CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphs

Davide Buffelli, Farzin Soleymani, Bastian Rieck

Keywords: Graph Neural Networks, Persistent Homology, Graph Machine Learning

Abstract: Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes beyond pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to 31% improvements in test accuracy.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 15