| Autor: |
Giraldo, Jhony H., Einizade, Aref, Todorovic, Andjela, Castro-Correa, Jhon A., Badiey, Mohsen, Bouwmans, Thierry, Malliaros, Fragkiskos D. |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
IEEE Transactions on Signal and Information Processing over Networks, 2024 |
| Druh dokumentu: |
Working Paper |
| Popis: |
Graph Neural Networks (GNNs) have shown great promise in modeling relationships between nodes in a graph, but capturing higher-order relationships remains a challenge for large-scale networks. Previous studies have primarily attempted to utilize the information from higher-order neighbors in the graph, involving the incorporation of powers of the shift operator, such as the graph Laplacian or adjacency matrix. This approach comes with a trade-off in terms of increased computational and memory demands. Relying on graph spectral theory, we make a fundamental observation: the regular and the Hadamard power of the Laplacian matrix behave similarly in the spectrum. This observation has significant implications for capturing higher-order information in GNNs for various tasks such as node classification and semi-supervised learning. Consequently, we propose a novel graph convolutional operator based on the sparse Sobolev norm of graph signals. Our approach, known as Sparse Sobolev GNN (S2-GNN), employs Hadamard products between matrices to maintain the sparsity level in graph representations. S2-GNN utilizes a cascade of filters with increasing Hadamard powers to generate a diverse set of functions. We theoretically analyze the stability of S2-GNN to show the robustness of the model against possible graph perturbations. We also conduct a comprehensive evaluation of S2-GNN across various graph mining, semi-supervised node classification, and computer vision tasks. In particular use cases, our algorithm demonstrates competitive performance compared to state-of-the-art GNNs in terms of performance and running time. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
