用团图的拓扑分析提升图神经网络对高阶结构的捕捉能力
CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphs
- 构建团图并应用低维持久同调，高效提取高阶拓扑特征
- 在标准数据集上最高提升31%测试准确率
- 适合关注图神经网络拓扑建模的研究者与应用开发者
图神经网络已成为图分类和节点分类等任务的主流方法。然而，现有模型仍难以捕捉超越成对交互的高阶信息。近期研究表明，拓扑数据分析中的持久同调可为图神经网络引入原本无法捕获的拓扑特征。虽然该方法在0维（连通分量）和1维（环）下计算高效，但在高阶结构上存在复杂度高达$O(n^d)$的问题，难以扩展。本文提出CliquePH，通过在团图上应用高效的低维持久同调算法，有效提取高阶结构信息。在标准基准数据集上，该方法可实现最高31%的测试准确率提升。
原文摘要 · Abstract (English)
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes \emph{beyond} pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to $31\%$ improvements in test accuracy.
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