Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference

Christoph Alexander Weitkamp, Katharina Proksch, Carla Tameling, Axel Munk

Research output: Working paper

6 Downloads (Pure)

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 $\beta$-trimmed 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 $U$-type 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.
Original languageEnglish
PublisherarXiv.org
Publication statusPublished - 22 Jun 2020

Keywords

  • math.ST
  • stat.TH
  • 62E20, 62G20, 65C60 (Primary) 60E05 (Secondary)

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