Outlier-Robust Gromov-Wasserstein for Graph Data

TL;DR

This paper introduces RGW, a robust version of Gromov-Wasserstein distance that reduces sensitivity to outliers in graph data, with an efficient algorithm and validated effectiveness on real-world tasks.

Contribution

We propose RGW, a novel outlier-robust Gromov-Wasserstein distance, along with a provably efficient optimization algorithm for improved graph data comparison.

Findings

RGW outperforms standard GW in outlier scenarios.

The proposed algorithm is computationally efficient and theoretically sound.

Experimental results show improved accuracy on graph matching tasks.

Abstract

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient and theoretically provable procedure using Bregman proximal alternating linearized minimization algorithm. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.