Math @ Duke

Publications [#303545] of John Harer
Papers Published
 Turner, K; Mileyko, Y; Mukherjee, S; Harer, J, Fréchet Means for Distributions of Persistence diagrams
(June, 2012) [1206.2790v2]
(last updated on 2019/04/24)
Abstract: Given a distribution $\rho$ on persistence diagrams and observations
$X_1,...X_n \stackrel{iid}{\sim} \rho$ we introduce an algorithm in this paper
that estimates a Fr\'echet mean from the set of diagrams $X_1,...X_n$. If the
underlying measure $\rho$ is a combination of Dirac masses $\rho = \frac{1}{m}
\sum_{i=1}^m \delta_{Z_i}$ 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 $\rho$. 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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