Warping methods for means and variances in functional data.

Abstract

In this thesis, we develop a methodology for identifying and visualizing the important dimensions of variation for nonlinear functional data An algorithm for finding an appropriate pleasure of center for unregistered functional data aligned using dynamic time warping is presented. The strengths of dynamic time warping and isometric feature mapping are combined to produce a dimensionality reduction technique that provides intuitive, interpretable results for nonlinear functional data. This methodology is demonstrated on human motion data obtained from the University of North Carolina School of Dentistry Orthodontic and Dentofacial Clinics.