TY - UNPB
T1 - Gromov-Wasserstein Distance based Object Matching
T2 - Asymptotic Inference
AU - Weitkamp, Christoph Alexander
AU - Proksch, Katharina
AU - Tameling, Carla
AU - Munk, Axel
N1 - For a version with the complete supplement see [v2]
PY - 2020/6/22
Y1 - 2020/6/22
N2 - 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.
AB - 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.
KW - math.ST
KW - stat.TH
KW - 62E20, 62G20, 65C60 (Primary) 60E05 (Secondary)
M3 - Working paper
BT - Gromov-Wasserstein Distance based Object Matching
PB - ArXiv.org
ER -