Structured Matching via Cost-Regularized Unbalanced Optimal Transport

• URL: http://arxiv.org/abs/2511.19075v1
• Date: Mon, 24 Nov 2025 13:11:27 GMT
• Title: Structured Matching via Cost-Regularized Unbalanced Optimal Transport
• Authors: Emanuele Pardini, Katerina Papagiannouli,
• Abstract summary: Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures.<n>We introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal.
• Score: 0.8594140167290097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov-Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov-Wasserstein type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures or point clouds across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches.

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