论文标题
关于随机持久图的普遍性
On the Universality of Random Persistence Diagrams
论文作者
论文摘要
拓扑数据分析领域中最难以捉摸的挑战之一是了解持久图的分布。尽管付出了很多努力，但这在很大程度上仍然是一个空旷的问题。在本文中，我们提出了一系列关于由随机点云引起的持久图的行为的新颖猜想。我们声称这些图遵守了普遍的概率法，并将明确的表达方式包括作为本法律的候选者。我们使用详尽的实验（包括模拟和真实数据）来支持这些猜想。我们通过为持久图内的各个特征提出一个新的假设测试框架来证明这些猜想的力量。
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of novel conjectures regarding the behavior of persistence diagrams arising from random point-clouds. We claim that these diagrams obey a universal probability law, and include an explicit expression as a candidate for what this law is. We back these conjectures with an exhaustive set of experiments, including both simulated and real data. We demonstrate the power of these conjectures by proposing a new hypothesis testing framework for individual features within persistence diagrams.
