Affine non-negative collaborative representation based pattern classification

During the past decade, representation-based classification methods have received considerable attention in pattern recognition. In particular, the recently proposed non-negative representation based classification (NRC) method has been reported to achieve promising results in a wide range of classification tasks. However, NRC has two major drawbacks. First, there is no regularization term in the formulation of NRC, which may result in unstable solution and misclassification. Second, NRC ignores the fact that data usually lies in a union of multiple affine subspaces, rather than linear subspaces in practical applications. To address the above issues, this paper presents an affine non-negative collaborative representation (ANCR) model for pattern classification. To be more specific, ANCR imposes a regularization term on the coding vector. Moreover, since each point in an affine subspace can be expressed as an affine combination of other points in this affine subspace, ANCR introduces an affine constraint to better represent the data from affine subspaces. The experimental results on several benchmarking datasets demonstrate the merits of the proposed ANCR method. Concretely, on the Hopkins and Aircraft datasets, ANCR achieves accuracy of 97.8% and 87.7%, respectively, which represents an improvement of 2.2% and 0.4% over NRC. The source code of our ANCR is publicly available at https://github.com/yinhefeng/ANCR.