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Sparse representation-based classification (SRC) and collaborative representation-based classification (CRC) have shown promising classification results. Both methods are distance-based classifiers, and they represent a test sample with coefficients solved by different sparsity regularizations. The reason why the representation coefficient vector can be sparse is that the test sample can be represented by only a small subset of the whole dictionary, which means that only a few entries of the coefficient vector have nonzero values. Previous studies show that sparsity of representation coefficients of SRC and CRC is significant for achieving good classification performance. However, the parameter of the algorithm is closely associated with the sparsity and it is very hard to obtain the optimal parameter value. In this paper, we propose two novel versions of SRC and CRC and implement four algorithms. The first version has two implementation named SQ_SRC and SQ_CRC, which use squared value of each entry of the representation coefficient vector to enhance sparsity of representation coefficients. SQ_SRC and SQ_CRC allow us to obtain more robust representation and classification performance of the test sample. The second version has another two implementation named SQF_SRC and SQF_CRC, which integrate original SRC and CRC with the SQ_SRC and SQ_CRC to perform classification. We conduct extensive experiments on a number of facial datasets, as well as a couple of non-facial datasets. The experimental results demonstrated that our methods output much more promising classification results than naive SRC and CRC in most scenarios.
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