线性Gromov-Wasserstein距离的多边缘逼近
Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance
摘要：
最近，最优输运理论的两个概念已被成功地带到Gromov-Wasserstein（GW）设置。这引入了GW距离和多边缘GW传输的线性版本。前者在计算大量输入的所有GW距离时可以降低计算复杂性。后者允许同时匹配两个以上的边缘，这可以例如用于计算GW重心。本文的目的是显示一个近似的结果，其特征在于作为一个限制的多边缘GW制定的线性版本。
英文摘要：
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.
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