Linearized optimal transport on manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910473382789120 |
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| author | Sarrazin, Clément Schmitzer, Bernhard |
| author_facet | Sarrazin, Clément Schmitzer, Bernhard |
| contents | Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This in turn leads to a reduction of computational complexity and simplifies combination with other methods that require a linear structure. Recently this approach has been extended to the unbalanced Hellinger--Kantorovich (HK) distance. In this article we further extend the framework in various ways, including measures on manifolds, the spherical HK distance, a study of the consistency of discretization via the barycentric projection, and the continuity properties of the logarithmic map for the HK distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13901 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linearized optimal transport on manifolds Sarrazin, Clément Schmitzer, Bernhard Optimization and Control Functional Analysis Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This in turn leads to a reduction of computational complexity and simplifies combination with other methods that require a linear structure. Recently this approach has been extended to the unbalanced Hellinger--Kantorovich (HK) distance. In this article we further extend the framework in various ways, including measures on manifolds, the spherical HK distance, a study of the consistency of discretization via the barycentric projection, and the continuity properties of the logarithmic map for the HK distance. |
| title | Linearized optimal transport on manifolds |
| topic | Optimization and Control Functional Analysis |
| url | https://arxiv.org/abs/2303.13901 |