Recently, quaternion collaborative representation-based classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color channels. However, their performance is unstable in different conditions. For example, QSRC performs better than than QCRC on some situations but worse on other situations. To benefit from quaternion-based @math -norm minimization in QCRC and quaternion-based @math -norm minimization in QSRC, we propose the quaternion-based adaptive representation (QAR) that uses a quaternion-based @math -norm minimization ( @math ) for color face recognition. To obtain the high dimension correlation information among different color channels, we further propose the high-dimension quaternion-based adaptive representation (HD-QAR). The experimental results demonstrate that the proposed QAR and HD-QAR achieve better recognition rates than QCRC, QSRC and several state-of-the-art methods.
proposed sparse representation classification (SRC) in 2009. It represents the testing sample by the linear combination of training samples of all classes. SRC solves @math -minimization optimization problem as To reduce the computation cost and obtain the better representation, proposed the collaborative representation based classification (CRC). In CRC, the authors argued that the collaborative representation should be better than the linear combination of training samples. CRC solves the @math -minimization optimization problem as They are two typical sparse-based methods. A lot modifications of SRC CRC have been proposed for various visual recognition tasks @cite_2 @cite_15 @cite_0 @cite_7 @cite_3 . For example, denoted that the nonlinear high dimensional features are useful for sparse representation, and then proposed kernel-based sparse representation classification (KSRC) @cite_23 @cite_6 , proposed kernel-based collaborative representation classification (KCRC) @cite_38 , which is described as denoted that quaternion can help sparse representation to obtain the correlation information among different color channels. Then, they proposed quaternion sparse representation classification (QSRC) and quaternion collaborative representation based classification (QCRC). QSRC is described as QCRC is described as
@cite_38 @cite_7 @cite_3 @cite_6 @cite_0 @cite_23 @cite_2 @cite_15
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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. Sparse representation has attracted great attention in the past few years. Sparse representation based classification (SRC) algorithm was developed and successfully used for classification. In this paper, a kernel sparse representation based classification (KSRC) algorithm is proposed. Samples are mapped into a high dimensional feature space first and then SRC is performed in this new feature space by utilizing kernel trick. Since samples in the high dimensional feature space are unknown, we cannot perform KSRC directly. In order to overcome this difficulty, we give the method to solve the problem of sparse representation in the high dimensional feature space. If an appropriate kernel is selected, in the high dimensional feature space, a test sample is probably represented as the linear combination of training samples of the same class more accurately. Therefore, KSRC has more powerful classification ability than SRC. Experiments of face recognition, palmprint recognition and finger-knuckle-print recognition demonstrate the effectiveness of KSRC. 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. 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.