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.
 The traditional data uncertainty (DU) classifier fails to encode the importance of each sample for solving the minimum problem. Moreover, it considers only linear information for classification. To overcome these, we propose four classifiers for action recognition. They are called regularized DU (RDU) classifier, RDU coefficient (RDUC) classifier, kernel RDU (KRDU) classifier, and kernel RDUC (KRDUC) classifier, respectively. Extensive experiments on four benchmark action databases demonstrate that the proposed four classifiers achieve better recognition rates than the traditional DU classifier and several state-of-the-art methods. Moreover, the computation costs of the KRDU and KRDUC classifiers are much less than that of the DU classifier. Motivated by the idea that the correlation structure of the entire training set can disclose the relationship between the test sample and the training samples, we propose the combined sparse representation (CSR) classifier for disease recognition. The CSR classifier minimizes the correlation structure of the entire training set multiplied by its transposition and the sparse coefficient together for classification. Including the kernel concept, we propose the kernel combined sparse representation classifier utilizing the high-dimensional nonlinear information instead of the linear information in the CSR classifier. Furthermore, considering the information of the training samples and the class center, we then propose the center-based kernel combined sparse representation (CKCSR) classifier. CKCSR uses the center-based kernel matrix to increase the center-based information that is helpful for classification. The proposed classifiers have been evaluated by extensive experiments on several well-known databases including the EXACT09 database, Emphysema-CT database, mini-MIAS database, Wisconsin breast cancer database, and HD-PECTF database. The experimental results demonstrate that the proposed classifiers achieve better recognition rates than the sparse representation-based classification, collaborative representation based classification, and several state-of-the-art methods.  Using the @math -norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, called the trace Lasso, uses the trace norm, which is a convex surrogate of the rank, of the selected covariates as the criterion of model complexity. We analyze the properties of our norm, describe an optimization algorithm based on reweighted least-squares, and illustrate the behavior of this norm on synthetic data, showing that it is more adapted to strong correlations than competing methods such as the elastic net. Recent research has shown the effectiveness of using sparse coding(Sc) to solve many computer vision problems. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which may reduce the feature quantization error and boost the sparse coding performance, we propose Kernel Sparse Representation(KSR). KSR is essentially the sparse coding technique in a high dimensional feature space mapped by implicit mapping function. We apply KSR to both image classification and face recognition. By incorporating KSR into Spatial Pyramid Matching(SPM), we propose KSRSPM for image classification. KSRSPM can further reduce the information loss in feature quantization step compared with Spatial Pyramid Matching using Sparse Coding(ScSPM). KSRSPM can be both regarded as the generalization of Efficient Match Kernel(EMK) and an extension of ScSPM. Compared with sparse coding, KSR can learn more discriminative sparse codes for face recognition. Extensive experimental results show that KSR outperforms sparse coding and EMK, and achieves state-of-the-art performance for image classification and face recognition on publicly available datasets. In this paper, we propose a two-phase test sample representation method for face recognition. The first phase of the proposed method seeks to represent the test sample as a linear combination of all the training samples and exploits the representation ability of each training sample to determine M “nearest neighbors” for the test sample. The second phase represents the test sample as a linear combination of the determined M nearest neighbors and uses the representation result to perform classification. We propose this method with the following assumption: the test sample and its some neighbors are probably from the same class. Thus, we use the first phase to detect the training samples that are far from the test sample and assume that these samples have no effects on the ultimate classification decision. This is helpful to accurately classify the test sample. We will also show the probability explanation of the proposed method. A number of face recognition experiments show that our method performs very well. 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.