Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
Abstract
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem.
Keywords
Cite
@article{arxiv.1306.0895,
title = {Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances},
author = {Marco Cuturi},
journal= {arXiv preprint arXiv:1306.0895},
year = {2014}
}