English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Given a distribution $\rho$ on persistence diagrams and observations$X_1,...X_n \stackrel{iid}{\sim} \rho$ we introduce an algorithm in this paperthat estimates a Fr\'echet mean from the set of diagrams $X_1,...X_n$. If theunderlying 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 localminimum and a law of large numbers result for a Fr\'echet mean computed by thealgorithm given observations drawn iid from $\rho$. We illustrate theconvergence of an empirical mean computed by the algorithm to a population meanby simulations from Gaussian random fields.

Fr\'echet Means for Distributions of Persistence diagrams