Math @ Duke
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Publications [#221198] of John Harer
Papers Published
- 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.
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