Graph Classification via Heat Diffusion on Simplicial Complexes

TL;DR

This paper introduces a novel method for graph classification that leverages heat diffusion on higher-dimensional simplices, capturing complex topological features to improve classification accuracy in bioinformatics networks.

Contribution

It is the first to apply heat diffusion on simplices for graph mining, enhancing the encoding of higher-order structures in graph classification tasks.

Findings

Diffusion Fréchet function effectively encodes higher-order topology.

Method outperforms baseline approaches on bioinformatics networks.

Potential for extension to other graph mining domains.

Abstract

In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent vertex-labeled graphs as simplex-weighted super-graphs. We then define the diffusion Frechet function over their simplices to encode the higher-order network topology and finally reach our goal by combining the function values with machine learning algorithms. Our experiments on real-world bioinformatics networks show that using diffusion Fr{\'e}chet function on simplices is promising in graph classification and more effective than the baseline methods. To the best of our knowledge, this paper is the first paper in the literature using heat diffusion on higher-dimensional simplices in a graph mining problem. We believe that our method can be extended to different graph mining domains, not only the graph classification problem.