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Zigzag Persistence

Abstract

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.

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Correspondence to Gunnar Carlsson.

Additional information

Communicated by Herbert Edelsbrunner.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Carlsson, G., de Silva, V. Zigzag Persistence. Found Comput Math 10, 367–405 (2010). https://doi.org/10.1007/s10208-010-9066-0

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  • DOI: https://doi.org/10.1007/s10208-010-9066-0

Keywords

  • Applied topology
  • Persistent topology
  • Quiver representations

Mathematics Subject Classification (2000)

  • 68W30
  • 55N99