2020/06/22 by Christoph Alexander Weitkamp, Katharina Proksch, Weitkamp, Christoph Alexander +5
Computer Science · Mathematics · #62E20 #62G20 #65C60 (Primary) 60E05 (Secondary) #FOS: Mathematics #Point processes and geometric inequalities #Statistical Methods and Inference #Statistics Theory (math.ST) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2006.12287
openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.