Foundations of Computational Mathematics

, Volume 10, Issue 2, pp 127–139 | Cite as

Lipschitz Functions Have Lp-Stable Persistence

  • David Cohen-Steiner
  • Herbert Edelsbrunner
  • John Harer
  • Yuriy Mileyko
Article

Abstract

We prove two stability results for Lipschitz functions on triangulable, compact metric spaces and consider applications of both to problems in systems biology. Given two functions, the first result is formulated in terms of the Wasserstein distance between their persistence diagrams and the second in terms of their total persistence.

Keywords

Continuous functions Metric spaces Persistent homology Wasserstein distance Total persistence Stability Gene expression Comparison Classification 

Mathematics Subject Classification (2000)

55N99 68W30 92-08 

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Copyright information

© SFoCM 2010

Authors and Affiliations

  • David Cohen-Steiner
    • 1
  • Herbert Edelsbrunner
    • 2
    • 3
  • John Harer
    • 4
  • Yuriy Mileyko
    • 5
  1. 1.INRIASophia-AntipolisFrance
  2. 2.Departments of Computer Science and of MathematicsDuke UniversityDurhamUSA
  3. 3.GeomagicResearch Triangle ParkUSA
  4. 4.Department of Mathematics and Section in Computational Biology and BioinformaticsDuke UniversityDurhamUSA
  5. 5.Department of Computer ScienceDuke UniversityDurhamUSA

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