Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference

06/22/2020

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by   Christoph Alexander Weitkamp, et al.

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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 β-trimmed lower bound of the Gromov-Wasserstein distance. We derive for β∈[0,1/2) distributional limits of this test statistic. To this end, we introduce a novel U-type process indexed in β and show its weak convergence. Finally, the theory developed is investigated in Monte Carlo simulations and applied to structural protein comparisons.