A Multi-scale Graph Signature for Persistence Diagrams based on Return Probabilities of Random Walks
This work addresses the challenge of improving graph classification accuracy for researchers and practitioners in machine learning, though it is incremental as it builds on existing persistent homology methods.
The paper tackles the problem of enhancing the robustness of topological features in graph classification by using a family of multi-scale graph signatures to construct persistence diagrams, and it demonstrates that their proposed deep learning architecture outperforms other persistent homology-based methods and achieves competitive performance with state-of-the-art graph neural networks on benchmark datasets.
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.