Functional Data Analysis for Three-Dimensional Curves

• Activity Number: 104
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Juhyun Park*+
• Companies: Lancaster University
• Keywords: functional data ; curvature ; frenet-serret frames ; mean function ; multi-dimensional curves

Abstract

Three-dimensional curves naturally arise from recordings of movements in space but they can also be formed from three correlated curves. Understanding and characterising variability of the curves is still the main interest of the analysis, yet, extending the standard framework of analysing one dimensional curves through curve alignment and functional principal component analysis is not trivial. Motivated by the fact that general smooth curves in multidimensional space can be represented with Frenet-Serret (moving) frames, we utilise this framework to analyse the sample of three-dimensional curves. We show how to estimate a mean curve that exploits geometric features of the curve. Moreover we use this framework for defining shape and phase variability, in order to address curve alignment of multidimensional data that preserves curvature (and torsion).