Spatially Penalised Registration of Multivariate Functional Data

TL;DR

This paper introduces a novel registration method for multivariate functional data that accounts for spatially correlated phase variations, improving alignment accuracy by incorporating spatial correlation through a kriging-based penalty.

Contribution

It proposes a new algorithm that models spatial correlation in phase variations of multivariate functional data using a kriging estimate, enhancing registration performance.

Findings

Outperforms existing methods that ignore spatial correlation.

Effective on simulated data and real EEG and ozone datasets.

Regularizes phase alignment to prevent overfitting.

Abstract

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase random field. The penalty term encourages the overall phase at a particular location to be similar to the spatially weighted average phase in its neighbourhood, and thus engenders a regularization that prevents over-alignment. Utility of the registration method, and its superior performance compared to methods that fail to account for the spatial correlation, is demonstrated through performance on simulated examples and two multivariate functional datasets pertaining to EEG signals and ozone concentrations. The generality of the framework opens up the possibility for extension to settings involving different forms of correlation between the component functions and their phases.