Continuation of point clouds via persistence diagrams

Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton–Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D', we gradually move from D to D', by successively computing intermediate point clouds until we finally find a point cloud P' having D' as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.

Original languageEnglish
Pages (from-to)118-132
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume334
DOIs
Publication statusPublished - Nov 1 2016
Externally publishedYes

Keywords

  • Continuation
  • Persistence diagram
  • Persistent homology
  • Point cloud

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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