1. A face recognition method on a computing device, comprising: storing a plurality of training face images, each training face image corresponding to a face class, each face class including one or more training face images; obtaining one or more face test samples; applying a representation model to represent the face test sample as a combination of the training face images and error terms, wherein a coefficient vector is corresponded to the training face images; estimating the coefficient vector and the error terms by solving a constrained optimization problem; computing a residual error for each face class, the residual error for a face class being an error between the face test sample and the face test sample's representation model represented by the training samples in the face class; classifying the face test sample by selecting the face class that yields the minimal residual error; and presenting the face class of the face test sample.