Session A4 - Computational Geometry and Topology
July 10, 14:30 ~ 14:55
Generalized Persistence Diagrams
Colorado State University, USA - email@example.com
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 define a new metric between persistence diagrams we call the erosion distance which closely resembles the interleaving distance between persistence modules. We show that our assignment of a type B persistence diagram to a constructible persistence module is $1$-Lipschitz.