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. 
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