Joint Metric Space Embedding by Unbalanced Optimal Transport with Gromov-Wasserstein Marginal Penalization

This paper proposes the use of the Hellinger-Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of regular OT and Euclidean-based dimensionality reduction methods on several benchmark datasets including MedMNIST. The experimental results demonstrate that, on average, UOT shows improvement over both Euclidean and OT-based methods as verified by statistical hypothesis tests. In particular, on the MedMNIST datasets, UOT outperforms OT in classification 81% of the time. For clustering MedMNIST, UOT outperforms OT 83% of the time and outperforms both other metrics 58% of the time.