Topological Relational Learning on Graphs
- URL: http://arxiv.org/abs/2110.15529v1
- Date: Fri, 29 Oct 2021 04:03:27 GMT
- Title: Topological Relational Learning on Graphs
- Authors: Yuzhou Chen, Baris Coskunuzer, Yulia R. Gel
- Abstract summary: Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning.
We propose a novel topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs.
We show that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations.
- Score: 2.4692806302088868
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Graph neural networks (GNNs) have emerged as a powerful tool for graph
classification and representation learning. However, GNNs tend to suffer from
over-smoothing problems and are vulnerable to graph perturbations. To address
these challenges, we propose a novel topological neural framework of
topological relational inference (TRI) which allows for integrating
higher-order graph information to GNNs and for systematically learning a local
graph structure. The key idea is to rewire the original graph by using the
persistent homology of the small neighborhoods of nodes and then to incorporate
the extracted topological summaries as the side information into the local
algorithm. As a result, the new framework enables us to harness both the
conventional information on the graph structure and information on the graph
higher order topological properties. We derive theoretical stability guarantees
for the new local topological representation and discuss their implications on
the graph algebraic connectivity. The experimental results on node
classification tasks demonstrate that the new TRI-GNN outperforms all 14
state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to
perturbations, yielding up to 10\% better performance under noisy scenarios.
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