Topological Analysis of Variance and the Maxillary Complex

• 成果类型: Article
• 署名作者: Heo, Giseon; Gamble, Jennifer; Kim, Peter T.
• 署名单位: University of Alberta; North Carolina State University; University of Guelph
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2011.641430
• 发表日期: 2012
• 页码: 477-492
• 关键词: extrinsic sample means; persistence; MANIFOLDS; confidence; reduction; HOMOLOGY

摘要

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.