Linearized optimal transport on manifolds
2023 | preprint. A publication with affiliation to the University of Göttingen.
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- Authors
- Sarrazin, Clément; Schmitzer, Bernhard
- Abstract
- 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.
- Issue Date
- 2023
- Project
- SFB 1456 | Cluster A | A03: Dimensionality reduction and regression in Wasserstein space for quantitative 3D histology
SFB 1456 | Cluster A: Data with Geometric Nonlinearities
SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften