This paper addresses the problem of face recognition when there is only few,or even only a single, labeled examples of the face that we wish to recognize.Moreover, these examples are typically corrupted by nuisance variables, bothlinear (i.e., additive nuisance variables such as bad lighting, wearing ofglasses) and non-linear (i.e., non-additive pixel-wise nuisance variables suchas expression changes). The small number of labeled examples means that it ishard to remove these nuisance variables between the training and testing facesto obtain good recognition performance. To address the problem we propose amethod called Semi-Supervised Sparse Representation based Classification(S$^3$RC). This is based on recent work on sparsity where faces are representedin terms of two dictionaries: a gallery dictionary consisting of one or moreexamples of each person, and a variation dictionary representing linearnuisance variables (e.g., different lighting conditions, different glasses).The main idea is that (i) we use the variation dictionary to characterize thelinear nuisance variables via the sparsity framework, then (ii) prototype faceimages are estimated as a gallery dictionary via a Gaussian Mixture Model(GMM), with mixed labeled and unlabeled samples in a semi-supervised manner, todeal with the non-linear nuisance variations between labeled and unlabeledsamples. We have done experiments with insufficient labeled samples, even whenthere is only a single labeled sample per person. Our results on the AR,Multi-PIE, CAS-PEAL, and LFW databases demonstrate that the proposed method isable to deliver significantly improved performance over existing methods.
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