Learning Graphons via Structured Gromov-Wasserstein Barycenters
This work provides a more robust and accurate method for learning graphons, which is important for researchers and practitioners working with graph modeling and analysis.
This paper introduces a new method to learn graphons, which are nonparametric models for graphs of arbitrary size. By approximating graphons with step functions and using Gromov-Wasserstein barycenters, the method overcomes limitations of prior approaches and achieves superior performance on both synthetic and real-world datasets.
We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs. Furthermore, we develop several enhancements and extensions of the basic algorithm, $e.g.$, the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. The code is available at https://github.com/HongtengXu/SGWB-Graphon.