Neighbor Embeddings Using Unbalanced Optimal Transport Metrics

2025-09-23

AI Summary

To address class imbalance and inadequate manifold structure modeling in high-dimensional medical imaging data, this paper proposes the Hellinger–Kantorovich (HK) metric based on unbalanced optimal transport (UOT), establishing a unified framework for dimensionality reduction and supervised/unsupervised learning. Unlike Euclidean distance or balanced optimal transport (OT), the HK metric explicitly accounts for mass non-conservation, yielding greater robustness in characterizing heterogeneous sample distributions. Comprehensive evaluation on benchmarks including MedMNIST demonstrates that our method significantly outperforms standard OT in classification—achieving superior performance in 81% of experimental settings—and surpasses both Euclidean distance and OT baselines in clustering across 58% of scenarios. The core contribution lies in the first integration of the HK metric into manifold learning pipelines, thereby introducing a representation learning paradigm for imbalanced medical data that jointly ensures geometric fidelity and statistical robustness.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Proposing unbalanced optimal transport metrics for dimensionality reduction tasks
• Comparing UOT performance against Euclidean and regular OT methods
• Evaluating UOT effectiveness on medical imaging datasets like MedMNIST

Innovation

• Uses Hellinger-Kantorovich metric from unbalanced optimal transport
• Applies UOT for dimensionality reduction and learning tasks
• Outperforms regular OT and Euclidean methods on MedMNIST