论文标题
圆柱网络上持续的betti数字的功能性中心限制定理
Functional central limit theorems for persistent Betti numbers on cylindrical networks
论文作者
论文摘要
我们研究了从泊松点过程中定义的网络获得的持久性betti数字的功能中心限制定理。极限以大量的圆柱形形状形成，仅在一个维度上拉伸。结果涵盖了用于稳定网络的定向超级滤波，以及随机几何图上的Cech和Cech和vietoris-Rips复合物。 提出的功能性中心限制定理为拓扑数据分析中的各种统计应用打开了大门，我们在仿真研究中考虑了拟合优点测试。
We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Cech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.
