论文标题
稳定且歧视性的拓扑图分析
Stable and Discriminative Topological Graph Analysis
论文作者
论文摘要
我们提出了一种基于\ textIt {持久性同源性}的未加权图的拓扑分析的新方法。提出的方法将输入图映射到完整的加权图，其中加权函数将每个边缘映射到指示其属于集团的程度的值。随后计算了此加权图的持续同源性，以给出描述输入图的拓扑特征以及其意义。 提出了对拓扑图分析提出的和现有方法的正式和实验分析。通过此分析，我们发现所提出的方法具有稳定和执行准确歧视的特性。因此，此方法可以对给定图的拓扑特征进行准确的推论。另一方面，我们发现所考虑的现有方法没有这些属性，因此很难从中推断出这种推断。这些发现是使用许多随机和现实世界图在实验中证明的。
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a value indicating the degree to which it belongs to a clique. The persistent homology of this weighted graph is subsequently computed to give a topological representation describing the topological features of the input graph plus their significance. A formal and experimental analysis of the proposed and existing methods for topological graph analysis is presented. Through this analysis, we find that the proposed method possesses the properties of being stable and performing accurate discrimination. Therefore this method can make accurate inferences regarding the topological features of a given graph. On the other hand, we find that the existing methods considered do not possess these properties making it difficult from them to make such inferences. These findings are experimentally demonstrated using a number of random and real world graphs.
