Fréchet Means for Distributions of Persistence Diagrams

Journal Article (Journal Article)

Given a distribution ρ on persistence diagrams and observations (Formula presented.) we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1,...,Xn. If the underlying measure ρ is a combination of Dirac masses (Formula presented.) then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the algorithm given observations drawn iid from ρ. We illustrate the convergence of an empirical mean computed by the algorithm to a population mean by simulations from Gaussian random fields. © 2014 Springer Science+Business Media New York.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 52 / 1

Start / End Page

  • 44 - 70

Electronic International Standard Serial Number (EISSN)

  • 1432-0444

International Standard Serial Number (ISSN)

  • 0179-5376

Digital Object Identifier (DOI)

  • 10.1007/s00454-014-9604-7

Citation Source

  • Scopus