COPT: Coordinated Optimal Transport on Graphs Supplementary Material Supplement Outline

In this supplement, we give full proofs of Lemmas 3.1 and 3.2, further discuss COPT optimizations We give full proofs to Lemma 3.1, an analytic formula for the COPT metric, and Lemma 3.2, the Combining these, we get exactly the stated formula. Symmetry is easiest to check using Lemma 3.1 and the fact that the trace of the square root of a Finally, we check the triangle inequality. Here we elaborate further on COPT's optimization routine. As the objective Equation 3.1 is not globally convex, gradient descent can fall into local minima. This is repeated 20 times.