Date: February 2023.
Source:, 2023020520.
Abstract: Multilevel functional principal components analysis (mFPCA) is used to treat dynamical changes in shape in this article. Results of standard (single-level) FPCA are presented here also as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contains two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that represent (broadly) an eye; this data also has two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed-up by an application of mFPCA and single-level FPCA to “real” data consisting of twelve 3D landmark outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories variation are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed, as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the “blinking” and “surprised” trajectories for the MC “eye” data. Results for the “smile” data show that the smile trajectory is modelled correctly, namely: the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mFPCA model show only subtle and minor changes in mouth shape due to sex, whereas the first mode of variation at level 2 of the mFPCA model govern whether the mouth is upturned or downturned. These results are all an excellent test of mFPCA, which show that mFPCA presents a viable method of modelling dynamical changes in shape.

Article: Multilevel Functional Principal Components Analysis Presents a Viable Method of Modelling Dynamical Shape Changes.
Authors: DJJ Farnell, P Claes. School of Dentistry, Cardiff University, Cardiff, United Kingdom.