论文标题
线性Gromov-Wasserstein距离的多界线近似
Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance
论文作者
论文摘要
最近，最佳运输理论的两个概念成功地被带到了Gromov-Wasserstein（GW）设置。这引入了GW距离和多核心GW传输的线性版本。当计算大量输入的所有GW距离时，前者可以降低计算复杂性。后者允许同时匹配两个以上的边缘，例如可以用于计算GW Barycenters。本文的目的是显示一个近似结果，该结果将线性版本描述为多界数GW公式的限制。
Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the computational complexity when computing all GW distances of a large set of inputs. The latter allows for a simultaneous matching of more than two marginals, which can for example be used to compute GW barycenters. The aim of this paper is to show an approximation result which characterizes the linear version as a limit of a multi-marginal GW formulation.
