The Gromov-Wasserstein distance between spheres
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914867111264256 |
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| author | Arya, Shreya Auddy, Arnab Edmonds, Ranthony Lim, Sunhyuk Memoli, Facundo Packer, Daniel |
| author_facet | Arya, Shreya Auddy, Arnab Edmonds, Ranthony Lim, Sunhyuk Memoli, Facundo Packer, Daniel |
| contents | In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we determine the exact value of the distance dGW4,2 between all pairs of unit spheres of different dimension endowed with their Euclidean distance and their uniform measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10586 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gromov-Wasserstein distance between spheres Arya, Shreya Auddy, Arnab Edmonds, Ranthony Lim, Sunhyuk Memoli, Facundo Packer, Daniel Metric Geometry Optimization and Control In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we determine the exact value of the distance dGW4,2 between all pairs of unit spheres of different dimension endowed with their Euclidean distance and their uniform measure. |
| title | The Gromov-Wasserstein distance between spheres |
| topic | Metric Geometry Optimization and Control |
| url | https://arxiv.org/abs/2306.10586 |