Mining discriminative components with low-rank and sparsity constraints for face recognition

This paper introduces a novel image decomposition approach for an ensemble of correlated images, using low-rank and sparsity constraints. Each image is decomposed as a combination of three components: one common component, one condition component, which is assumed to be a low-rank matrix, and a sparse residual. For a set of face images of Nsubjects, the decomposition finds N common components, one for each subject, K low-rank components, each capturing a different global condition of the set (e.g., different illumination conditions), and a sparse residual for each input image. Through this decomposition, the proposed approach recovers a clean face image (the common component) for each subject and discovers the conditions (the condition components and the sparse residuals) of the images in the set. The set of N+K images containing only the common and the low-rank components form a compact and discriminative representation for the original images. We design a classifier using only these N+K images. Experiments on commonly-used face data sets demonstrate the effectiveness of the approach for face recognition through comparing with the leading state-of-the-art in the literature. The experiments further show good accuracy in classifying the condition of an input image, suggesting that the components from the proposed decomposition indeed capture physically meaningful features of the input.