Topological Relational Learning on Graphs
Topological Relational Learning on Graphs
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发表时间：
2021-10
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通讯作者：
Yuzhou Chen;Baris Coskunuzer;Y. Gel
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作者：
Yuzhou Chen;Baris Coskunuzer;Y. Gel
图神经网络（GNN）已经成为图分类和表示学习的强大工具。然而，GNN往往会遭受过度平滑问题，并且容易受到图形扰动的影响。为了解决这些挑战，我们提出了一种新的拓扑关系推理（TRI）的拓扑神经框架，它允许将高阶图信息集成到GNN中，并系统地学习局部图结构。该算法的核心思想是利用节点邻域的持续同调性对原图进行重新布线，然后将提取的拓扑摘要作为边信息加入局部算法。因此，新的框架使我们能够利用传统的信息图的结构和信息图的高阶拓扑性质。我们推导出新的局部拓扑表示的理论稳定性保证，并讨论了它们对图代数连通性的影响。节点分类任务的实验结果表明，新的TRI-GNN优于所有14个国家的最先进的基线6出7图，并表现出更高的鲁棒性扰动，产生高达10%的噪声情况下的性能提高。
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.