Generalized Persistence Diagrams
Algebraic Topology
2020-10-16 v5
Abstract
We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type A persistence diagram of a persistence module. If the category is also abelian, then we define a second type B persistence diagram. In addition, we show that both diagrams are stable to all sufficiently small perturbations of the module.
Cite
@article{arxiv.1601.03107,
title = {Generalized Persistence Diagrams},
author = {Amit Patel},
journal= {arXiv preprint arXiv:1601.03107},
year = {2020}
}