**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. 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.