Stability of Persistence Diagrams

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.

Authors and Affiliations

1. INRIA, 2004 Route des Lucioles, BP 93, 06904, Sophia-Antipolis, France

   David Cohen-Steiner

2. Department of Computer Science, Duke University, Durham, NC 27708 and Geomagic, Research Triangle Park, NC 27709, USA

   Herbert Edelsbrunner

3. Department of Mathematics, Duke University, Durham, NC 27708, USA

   John Harer

Corresponding authors

Correspondence to David Cohen-Steiner, Herbert Edelsbrunner or John Harer.

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