Supervised Gromov-Wasserstein Optimal Transport with Metric-Preserving Constraints.

ABSTRACT: We introduce the supervised Gromov-Wasserstein (sGW) optimal transport, an extension of Gromov-Wasserstein that incorporates potential infinity entries in the cost tensor. These infinity entries enable sGW to enforce application-induced constraints on preserving pairwise distance to a certain extent. A numerical solver is proposed for the sGW problem and the effectiveness is demonstrated in various numerical experiments. The high-order constraints in sGW are transferred to constraints on the coupling matrix by solving a minimal vertex cover problem. The transformed problem is solved by the mirror-C descent iteration coupled with the supervised optimal transport solver. In the numerical experiments, we first validate the proposed framework by applying it to matching synthetic datasets and i

SUBMITTER: Cang Z 

PROVIDER: S-EPMC12395365 | biostudies-literature | 2025

REPOSITORIES: biostudies-literature