Topological Analysis of Variance and the Maxillary Complex

Giseon Heo, Jennifer Gamble and Peter T. Kim

Journal of the American Statistical Association, 2012, vol. 107, issue 498, 477-492

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.

Date: 2012
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DOI: 10.1080/01621459.2011.641430

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