Geometry-Based Visualization of Functional Data

• Activity Number: 220 - Robust Multivariate and High-Dimensional Analysis Using Functional Data Ranking
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Karthik Bharath* and Weiyi Xie and Sebastian Kurtek and Ying Sun
• Companies: University of Nottingham and Ohio State University and The Ohio State University and King Abdullah University of Science and Technology

Abstract

The construction and visualization of boxplot-type displays for functional data, based on the geometry of the function space, is proposed. Employing a representation of the functions, referred to as the square-root slope representation, a Riemannian-geometric framework is used to decompose observed variation into amplitude, phase and vertical translation components, and a separate display is constructed for each component. The metric-based framework allows for the computation of a median and two quartile functions, and enables identification of outlying functions.