Persistent homology of directed networks
Persistent homology of directed networks
复制标题
有向网络的持久同源性
DOI：
10.1109/acssc.2016.7868997
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
F. Mémoli
中科院分区：
文献类型：
--
作者：
Samir Chowdhury;F. Mémoli
虽然持久同源性已成功用于提供点云数据的拓扑摘要，但计算图或网络的持久同源性问题仍不清楚。特别是，现有文献没有提供对不对称性敏感的有向网络的持久同源性处理。我们研究了一种从加权有向网络构建单纯复形的方法，该网络捕获方向性信息，并且我们能够证明此类复形的持久同源性对于特定的网络距离概念是稳定的。我们说明了我们对模拟海马网络数据库的构建。
While persistent homology has been successfully used to provide topological summaries of point cloud data, the question of computing persistent homology of graphs or networks remains unclear. In particular, the existing literature does not provide a treatment of persistent homology for directed networks that is sensitive to asymmetry. We study a method for constructing simplicial complexes from weighted, directed networks that captures directionality information, and we are able to prove that the persistent homology of such complexes is stable with respect to a certain notion of network distance. We illustrate our construction on a database of simulated hippocampal networks.