  We extend the definition of functional data registration to encompass a
larger class of registered functions. In contrast to traditional registration
models, we allow for registered functions that have more than one primary
direction of variation. The proposed Bayesian hierarchical model simultaneously
registers the observed functions and estimates the two primary factors that
characterize variation in the registered functions. Each registered function is
assumed to be predominantly composed of a linear combination of these two
primary factors, and the function-specific weights for each observation are
estimated within the registration model. We show how these estimated weights
can easily be used to classify functions after registration using both
simulated data and a juggling data set.
