Nudged elastic band in topological data analysis

Henry Adams, Atanas Atanasov, Gunnar Carlsson

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We use the nudged elastic band method from computational chemistry to analyze high-dimensional data. Our approach is inspired by Morse theory, and as output we produce an increasing sequence of small cell complexes modeling the dense regions of the data. We test the method on data sets arising in social networks and in image processing. Furthermore, we apply the method to identify new topological structure in a data set of optical flow patches.

Original languageEnglish (US)
Pages (from-to)247-272
Number of pages26
JournalTopological Methods in Nonlinear Analysis
Volume45
Issue number1
DOIs
StatePublished - Mar 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Juliusz Schauder Centre for Nonlinear Studies.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • Morse theory
  • Nudged elastic band
  • Topological data analysis

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