Stability of persistence spaces of vector-valued continuous functions
Dynamical Systems
2013-05-29 v1 Computational Geometry
Abstract
Multidimensional persistence modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. The main result is its stability under function perturbations: any change in vector-valued functions implies a not greater change in the Hausdorff distance between their persistence spaces.
Cite
@article{arxiv.1305.6425,
title = {Stability of persistence spaces of vector-valued continuous functions},
author = {Andrea Cerri and Claudia Landi},
journal= {arXiv preprint arXiv:1305.6425},
year = {2013}
}