A fast algorithm for Earth Mover's Distance based on optimal transport and L1 type Regularization
This work provides a faster approximation for Earth Mover's Distance, which is a computationally expensive metric used in various fields like computer vision and machine learning.
The authors propose a fast algorithm for approximating the Earth Mover's Distance by reformulating it as an L1-type minimization with regularization, enabling the use of efficient primal-dual methods from compressed sensing. Numerical examples demonstrate rapid convergence.
We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar $L_1$ type minimization. We use a regularization which gives us a unique solution for this $L_1$ type problem. The new regularized minimization is very similar to problems which have been solved in the fields of compressed sensing and image processing, where several fast methods are available. In this paper, we adopt a primal-dual algorithm designed there, which uses very simple updates at each iteration and is shown to converge very rapidly. Several numerical examples are provided.