PARETO QUANTILES OF UNLABELED TREE OBJECTS

• 成果类型: Article
• 署名作者: Sienkiewicz, Ela; Wang, Haonan
• 署名单位: Colorado State University System; Colorado State University Fort Collins
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1593
• 发表日期: 2018
• 页码: 1513-1540
• 关键词: hippocampal neuronal loss; oriented data-analysis; alzheimers-disease; ca1; MODEL; generation; regression; morphology; rats

摘要

In this paper, we consider a set of unlabeled tree objects with topological and geometric properties. For each data object, two curve representations are developed to characterize its topological and geometric aspects. We further define the notions of topological and geometric medians as well as quantiles based on both representations. In addition, we take a novel approach to define the Pareto medians and quantiles through a multi-objective optimization problem. In particular, we study two different objective functions which measure the topological variation and geometric variation, respectively. Analytical solutions are provided for topological and geometric medians and quantiles, and in general, for Pareto medians and quantiles, the genetic algorithm is implemented. The proposed methods are applied to analyze a data set of pyramidal neurons.