Structured Matching via Cost-Regularized Unbalanced Optimal Transport
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914240845053952 |
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| author | Pardini, Emanuele Papagiannouli, Katerina |
| author_facet | Pardini, Emanuele Papagiannouli, Katerina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured Matching via Cost-Regularized Unbalanced Optimal Transport Pardini, Emanuele Papagiannouli, Katerina Machine Learning Applications 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. |
| title | Structured Matching via Cost-Regularized Unbalanced Optimal Transport |
| topic | Machine Learning Applications |
| url | https://arxiv.org/abs/2511.19075 |