Learning Graphons via Structured Gromov-Wasserstein Barycenters

12/10/2020
by   Hongteng Xu, et al.
0

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.

READ FULL TEXT
research
05/26/2022

Efficient Approximation of Gromov-Wasserstein Distance using Importance Sparsification

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) dist...
research
07/08/2020

Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks

Wasserstein Barycenter is a principled approach to represent the weighte...
research
10/04/2019

Fused Gromov-Wasserstein Alignment for Hawkes Processes

We propose a novel fused Gromov-Wasserstein alignment method to jointly ...
research
04/26/2020

Improved Image Wasserstein Attacks and Defenses

Robustness against image perturbations bounded by a ℓ_p ball have been w...
research
05/30/2022

Hilbert Curve Projection Distance for Distribution Comparison

Distribution comparison plays a central role in many machine learning ta...
research
05/29/2021

Learning Graphon Autoencoders for Generative Graph Modeling

Graphon is a nonparametric model that generates graphs with arbitrary si...
research
05/10/2021

Robust Graph Learning Under Wasserstein Uncertainty

Graphs are playing a crucial role in different fields since they are pow...

Please sign up or login with your details

Forgot password? Click here to reset