Fast Algorithms for Earth Mover Distance Based on Optimal Transport and L1 Regularization Ii

We modify a fast algorithm which we designed in [15] for computing the Earth mover’s distance (EMD), whose cost is a Manhattan metric. From the theory of optimal transport, the EMD problem can be reformulated as a familiar L1 minimization. We use a regularization which gives us a unique solution for this non strictly convex L1 problem. We adopt a primal-dual algorithm for the regularized problem, which uses very simple updates at each iteration and converges very rapidly. Several numerical examples are presented.