A Simple Way to Learn Metrics Between Attributed Graphs

TL;DR

This paper introduces SGML, a new graph metric learning model using simple graph convolutional networks and optimal transport, enabling efficient and effective distance learning for attributed graphs to enhance classification tasks.

Contribution

The paper proposes SGML, a novel, lightweight graph metric learning method combining SGCN and optimal transport, addressing the challenge of learning distances between attributed graphs.

Findings

SGML can be trained quickly with good classification performance.

The learned graph distances improve k-NN classification accuracy.

Experimental results demonstrate SGML's efficiency and effectiveness.

Abstract

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to improve performance of classification or clustering methods. However, due to difficulties in establishing computable, efficient and differentiable distances between attributed graphs, few metric learning algorithms adapted to graphs have been developed despite the strong interest of the community. In this paper, we address this issue by proposing a new Simple Graph Metric Learning - SGML - model with few trainable parameters based on Simple Graph Convolutional Neural Networks - SGCN - and elements of Optimal Transport theory. This model allows us to build an appropriate distance from a database of labeled (attributed) graphs to improve the performance of simple classification algorithms such as $k$-NN. This distance can be quickly trained while maintaining good performances as illustrated by the experimental study presented in this paper.