# 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} }

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.

## 959 Citations

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