Combining Functional Data Registration and Factor Analysis

TL;DR

This paper introduces a Bayesian hierarchical model that extends functional data registration to handle multiple primary variation directions, enabling simultaneous registration, factor estimation, and classification of functions.

Contribution

It proposes a novel registration framework that captures multiple variation directions and integrates factor analysis within a Bayesian hierarchical model.

Findings

Successfully registers functions with multiple variation directions

Estimates primary factors and weights for classification

Demonstrates effectiveness on simulated and real juggling data

Abstract

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.