Sparse metric learning via smooth optimization

Abstract

In this paper we study the problem of learning a low-rank (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle representation, we develop an efficient smooth optimization approach [15] for sparse metric learning, although the learning model is based on a non-differentiable loss function. This smooth optimization approach has an optimal convergence rate of O(1=t2) for smooth problems where t is the iteration number. Finally, we run experiments to validate the effectiveness and efficiency of our sparse metric learning model on various datasets.