Sparsity embedding projections for sparse representation-based classification

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.