Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#221198] of John Harer

Papers Published

  1. Katharine Turner, Yuriy Mileyko, Sayan Mukherjee, John Harer, Fréchet Means for Distributions of Persistence diagrams, Discrete and Computational Geometry, vol. 52 (July, 2014), pp. 44-70 [arXiv:1206.2790], [doi]
    (last updated on 2014/12/15)

    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.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320