Probability measures on the space of persistence diagrams

Journal Article (Journal Article)

This paper shows that the space of persistence diagrams has properties that allow for the definition of probability measures which support expectations, variances, percentiles and conditional probabilities. This provides a theoretical basis for a statistical treatment of persistence diagrams, for example computing sample averages and sample variances of persistence diagrams. We first prove that the space of persistence diagrams with the Wasserstein metric is complete and separable. We then prove a simple criterion for compactness in this space. These facts allow us to show the existence of the standard statistical objects needed to extend the theory of topological persistence to a much larger set of applications. © 2011 IOP Publishing Ltd.

Full Text

Duke Authors

Cited Authors

  • Mileyko, Y; Mukherjee, S; Harer, J

Published Date

  • December 1, 2011

Published In

Volume / Issue

  • 27 / 12

Electronic International Standard Serial Number (EISSN)

  • 1361-6420

International Standard Serial Number (ISSN)

  • 0266-5611

Digital Object Identifier (DOI)

  • 10.1088/0266-5611/27/12/124007

Citation Source

  • Scopus