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.
@cite_4: 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.
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 .