We present a new approach to factor rotation for functional data. This is
achieved by rotating the functional principal components toward a predefined
space of periodic functions designed to decompose the total variation into
components that are nearly-periodic and nearly-aperiodic with a predefined
period. We show that the factor rotation can be obtained by calculation of
canonical correlations between appropriate spaces which make the methodology
computationally efficient. Moreover, we demonstrate that our proposed rotations
provide stable and interpretable results in the presence of highly complex
covariance. This work is motivated by the goal of finding interpretable sources
of variability in gridded time series of vegetation index measurements obtained
from remote sensing, and we demonstrate our methodology through an application
of factor rotation of this data.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS518 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
