Sobolev Transport

Sobolev transport (ST) is a novel approach to optimal transport (OT) designed to overcome the computational limitations of traditional OT methods, particularly when dealing with probability measures on graph structures. Current research focuses on extending ST to handle unbalanced measures (where the total mass of the compared distributions differs) and generalizing it beyond the standard L^p geometric framework to incorporate more flexible Orlicz structures. This leads to faster computation and the creation of negative definite kernels suitable for kernel methods, demonstrating its utility in applications like document classification and topological data analysis.