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arXiv · 2511.19075

Structured Matching via Cost-Regularized Unbalanced Optimal Transport

Emanuele Pardini·Katerina Papagiannouli
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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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Emanuele Pardini, Katerina Papagiannouli. 2025-11-24. Structured Matching via Cost-Regularized Unbalanced Optimal Transport. https://arxiv.org/abs/2511.19075

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