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Exploring uses of persistent homology for statistical analysis of landmark-based shape data

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  • Gamble, Jennifer
  • Heo, Giseon

Abstract

A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained. Groups of configurations are compared using distances between persistence diagrams combined with dimensionality reduction methods. A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects. Comparisons are made with the traditional landmark-based statistical shape analysis methods of Dryden and Mardia, and Euclidean Distance Matrix Analysis.

Suggested Citation

  • Gamble, Jennifer & Heo, Giseon, 2010. "Exploring uses of persistent homology for statistical analysis of landmark-based shape data," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2184-2199, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2184-2199
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    Cited by:

    1. Eric Cawi & Patricio S La Rosa & Arye Nehorai, 2019. "Designing machine learning workflows with an application to topological data analysis," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-26, December.

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