Sparse representation (or coding)-based classification (SRC) has gained great success in face recognition in recent years. However, SRC emphasizes the sparsity too much and overlooks the correlation information which has been demonstrated to be critical in real-world face recognition problems. Besides, some paper considers the correlation but overlooks the discriminative ability of sparsity. Different from these existing techniques, in this paper, we propose a framework called adaptive sparse representation-based classification (ASRC) in which sparsity and correlation are jointly considered. Specifically, when the samples are of low correlation, ASRC selects the most discriminative samples for representation, like SRC; when the training samples are highly correlated, ASRC selects most of the correlated and discriminative samples for representation, rather than choosing some related samples randomly. In general, the representation model is adaptive to the correlation structure that benefits from both l 1 -norm and l 2 -norm. Extensive experiments conducted on publicly available data sets verify the effectiveness and robustness of the proposed algorithm by comparing it with the state-of-the-art methods.
Some works have focused on the above problem and provided several solutions. @cite_41 proposed locality constraints in spatial sparse representation. @cite_27 maximized the intra-individual correlations to address the pose difference for face recognition. imposed the @math -norm constraint on the coefficients and proposed CRC (Collaborative Representation based Classification with regularized least square). In @cite_18 , Zhang pointed out that the success of SRC comes from the collaborative representation of @math over all training samples. The @math -norm is supposed to take advantage of data correlation @cite_25 . Thus, the query image @math is represented by the over-complete dictionary with @math -norm rather than @math -norm to constrain the coding vector in CRC. The objective function is defined as: The @math -minimization guarantees that CRC gets a stable result with a much denser representation vector. However, CRC does not perform sample selection for representation. It may not perform well when the training data are not highly correlated.
@cite_41 @cite_27 @cite_18 @cite_25
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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. Sparse representation based classification (SRC) has received much attention in computer vision and pattern recognition. SRC codes a testing sample by sparse linear combination of all the training samples and classifies the testing sample into the class with the minimum representation error. Recently, Zhang analyzes the working mechanism of SRC and points out that it is the collaborative representation but not the L1-norm sparsity that makes SRC powerful. Based on the analysis, they propose a very simple and much more efficient classification scheme, called collaborative representation based classification with regularized least square (CRC_RLS). CRC_RLS is a linear method in nature. Here we propose a kernel collaborative representation based classification with regularized least square (Kernel CRC_RLS, KCRC_RLS) by implicitly mapping the sample into high-dimensional space via kernel tricks. Our approach is highly motivated by the kernel methods which can capture the nonlinear similarity among samples and have been successfully applied in pattern recognition and machine learning. The experimental results on the CENPAMI handwritten digital database, ETH80 database, FERET face database, ORL database, AR face database, demonstrate that Kernel CRC_RLS is effective in classification, leading to promising performance. Applications of sparse signal representation in image processing and pattern recognition have attracted a great deal of attention. Sparse representation based classification (SRC) methods emphasizes on sparse representation computed by l"1-minimization to exploit the underlying sparsity in the problem domain, and argued the importance of sparse representation that improved the discrimination to achieve robust and accurate classification results. Recently, many studies have shown the role of collaborative representation (CR) in SRC, which actually improved the classification accuracy. In this paper, we proposed a novel collaborative neighbor representation method for multi-class classification based on l"2-minimization approach with the assumption of locally linear embedding (LLE). The proposed method represents a test sample over the dictionary by automatically choosing optimal nearest basis spanned in the same linear subspace as of test sample. The proposed representation method achieves competitive classification accuracy via optimal neighbor representation having discriminative learning power. Extensive experiments on real-world face and digit databases are performed to analyze the performance of the proposed method against SRC methods. Result clearly shows that the proposed method achieves competitive results for face recognition and pattern classification, and is significantly much faster and comparably accurate than SRC based classification methods. As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l 1 -norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.