Adaptive and Weighted Collaborative Representations for image classification

• We propose the Weighted Collaborative Representation based Classifier (WCRC) and its variants.
• Weighting independently of the query keeps the complexity and improves over CRC.
• Weighting adaptive to the query can improve the performance, but increases the computation.
• We investigate kernel extensions.
• We validate on faces, handwritten digits, and traffic signs datasets.

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 l1l1-Regularized Least Squares decomposition, CR starts from an l2l2-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.