Daniel Lundin: Metrics for Multidimensional Persistence

Abstract:

A fundamental mathematical object in topological data analysis today is the persistence module. This thesis explores different metrics on multidimensional persistence modules, where spaces are parametrized along multiple dimensions. The focus is especially on metrics constructed by the use of so called noise systems, introduced by Scolamiero et al. in 2015. Furthermore, suggestions for new noise systems are given and bounds for their metrics are presented. An exact computation for the metric induced by the volume noise system is also shown for pairs of modules satisfying certain conditions.