Inverse Problems for Persistence Diagrams

Abstract

Persistence homology is an important tool for topological data analysis(TDA), and a persistence diagram is a visualization tool of persistent homology. We can compute the geometric features of the data quantitatively using persistence diagrams. When using persistence diagrams, we often want to know which part of the input data is related to the geometric features shown in the persistence diagram. In this paper, we show some approaches to the problem.