On a linear fused Gromov-Wasserstein distance for graph structured data

TL;DR

This paper introduces linearFGW, a new graph distance that embeds graphs into a vector space considering node features and topology, enabling faster and scalable graph similarity measurements for classification and clustering.

Contribution

The paper proposes linearFGW, a novel Euclidean-based graph distance that incorporates node features and structure, offering computational efficiency over traditional OT-based methods.

Findings

linearFGW effectively captures graph similarity in classification tasks

It significantly reduces computation time compared to fused Gromov-Wasserstein

Experimental results demonstrate its effectiveness on large-scale graph datasets

Abstract

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named linearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it can take into account node feature and structure of graphs for measuring the similarity between graphs in a kernel-based framework, 2) it can be much faster for computing kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein, making it possible to deal with large-scale data sets. After discussing theoretical properties of linearFGW, we demonstrate experimental results on classification and clustering tasks, showing the effectiveness of the proposed linearFGW.