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arXiv · 2205.08115

Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Data

Jiajin Li·Jianheng Tang·Lemin Kong·Huikang Liu·Jia Li·Anthony Man-Cho So·Jose Blanchet
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Abstract

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound condition~\citep{luo1992error}, two proposed algorithms, called Bregman Alternating Projected Gradient (BAPG) and hybrid Bregman Proximal Gradient (hBPG) enjoy the convergence guarantees. Upon task-specific properties, our analysis further provides novel theoretical insights to guide how to select the best-fit method. As a result, we are able to provide comprehensive experiments to validate the effectiveness of our methods on a host of tasks, including graph alignment, graph partition, and shape matching. In terms of both wall-clock time and modeling performance, the proposed methods achieve state-of-the-art results.

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Jiajin Li, Jianheng Tang, Lemin Kong, Huikang Liu, Jia Li, Anthony Man-Cho So, Jose Blanchet. 2022-05-17. Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Data. https://arxiv.org/abs/2205.08115

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