Model-based curve registration via stochastic approximation EM algorithm

TL;DR

This paper introduces a computationally stable and efficient model-based method for curve registration in functional data, effectively handling noise and revealing meaningful phase-based groupings in real-world applications.

Contribution

It proposes a novel stochastic approximation EM algorithm for curve registration that improves computational stability and efficiency over existing methods.

Findings

More intuitive groupings of elephant seal dive profiles achieved

Enhanced phase variation analysis through warping function clustering

Method outperforms traditional approaches in noisy data scenarios

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 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. In this paper, we propose an alternative method for model-based curve registration which is computationally more stable and efficient than existing approaches in the literature. We apply our method to the analysis of elephant seal dive profiles and show that more intuitive groupings can be obtained by clustering on phase variations via the predicted warping functions.