Math @ Duke

Publications [#243565] of John Harer
Papers Published
 Turner, K; Mileyko, Y; Mukherjee, S; Harer, J, Fréchet Means for Distributions of Persistence Diagrams,
Discrete & Computational Geometry, vol. 52 no. 1
(July, 2014),
pp. 4470, ISSN 01795376 [arXiv:1206.2790], [doi]
(last updated on 2017/11/19)
Abstract: Given a distribution ρ on persistence diagrams and observations X1,...Xn∼iidρ we introduce an algorithm in this paper that estimates a Fr\'echet mean from the set of diagrams X1,...Xn. If the underlying measure ρ is a combination of Dirac masses ρ=1m∑mi=1δZi then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fr\'echet 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.


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