Learned Collaborative Representations for Image Classification

The collaborative representation-based classifier (CRC) is proposed as an alternative to the sparse representation based classifier (SRC) for image face recognition. CRC solves an l2-regularized least squares formulation, with algebraic solution, while SRC optimizes over an I1-regularized least squares problem. As an extension of CRC, the weighted collaborative representation-based classifier (WCRC) is further proposed. The weights in WCRC are picked intuitively, it remains unclear why such choice of weights works and how we optimize those weights. In this paper, we propose a learned collaborative representation based classifier (LCRC) and attempt to answer the above questions. Our learning technique is based on the fixed point theorem and we use a weights formulation similar to WCRC as the starting point. Through extensive experiments on face datasets we show that the learning procedure is stable and convergent, and that LCRC is able to improve in performance over CRC and WCRC, while keeping the same computational efficiency at test.