论文标题
基于随机步行的返回概率的持久图的多尺度图签名
A Multi-scale Graph Signature for Persistence Diagrams based on Return Probabilities of Random Walks
论文作者
论文摘要
持久图（PDS）通常以同源性类别的死亡和出生为特征，以提供图形结构的拓扑表示，通常在机器学习任务中有用。先前的工作依靠单个图形签名来构建PD。在本文中，我们探讨了使用多尺度图标志家族来增强拓扑特征的鲁棒性。我们提出了一个深度学习体系结构来处理该集合的输入。基准图分类数据集上的实验表明，与使用图神经网络的最新方法相比，我们所提出的架构优于其他基于同源的方法，并实现其他基于同源的方法，并实现了竞争性能。此外，我们的方法可以轻松地应用于大尺寸的输入图，因为它不会遭受有限的可伸缩性的影响，这可能是图内核方法的问题。
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely on a single graph signature to construct PDs. In this paper, we explore the use of a family of multi-scale graph signatures to enhance the robustness of topological features. We propose a deep learning architecture to handle this set input. Experiments on benchmark graph classification datasets demonstrate that our proposed architecture outperforms other persistent homology-based methods and achieves competitive performance compared to state-of-the-art methods using graph neural networks. In addition, our approach can be easily applied to large size of input graphs as it does not suffer from limited scalability which can be an issue for graph kernel methods.
