The Geometry of Nonparametric Filament Estimation

• 成果类型: Article
• 署名作者: Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry
• 署名单位: Carnegie Mellon University; Sapienza University Rome
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.682527
• 发表日期: 2012
• 页码: 788-799
• 关键词: global curvature; point-processes; principal; extraction; CURVES; probe

摘要

We consider the problem of estimating filamentary structure from d-dimensional point process data. We make some connections with computational geometry and develop nonparametric methods for estimating the filaments. We show that, under weak conditions, the filaments have a simple geometric representation as the medial axis of the data distribution's support. Our methods convert an estimator of the support's boundary into an estimator of the filaments. We also find the rates of convergence of our estimators. Proofs of all results are in the supplementary material available online.