each sample feature when generating the dictionary. Assume that is the training sample matrix, where @math represents the dimensions of the sample features, and are the number of training samples and the class number of training samples, respectively. The class of training sample matrix is denoted as , where and is the class of (). Liu build a weight coefficient matrix for , where is the dictionary size of CSDL-SRC and is the class of (). The objective function of CSDL-SRC is as follows: where is the sparse codes of , the -norm regularization term is utilized to enforce the sparsity, is the regularization parameter to control the tradeoff between fitting goodness and sparseness. The denote the column vector of matrix .
@cite_4
2324335215 2110383222 1996838598 1977580401
Recently, sparse representation based classification (SRC) and collaborative representation based classification (CRC) have been successfully used for visual recognition and have demonstrated impressive performance. Given a test sample, SRC or CRC formulates its linear representation with respect to the training samples and then computes the residual error for each class. SRC or CRC assumes that the training samples from each class contribute equally to the dictionary in the corresponding class, i.e., the dictionary consists of the training samples in that class. This, however, leads to high residual error and instability. To overcome this limitation, we propose a class specific dictionary learning algorithm. To be specific, by introducing the dual form of dictionary learning, an explicit relationship between the basis vectors and the original image features is represented, which also enhances the interpretability. SRC or CRC can be thus considered as a special case of the proposed algorithm. Blockwise coordinate descent algorithm and Lagrange multipliers are then adopted to optimize the corresponding objective function. Extensive experimental results on five benchmark face recognition datasets show that the proposed algorithm achieves superior performance compared with conventional classification algorithms. HighlightsA novel class specific dictionary learning (CSDL) approach is proposed, where the standard collaborative representation based classification (CRC) or sparse representation based classification (SRC) can be considered as its special cases.The dual form of dictionary learning is proposed to enhance the interpretability.Our proposed CSDL achieves superior face recognition performance on several benchmark datasets. We propose to detect abnormal events via a sparse reconstruction over the normal bases. Given a collection of normal training examples, e.g., an image sequence or a collection of local spatio-temporal patches, we propose the sparse reconstruction cost (SRC) over the normal dictionary to measure the normalness of the testing sample. By introducing the prior weight of each basis during sparse reconstruction, the proposed SRC is more robust compared to other outlier detection criteria. To condense the over-completed normal bases into a compact dictionary, a novel dictionary selection method with group sparsity constraint is designed, which can be solved by standard convex optimization. Observing that the group sparsity also implies a low rank structure, we reformulate the problem using matrix decomposition, which can handle large scale training samples by reducing the memory requirement at each iteration from O(k^2) to O(k) where k is the number of samples. We use the columnwise coordinate descent to solve the matrix decomposition represented formulation, which empirically leads to a similar solution to the group sparsity formulation. By designing different types of spatio-temporal basis, our method can detect both local and global abnormal events. Meanwhile, as it does not rely on object detection and tracking, it can be applied to crowded video scenes. By updating the dictionary incrementally, our method can be easily extended to online event detection. Experiments on three benchmark datasets and the comparison to the state-of-the-art methods validate the advantages of our method. This paper proposes a graph regularized low-rank sparse representation recovery (GLRSRR) method for sparse representation-based robust face recognition, in which both the training and test samples might be corrupted because of illumination variations, pose changes, and occlusions. On the one hand, GLRSRR imposes both the lowest-rank and sparsest constraints on the representation matrix of the training samples, which makes the recovered clean training samples discriminative while maintaining the global structure of data. Simultaneously, GLRSRR explicitly encodes the local structure information of data and the discriminative information of different classes by incorporating a graph regularization term, which further improves the discriminative ability of the recovered clean training samples for sparse representation. As a result, a test sample is compactly represented by more clean training samples from the correct class. On the other hand, since the error matrix obtained by GLRSRR can accurately and intuitively characterize the corruption and occlusion of face image, it can be used as occlusion dictionary for sparse representation. This will bring more accurate representations of the corrupted test samples. The experimental results on several benchmark face image databases manifest the effectiveness and robustness of GLRSRR. A graph regularized low-rank sparse representation recovery method is proposed.The recovered clean training samples have more discriminative ability.The obtained errors can accurately depict corruption and occlusion of face image.A corrupted test sample is encoded by more training samples from the correct class.Our method improves the performance of sparse representation-base classification. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.