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Sparse representation-based classification (SRC) has become a powerful tool for image recognition. SRC sparsely encodes a test sample over all training samples and then classifies the test sample into the class that generates the minimal reconstruction residual. However, in many real-world applications, nuisances (e.g. illuminations, view directions, pixel corruptions, and occlusion, etc.) may make the representation coefficients of a test sample associated with the training samples from another class greatly larger than those associated with the training samples from the correct class. As a result, the reconstruction residual of the test sample with respect to the other class is smaller than that with respect to the correct class. This inevitably brings a wrong classification of SRC. To address this issue, we propose a sparsity embedding projections (SEP) method, which seeks a low-dimensional embedding subspace where the sparse representation coefficients of a test sample associated with the training samples from the correct class are enlarged, and simultaneously those associated with the training samples from all of the other classes are compressed. Specially, given a training data matrix, SEP tries to find a linear transformation by enhancing the intraclass reconstructive relationship meanwhile suppressing the interclass reconstructive relationship in the low-dimensional embedding subspace. Experimental results on the COIL-20, Extend Yale B, and AR databases show that the proposed method is more effective and robust than other state-of-the-art feature extraction methods with respect to SRC. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel Schatten p -norm-based two-dimensional principal component analysis (2DPCA) method, which is named after 2DPCA-Sp, for image feature extraction. Different from the conventional 2DPCA that is based on Frobenius-norm, 2DPCA-Sp learns an optimal projection matrix by maximizing the total scatter criterion based on Schatten p -norm in the low-dimensional feature space. Since p can take different values, 2DPCA-Sp is regarded as a general framework of 2DPCA. We also propose an iterative algorithm to solve the optimization problem of 2DPCA-Sp with 0 < p < 1 , which is simple, effective, and easy to implement. Experimental results on several popular image databases show that 2DPCA-Sp with 0 < p < 1 is robust to impact factors (e.g. illuminations, view directions, and expressions) of images. [ABSTRACT FROM AUTHOR]

A Schatten p -norm-based two-dimensional principal component analysis (2DPCA-SP) method was proposed for image feature extraction in our previous work. As an unsupervised method, 2DPCA-SP ignores the label information of training samples, which is essential to classification tasks. In this paper, we propose a novel Schatten p -norm-based two-dimensional discriminant analysis (2DDA-SP) method for image feature extraction, which learns an optimal projection matrix by maximizing the difference of Schatten p -norm-based between-class dispersion and Schatten p -norm-based within-class dispersion in low-dimensional feature space. By using both the Schatten p -norm metric and the label information of training samples, 2DDA-SP not only can efficiently extract discriminative features, but is also robust to outliers. We also propose an efficient iterative algorithm to solve the optimization problem of 2DDA-SP with 0 < p < 1 . Experimental results on several image databases show that 2DDA-SP with 0 < p < 1 is effective and robust for image feature extraction. [ABSTRACT FROM AUTHOR]