GOT: An Optimal Transport framework for Graph comparison

TL;DR

This paper introduces a novel optimal transport-based framework for comparing graphs by leveraging graph signal distributions and the Wasserstein distance, enabling more meaningful global graph comparisons.

Contribution

The paper proposes a new graph comparison measure based on optimal transport and develops an efficient stochastic algorithm for graph alignment, outperforming existing methods.

Findings

Significant improvements in graph alignment accuracy.

Enhanced graph classification performance.

Effective graph signal prediction results.

Abstract

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an explicit expression of the Wasserstein distance between graph signal distributions in terms of the graph Laplacian matrices. This leads to a structurally meaningful measure for comparing graphs, which is able to take into account the global structure of graphs, while most other measures merely observe local changes independently. Our measure is then used for formulating a new graph alignment problem, whose objective is to estimate the permutation that minimizes the distance between two graphs. We further propose an efficient stochastic algorithm based on Bayesian exploration to accommodate for the non-convexity of the graph alignment problem. We finally demonstrate the performance of our novel framework on different tasks like graph alignment, graph classification and graph signal prediction, and we show that our method leads to significant improvement with respect to the-state-of-art algorithms.