论文标题
基于Gromov-Wasserstein的基于距离的对象匹配：渐近推理
Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference
论文作者
论文摘要
在本文中，我们旨在为基于Gromov-Wasserstein距离的对象匹配提供统计理论。为此，我们将一般对象建模为公制测量空间。基于此，我们提出了一个简单，有效地计算的渐近统计检验，以实现姿势不变对象歧视。这是基于Gromov-Wasserstein距离的$β$ Trimmed下限的经验版本。我们在[0,1/2）中以$β\得出此测试统计量的分布限制。为此，我们引入了一个新颖的$ u $ type过程，该过程以$β$索引，并显示其较弱的收敛性。最后，在蒙特卡洛模拟中研究了这一理论，并应用于结构蛋白质比较。
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 $β\in[0,1/2)$ 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.
