Density-Reweighted Entropic Optimal Transport: Decoupling Geometry from Sampling Density

2026-08-17

AI Summary

This study addresses the issue where Entropic Optimal Transport (EOT) yields alignments deviating from true geometric structures under significant sampling density disparities. To overcome this, we propose a density-reweighted EOT framework that employs adjustable weights to effectively decouple geometric structure from sampling density effects, with theoretical proof of population-level convergence for the reweighted transport plan. Experiments demonstrate that the proposed algorithm successfully recovers faithful geometric correspondences in density-heterogeneous scenarios, significantly outperforming existing EOT methods. These results establish a reliable theoretical and algorithmic foundation for purely geometry-driven data alignment, ensuring robustness against variations in sampling density while preserving intrinsic geometric relationships.

Abstract

Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.

Problem

• Dataset Alignment
• Entropic Optimal Transport
• Sampling Density
• Geometric Correspondence

Innovation

• Density-Reweighted Entropic Optimal Transport
• Geometry-Density Decoupling
• Dataset Alignment
• Sampling Density Disparity
• Population-Level Convergence