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arXiv · 2306.10586

The Gromov-Wasserstein distance between spheres

Shreya Arya·Arnab Auddy·Ranthony Edmonds·Sunhyuk Lim·Facundo Memoli·Daniel Packer
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Abstract

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.

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Shreya Arya, Arnab Auddy, Ranthony Edmonds, Sunhyuk Lim, Facundo Memoli, Daniel Packer. 2023-06-18. The Gromov-Wasserstein distance between spheres. https://arxiv.org/abs/2306.10586

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