Neural Approximation of Extended Persistent Homology on Graphs
Neural Approximation of Extended Persistent Homology on Graphs
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发表时间：
2022
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通讯作者：
Zuoyu Yan;Tengfei Ma;Liangcai Gao;Zhi Tang;Yusu Wang;Chao Chen
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作者：
Zuoyu Yan;Tengfei Ma;Liangcai Gao;Zhi Tang;Yusu Wang;Chao Chen
基于持久同源性的拓扑特征捕捉高阶结构信息，从而增强图神经网络方法。然而，计算扩展的持久同源性摘要对于大而密集的图仍然很慢，并且可能是学习管道的严重瓶颈。受最近神经算法推理成功的启发，我们提出了一种新的图神经网络来有效地估计图上的扩展持久性图（EPD）。我们的模型建立在算法见解的基础上，并贝内于更好的监督和与EPD计算算法更紧密的一致性。我们验证了我们的方法与令人信服的实证结果近似EPD和下游图表示学习任务。我们的方法也很有效;在大而密集的图上，我们将计算速度加快了近100倍。
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.