Variable Domain Multivariate Functional Principal Component Analysis

TL;DR

This paper introduces a novel multivariate functional principal component analysis method that explicitly handles variable observation domains across subjects, improving analysis of practical functional data with differing observation periods.

Contribution

It extends existing MFPCA techniques to accommodate variable domains by combining univariate variable domain FPCA with covariance smoothing, outperforming previous methods.

Findings

The proposed method outperforms binning strategies in simulations.

It effectively analyzes COVID-19 patient data with varying observation periods.

The approach accurately estimates multivariate eigenfunctions and scores.

Abstract

Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are recorded over a common, fixed domain. This assumption is often violated in practical applications where the observation period varies across subjects, leading to what is known as variable domain functional data. We propose a novel approach for MFPCA that explicitly accommodates variable domains by extending existing multivariate functional principal component analysis to the variable domain setting. Our methodology involves performing univariate variable domain FPCA for each functional variable separately, stacking the resulting univariate scores, and then smoothing the empirical covariance matrix of these stacked scores over the domain length. This allows us to estimate multivariate eigenfunctions and scores that properly account for varying observation periods. We demonstrate through extensive simulation studies that our proposed method outperforms approaches that ignore the variable domain structure and rely on binning strategies. The practical utility of our method is illustrated through an application analyzing body temperature and capillary oxygen saturation (SpO$_2$) trajectories in COVID-19 hospital admitted patients, where patients experienced varying lengths of stay and monitoring periods.