### Coupling Matrix Manifolds and Their Applications in Optimal Transport. (arXiv:1911.06905v1 [cs.LG])

Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded as the transportation plan of the OT problem. We firstly explore the Riemannian geometry of CMM with…