Collaboratively Regularized Nearest Points for Set Based Recognition

Set based recognition (i.e, using a set of instances together for recognition) has been attracting more and more attention in recent years, benefitting from two facts: the difficulty of collecting sets of images for recognition fades quickly, and set based recognition models generally outperform the ones for single instance based recognition. In the past few years various approaches have been proposed, which were reviewed in [4] and [7]. In this paper, we propose a novel model called collaboratively regularized nearest points (CRNP) which inherits the merits of simplicity, robustness, and high-efficiency from the very recently introduced regularized nearest points (RNP) method [7] on finding the set-to-set distance using the l2-norm regularized affine hulls. Meanwhile, CRNP makes use of the powerful discriminative ability induced by collaborative representation, following the same idea as that in sparse recognition for classification (SRC) for image-based recognition [3] and collaborative sparse approximation (CSA) for set-based recognition [5]. However, CRNP uses l2-norm instead of the expensive l1-norm for coefficients regularization, which makes it much more efficient. Given the test/query set Q and all the training/gallery sets Xi, i ∈ {1, . . . ,n}, CRNP solves the following optimization problem: