Lipschitz Functions Have L p -Stable Persistence


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.

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Author information

Correspondence to Herbert Edelsbrunner.

Additional information

This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057 and by CNRS under grant PICS-3416.

Communicated By Peter Olver.

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Cohen-Steiner, D., Edelsbrunner, H., Harer, J. et al. Lipschitz Functions Have L p -Stable Persistence. Found Comput Math 10, 127–139 (2010).

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

Mathematics Subject Classification (2000)

  • 55N99
  • 68W30
  • 92-08