# Stability of Persistence Diagrams

@article{CohenSteiner2007StabilityOP,
title={Stability of Persistence Diagrams},
author={David Cohen-Steiner and Herbert Edelsbrunner and John Harer},
journal={Discrete \& Computational Geometry},
year={2007},
volume={37},
pages={103-120}
}
• Published 6 June 2005
• Mathematics
• Discrete & Computational Geometry
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.
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