SERAPH: Semi-supervised Metric Learning Paradigm with Hyper Sparsity

We consider the problem of learning a distance metric from a limited amount of pairwise information as effectively as possible. The proposed SERAPH (SEmi-supervised metRic leArning Paradigm with Hyper sparsity) is a direct and substantially more natural approach for semi-supervised metric learning, since the supervised and unsupervised parts are based on a unified information theoretic framework. Unlike other extensions, the unsupervised part of SERAPH can extract further pairwise information from the unlabeled data according to temporary results of the supervised part, and therefore interacts with the supervised part positively. SERAPH involves both the sparsity of posterior distributions over the unobserved weak labels and the sparsity of the induced projection matrices, which we call the hyper sparsity. The resulting optimization is solved by an EM-like scheme, where the M-Step is convex, and the E-Step has analytical solution. Experimental results show that SERAPH compares favorably with existing metric learning algorithms based on weak labels.