Structured Functional Principal Component Analysis

TL;DR

This paper introduces a new class of functional models that handle complex sampling designs and correlation structures in high-dimensional functional data, with scalable estimation methods demonstrated on diverse real-world datasets.

Contribution

It develops a novel structured functional principal component analysis framework that accounts for nested and crossed designs in functional data analysis.

Findings

Effective modeling of correlation structures in high-dimensional functional data

Scalable estimation procedure suitable for ultra-high dimensional datasets

Successful application to accelerometer, linguistic, and EEG data

Abstract

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where the fundamental sampling unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for ultra-high dimensional data. Methods are illustrated in three examples: high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.