A General Neural Network Architecture for Persistence Diagrams and Graph Classification

Mathieu Carriere (1) , Frédéric Chazal (2) , Yuichi Ike (3) , Théo Lacombe (2) , Martin Royer (2) , Yuhei Umeda (3)

1 Columbia University [New York]
2 DATASHAPE - Understanding the Shape of Data
3 Fujitsu Laboratories Ltd.

Graph classification is a difficult problem that has drawn a lot of attention from the machine learning community over the past few years. This is mainly due to the fact that, contrarily to Euclidean vectors, the inherent complexity of graph structures can be quite hard to encode and handle for traditional classifiers. Even though kernels have been proposed in the literature, the increase in the dataset sizes has greatly limited the use of kernel methods since computation and storage of kernel matrices has become impracticable. In this article, we propose to use extended persistence diagrams to efficiently encode graph structure. More precisely, we show that using the so-called heat kernel signatures for the computation of these extended persistence diagrams allows one to quickly and efficiently summarize the graph structure. Then, we build on the recent development of neural networks for point clouds to define an architecture for (extended) persistence diagrams which is modular and easy-to-use. Finally, we demonstrate the usefulness of our approach by validating our architecture on several graph datasets, on which the obtained results are comparable to the state-of-the-art for graph classification.

Domaines: Géométrie algorithmique [cs.CG]; Intelligence artificielle [cs.AI]; Machine Learning [stat.ML]

Mathieu Carriere, Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer, et al.. A General Neural Network Architecture for Persistence Diagrams and Graph Classification. 2019. ⟨hal-02105788⟩