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Topological Analysis of Variance and the Maxillary Complex

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  • Giseon Heo
  • Jennifer Gamble
  • Peter T. Kim
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2012)
    Issue (Month): 498 (June)
    Pages: 477-492

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    Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:477-492

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