Adaptive and Weighted Collaborative Representations for image classification

Recently, Zhang et al. (2011) proposed a classifier based on Collaborative Representations (CR) with Regularized Least Squares (CRC-RLS) for image face recognition. CRC-RLS can replace Sparse Representation (SR) based Classification (SRC) as a simple and fast alternative. With SR resulting from an l(1)-Regularized Least Squares decomposition, CR starts from an l(2)-Regularized Least Squares formulation. Moreover, it has an algebraic solution. We extend CRC-RLS to the case where the samples or features are weighted. Particularly, we consider weights based on the classification confidence for samples and the variance of feature channels. The Weighted Collaborative Representation Classifier (WCRC) improves the classification performance over that of the original formulation, while keeping the simplicity and the speed of the original CRC-RLS formulation. Moreover we investigate into query-adaptive WCRC formulations and kernelized extensions that show further performance improvements but come at the expense of increased computation time. (C) 2013 Elsevier B. V. All rights reserved.