Neighbor Embeddings Using Unbalanced Optimal Transport Metrics

2025/09/23 by Muhammad Rana, Rana, Muhammad, Keaton Hamm +1
Computer Science · Engineering · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Text and Document Classification Technologies #Traffic Prediction and Management Techniques

paper · pdf · doi:10.48550/arxiv.2509.19226

openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Manifold learning: what, how, and why
• Hellinger-Kantorovich barycenter between Dirac measures
• Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning
• The Linearized Hellinger--Kantorovich Distance
• Heuristic Framework for Multi-Scale Testing of the Multi-Manifold Hypothesis
• Invariant Scattering Convolution Networks
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Diffusion maps

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