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Stochastic Convergence of Persistence Landscapes and Silhouettes

Abstract : Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we can summarize the persistent homology with the persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.
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https://hal.archives-ouvertes.fr/hal-00923684
Contributor : Frédéric Chazal <>
Submitted on : Friday, January 3, 2014 - 7:13:56 PM
Last modification on : Friday, August 2, 2019 - 11:52:02 AM

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  • HAL Id : hal-00923684, version 1
  • ARXIV : 1312.0308

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Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman. Stochastic Convergence of Persistence Landscapes and Silhouettes. 30th ACM Symposium on Computational Geometry, Jun 2014, Kyoto, Japan. pp.474. ⟨hal-00923684⟩

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