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Scaling algorithms for unbalanced optimal transport problems
Open accessAbstract
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for many applications to be able to compute some sort of relaxed transportation between arbitrary positive measures. A generic class of such “unbalanced” optimal transport problems has been recently proposed by several authors. In this paper, we show how to extend the now classical entropic regularization scheme to these unbalanced problems. This gives rise to fast, highly parallelizable algorithms that operate by performing only diagonal scaling (i.e., pointwise multiplications) of the transportation couplings. They are generalizations of the celebrated Sinkhorn algorithm. We show how these methods can be used to solve unbalanced transport, unbalanced gradient flows, and to compute unbalanced barycenters. We showcase applications to 2-D shape modification, color transfer, and growth models.
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Cites
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Cited by
Schiebinger, G., Shu, J., Tabaka, M., Cleary, B., Subramanian, V., Solomon, A., Gould, J., Liu, S., Lin, S., Berube, P., et al. (2019) · Cell · doi:10.1016/j.cell.2019.01.006 · Cited by 829
Screening cell–cell communication in spatial transcriptomics via collective optimal transport
(2023) · doi:10.1038/s41592-022-01728-4 · Cited by 484
Statistical and machine learning methods for spatially resolved transcriptomics data analysis
Zeng, Z., Li, Y., Li, Y., & Luo, Y. (2022) · Genome Biology · doi:10.1186/s13059-022-02653-7 · Cited by 186
Shekhar, K., Whitney, I. E., Butrus, S., Peng, Y.-R., & Sanes, J. R. (2022) · eLife · doi:10.7554/elife.73809 · Cited by 68
Optimal transport for single-cell and spatial omics
Bunne, C., Schiebinger, G., Krause, A., Regev, A., & Cuturi, M. (2024) · Nature Reviews Methods Primers · doi:10.1038/s43586-024-00334-2 · Cited by 71
Metadata
- Authors
- Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F.-X.
- Venue
- Mathematics of Computation
- Publisher
- American Mathematical Society (AMS)
- Published
- 2018-02-06
- Volume
- 87
- Issue
- 314
- Pages
- 2563-2609
- ISSN
- 0025-5718 (ISSN-L)
- 1088-6842
- OpenAlex
- W2724892359
- Cited by
- 336
- References
- 52
- FWCI
- 27.48
- Type
- journal article
- Language
- en
- Open access
- bronze
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