论文标题
稳定和范围的集合持续存在
Steady and ranging sets in graph persistence
论文作者
论文摘要
拓扑数据分析可以提供有关加权图和挖掘的结构的见解。但是，给定（DI）图的基础属性几乎不能与简单复合物绘制。我们介绍\ textIt {steady}和\ textit {ranging}集：直接从图理论特征直接从图形理论特征中生成持久图的两种标准化方法。这两个构造在\ textit {indexing-hewawe持续函数}的上下文中进行了构架。此外，我们引入了足够的稳定条件。最后，我们将基于稳定和范围的持久性构造应用于玩具示例和现实世界应用。
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and \textit{ranging} sets: two standardized ways of producing persistence diagrams directly from graph-theoretical features. The two constructions are framed in the context of \textit{indexing-aware persistence functions}. Furthermore, we introduce a sufficient condition for stability. Finally, we apply the steady- and ranging-based persistence constructions to toy examples and real-world applications.
