Fréchet Means for Distributions of Persistence Diagrams

  title={Fr{\'e}chet Means for Distributions of Persistence Diagrams},
  author={Katharine Turner and Yuriy Mileyko and S. Mukherjee and J. Harer},
  journal={Discrete & Computational Geometry},
  • Katharine Turner, Yuriy Mileyko, +1 author J. Harer
  • Published 2014
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • Given a distribution $$\rho $$ρ on persistence diagrams and observations $$X_{1},\ldots ,X_{n} \mathop {\sim }\limits ^{iid} \rho $$X1,…,Xn∼iidρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams $$X_{1},\ldots ,X_{n}$$X1,…,Xn. If the underlying measure $$\rho $$ρ is a combination of Dirac masses $$\rho = \frac{1}{m} \sum _{i=1}^{m} \delta _{Z_{i}}$$ρ=1m∑i=1mδZi then we prove the algorithm converges to a local minimum and a law of large numbers result… CONTINUE READING
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