Sparse, collaborative, or nonnegative representation: Which helps pattern classification?. (April 2019) - Xu, Jun; An, Wangpeng; Zhang, Lei; Zhang, David
Highlights: We investigate the use of Nonnegative Representation (NR) for pattern classification. The idea is that given a query sample y, it should be the nonnegative coefficients over the homogeneous samples (i.e., samples from the same class with y ) that determine the class label of y . Constraining the coding coefficients to be nonnegative can automatically boost the representation power of homogeneous samples while limiting the representation power of heterogeneous samples, making the representation sparse while discriminative. We propose a simple yet effective NR based Classifier (NRC) for pattern classification. The proposed NR model can be reformulated as a linear equalityconstrained problem with two variables, and solved under the alternating direction method of multipliers framework. Each variable can be solved efficiently in closed-form, and the convergence to the global optimum can be guaranteed. Extensive experiments on various visual classification datasets were performed to validate the performance of the proposed NR based classifier (NRC), and the results demonstrated that NRC is very efficient and effective, outperforming the previous representation based classifiers. Besides, with deep features as inputs, NRC also achieves state-of-the-art performance on various visual classification tasks. Abstract: The use of sparse representation (SR) and collaborative representation (CR) for pattern classification has been widely studied in tasks such as face recognition and object categorization. Despite the success of SR/CR based classifiers, it is still arguable whether it is the ℓ1 -norm sparsity or the ℓ2 -norm collaborative property that brings the success of SR/CR based classification. In this paper, we investigate the use of nonnegative representation (NR) for pattern classification, which is largely ignored by previous work. Our analyses reveal that NR can boost the representation power of homogeneous samples while limiting the representation power of heterogeneous samples, making the representation sparse and discriminative simultaneously and thus providing a more effective solution to representation based classification than SR/CR. Our experiments demonstrate that the proposed NR based classifier (NRC) outperforms previous representation based classifiers. With deep features as inputs, it also achieves state-of-the-art performance on various visual classification tasks.