Publications [#243565] of John Harer

Papers Published

  1. 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. 44-70, ISSN 0179-5376
    (last updated on 2018/09/18)

    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.