A Wasserstein Graph Distance Based on Distributions of Probabilistic Node Embeddings

TL;DR

This paper introduces a novel graph distance measure based on Wasserstein distance between Gaussian mixture models fitted to node embedding distributions, enabling interpretable and efficient graph comparisons.

Contribution

It proposes an unsupervised, optimal transport-based graph distance using Gaussian mixture models of node embeddings, with computational improvements and empirical validation.

Findings

Effective on synthetic and real-world data

Outperforms existing embedding methods

Provides interpretable graph comparisons

Abstract

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive representations of graphs as Gaussian mixture models, fitted to distributions of sampled node embeddings over the same space. The Wasserstein distance between these Gaussian mixture distributions then yields an interpretable and easily computable distance measure, which can further be tailored for the comparison at hand by choosing appropriate embeddings. We propose two embeddings for this framework and show that under certain assumptions about the shape of the resulting Gaussian mixture components, further computational improvements of this Wasserstein distance can be achieved. An empirical validation of our findings on synthetic data and real-world Functional Brain Connectivity networks shows promising performance compared to existing embedding methods.