SERAPH: Semi-supervised Metric Learning Paradigm with Hyper Sparsity

We propose a novel semi-supervised metric learning method from weak labels (i.e., partial pairwise similarity/dissimilarity). Our proposed method SERAPH explicitly models unlabeled data as related pairs rather than individual points, which allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Furthermore, SERAPH is equipped with the hyper-sparsity: the sparsity of posterior distributions over unobserved weak labels and the sparsity of induced projection matrices. Thanks to the hyper-sparsity, the metric learned by SERAPH possesses high discriminability even under a noisy environment. The optimization problem involved in SERAPH can be solved efficiently and stably by an EM-like scheme, where the E-Step is analytical and the M-Step is convex and smooth. Experiments show that SERAPH compares favorably with standard metric learning methods in terms of either accuracy or speed.