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A comparison framework for interleaved persistence modules

  • Shaun Harker
  • Miroslav Kramár
  • Rachel LevangerEmail author
  • Konstantin Mischaikow
Article
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Abstract

We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a generalization of the algebraic stability theorem for \({\mathbb {R}}\)-indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance.

Keywords

Persistence module Persistence diagram Persistent homology Error bounds Topological data analysis 

Mathematics Subject Classification

55N35 55U10 65G99 

Notes

Acknowledgements

R. L. would like to thank Charles Weibel, Michael Lesnick, and Ulrich Bauer for the many insightful discussions that led to the results presented in this paper. The authors also thank the anonymous reviewers for their suggested corrections. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Shaun Harker
    • 1
  • Miroslav Kramár
    • 2
  • Rachel Levanger
    • 3
    Email author
  • Konstantin Mischaikow
    • 1
  1. 1.Department of Mathematics, Hill Center-Busch CampusRutgers UniversityPiscatawayUSA
  2. 2.INRIA SaclayPalaiseauFrance
  3. 3.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA

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