Persistent Homology under Non-uniform Error

Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain. Keywords. Topological spaces, continuous functions, level sets, perturbations, homology, extended persistence, error models, stability, robustness.

• Type: Journal
• Year: 2010
• Where: MFCS
• Authors: Paul Bendich, Herbert Edelsbrunner, Michael Kerber, Amit K. Patel
• Keywords: Error Models, Extended Persistence Diagram, MFCS 2010, Robustness, Theoretical Computer Science