Modeling of persistent homology

Sarit Agami, Robert J. Adler*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

2 Scopus citations

Abstract

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams. In an earlier article we proposed a parametric representation for the probability distributions of persistence diagrams, and based on it provided a method for their replication. Since the typical situation for big data is that only one persistence diagram is available, these replications allow for conventional statistical inference, which, by its very nature, requires some form of replication. In the current paper we continue this analysis, and further develop its practical statistical methodology, by investigating a wider class of examples than treated previously.

Original languageAmerican English
Pages (from-to)4871-4888
Number of pages18
JournalCommunications in Statistics - Theory and Methods
Volume49
Issue number20
DOIs
StatePublished - 17 Oct 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Taylor & Francis Group, LLC.

Keywords

  • Hamiltonian
  • MCMC
  • Persistence diagram
  • Replicated persistence diagrams

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