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Event history and topological data analysis
[Persistence images: a stable vector representation of persistent homology]

Author

Listed:
  • K Garside
  • A Gjoka
  • R Henderson
  • H Johnson
  • I Makarenko

Abstract

SummaryPersistent homology is used to track the appearance and disappearance of features as we move through a nested sequence of topological spaces. Equating the nested sequence to a filtration and the appearance and disappearance of features to events, we show that simple event history methods can be used for the analysis of topological data. We propose a version of the well-known Nelson–Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson–Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is used to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.

Suggested Citation

  • K Garside & A Gjoka & R Henderson & H Johnson & I Makarenko, 2021. "Event history and topological data analysis [Persistence images: a stable vector representation of persistent homology]," Biometrika, Biometrika Trust, vol. 108(4), pages 757-773.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:4:p:757-773.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa097
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    Cited by:

    1. Moo K Chung & Hernando Ombao, 2021. "Discussion of ‘Event history and topological data analysis’ [Persistence images: A stable vector representation of persistent homology]," Biometrika, Biometrika Trust, vol. 108(4), pages 775-778.

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