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Topological Analysis of Variance and the Maxillary Complex

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  • Giseon Heo
  • Jennifer Gamble
  • Peter T. Kim

Abstract

It is common to reduce the dimensionality of data before applying classical multivariate analysis techniques in statistics. Persistent homology, a recent development in computational topology, has been shown to be useful for analyzing high-dimensional (nonlinear) data. In this article, we connect computational topology with the traditional analysis of variance and demonstrate the value of combining these approaches on a three-dimensional orthodontic landmark dataset derived from the maxillary complex. Indeed, combining appropriate techniques of both persistent homology and analysis of variance results in a better understanding of the data’s nonlinear features over and above what could have been achieved by classical means. Supplementary material for this article is available online.

Suggested Citation

  • Giseon Heo & Jennifer Gamble & Peter T. Kim, 2012. "Topological Analysis of Variance and the Maxillary Complex," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 477-492, June.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:477-492
    DOI: 10.1080/01621459.2011.641430
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    File URL: http://hdl.handle.net/10.1080/01621459.2011.641430
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    Cited by:

    1. Kovacev-Nikolic Violeta & Bubenik Peter & Nikolić Dragan & Heo Giseon, 2016. "Using persistent homology and dynamical distances to analyze protein binding," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(1), pages 19-38, March.

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