Neighbor Embeddings Using Unbalanced Optimal Transport Metrics
This work addresses the need for better metrics in machine learning pipelines for tasks like classification and clustering, particularly in medical imaging domains, but it is incremental as it builds on existing optimal transport methods.
The paper tackles the problem of dimensionality reduction and learning by proposing the Hellinger-Kantorovich metric from unbalanced optimal transport (UOT), showing that UOT improves over Euclidean and regular OT methods on benchmark datasets like MedMNIST, with UOT outperforming OT in classification 81% of the time and in clustering 83% of the time.
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.