Simultaneous inference for misaligned multivariate functional data

TL;DR

This paper introduces a new statistical modeling approach for misaligned multivariate functional data, capturing systematic shape differences and cross-covariance, with applications demonstrating improved classification performance.

Contribution

The paper proposes a novel model combining nonlinear warping and Gaussian processes for multivariate functional data, along with a maximum-likelihood estimation method.

Findings

Model effectively captures systematic shape differences.

Method outperforms existing techniques in classification tasks.

Applications include motion tracking, anthropometric data, and hand-path analysis.

Abstract

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.