Factor-guided functional PCA for high-dimensional functional data

TL;DR

This paper introduces FaFPCA, a novel method for high-dimensional functional data that captures both temporal dependence and variable correlation, improving feature extraction and prediction accuracy.

Contribution

The paper proposes a factor-guided FPCA approach that models both correlation among variables and dependence over time, with a closed-form estimation and theoretical guarantees.

Findings

Outperforms existing methods in accuracy and computational efficiency

Identifies 41 ROIs associated with Alzheimer's disease, 23 confirmed by literature

Demonstrates effectiveness on ADNI dataset

Abstract

The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method to consider both temporal dependence and correlation of variables so that the extracted features are as sufficient as possible. In particular, we use a factor process to consider the correlation among high-dimensional functional variables and then apply functional principal component analysis (FPCA) to the factor processes to address the dependence over time. Furthermore, to solve the computational problem arising from triple-infinite dimensions, we creatively build some moment equations to estimate loading, scores and eigenfunctions in closed form without rotation. Theoretically, we establish the asymptotical properties of the proposed estimator. Extensive simulation studies demonstrate that our proposed method outperforms other competitors in terms of accuracy and computational cost. The proposed method is applied to analyze the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, resulting in higher prediction accuracy and 41 important ROIs that are associated with Alzheimer's disease, 23 of which have been confirmed by the literature.