Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference
2020-06-22 | preprint
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- Authors
- Weitkamp, Christoph Alexander; Proksch, Katharina; Tameling, Carla; Munk, Axel
- Abstract
- In this paper, we aim to provide a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently computable asymptotic statistical test for pose invariant object discrimination. This is based on an empirical version of a $\betaehBtrimmed lower bound of the Gromov-Wasserstein distance. We derive for $\beta\in[0,1/2)$ distributional limits of this test statistic. To this end, we introduce a novel ehBtype process indexed in $\beta$ and show its weak convergence. Finally, the theory developed is investigated in Monte Carlo simulations and applied to structural protein comparisons.
- Issue Date
- 22-June-2020
- Project
- EXC 2067: Multiscale Bioimaging
- Working Group
- RG Munk