Model-based curve registration via stochastic approximation EM algorithm

Abstract

Functional data often exhibit both amplitude and phase variation around a common base shape, with phase variation represented by a so called warping function. The process of removing phase variation by curve alignment and inference of the warping functions is referred to as curve registration. When functional data are observed with substantial noise, model-based methods can be employed for simultaneous smoothing and curve registration. However, the nonlinearity of the model often renders the inference computationally challenging. An alternative method for model-based curve registration is proposed which is computationally more stable and efficient than existing approaches in the literature. The proposed method is applied to the analysis of elephant seal dive profiles. The result shows that more intuitive groupings can be obtained by clustering on phase variations via the predicted warping functions.