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

Davide Buffelli, Farzin Soleymani, Bastian Rieck
Proceedings of the Third Learning on Graphs Conference, PMLR 269:45:1-45:17, 2025.

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 \textdollar O(n\^{}d)\textdollar , where \textdollar n\textdollar is the number of nodes and \textdollar d\textdollar 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v269-buffelli25a, title = {CliquePH: Higher-Order Information for Graph Neural Networks Through Persistent Homology on Clique Graphs}, author = {Buffelli, Davide and Soleymani, Farzin and Rieck, Bastian}, booktitle = {Proceedings of the Third Learning on Graphs Conference}, pages = {45:1--45:17}, year = {2025}, editor = {Wolf, Guy and Krishnaswamy, Smita}, volume = {269}, series = {Proceedings of Machine Learning Research}, month = {26--29 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v269/main/assets/buffelli25a/buffelli25a.pdf}, url = {https://proceedings.mlr.press/v269/buffelli25a.html}, 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 \textdollar O(n\^{}d)\textdollar , where \textdollar n\textdollar is the number of nodes and \textdollar d\textdollar 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.} }
Endnote
%0 Conference Paper %T CliquePH: Higher-Order Information for Graph Neural Networks Through Persistent Homology on Clique Graphs %A Davide Buffelli %A Farzin Soleymani %A Bastian Rieck %B Proceedings of the Third Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2025 %E Guy Wolf %E Smita Krishnaswamy %F pmlr-v269-buffelli25a %I PMLR %P 45:1--45:17 %U https://proceedings.mlr.press/v269/buffelli25a.html %V 269 %X 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 \textdollar O(n\^{}d)\textdollar , where \textdollar n\textdollar is the number of nodes and \textdollar d\textdollar 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.
APA
Buffelli, D., Soleymani, F. & Rieck, B.. (2025). CliquePH: Higher-Order Information for Graph Neural Networks Through Persistent Homology on Clique Graphs. Proceedings of the Third Learning on Graphs Conference, in Proceedings of Machine Learning Research 269:45:1-45:17 Available from https://proceedings.mlr.press/v269/buffelli25a.html.

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