ON THE PATH DENSITY OF A GRADIENT FIELD

• 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: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS671
• 发表日期: 2009
• 页码: 3236-3271
• 关键词: principal curves; cosmic filaments; point process; extraction; skeleton; probe

摘要

We consider the problem of reliably finding filaments in point clouds. Realistic data sets often have numerous filaments of various sizes and shapes. Statistical techniques exist for finding one (or a few) filaments but these methods do not handle noisy data sets with many filaments. Other methods can be found in the astronomy literature but they do not have rigorous statistical guarantees. We propose the following method. Starting at each data point we construct the steepest ascent path along a kernel density estimator. We locate filaments by finding regions where these paths are highly concentrated. Formally, we define the density of these paths and we construct a consistent estimator of this path density.