A Multi-scale Graph Signature for Persistence Diagrams based on Return Probabilities of Random Walks

TL;DR

This paper introduces a multi-scale graph signature based on return probabilities of random walks to improve the robustness of persistence diagrams for graph classification, leveraging deep learning for set inputs.

Contribution

It proposes a novel multi-scale graph signature and a deep learning architecture to enhance topological feature robustness in graph analysis.

Findings

Outperforms other persistent homology-based methods on benchmark datasets.

Achieves competitive results with state-of-the-art graph neural networks.

Scales well to large graphs without scalability issues.

Abstract

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely on a single graph signature to construct PDs. In this paper, we explore the use of a family of multi-scale graph signatures to enhance the robustness of topological features. We propose a deep learning architecture to handle this set input. Experiments on benchmark graph classification datasets demonstrate that our proposed architecture outperforms other persistent homology-based methods and achieves competitive performance compared to state-of-the-art methods using graph neural networks. In addition, our approach can be easily applied to large size of input graphs as it does not suffer from limited scalability which can be an issue for graph kernel methods.