Fast Generalized Functional Principal Components Analysis

TL;DR

The paper introduces a rapid and scalable generalized functional principal components analysis method for non-Gaussian data, improving efficiency and performance over existing techniques, with applications to physical activity data from wearable devices.

Contribution

A novel fast-GFPCA algorithm that significantly accelerates dimension reduction for non-Gaussian functional data while maintaining or improving accuracy.

Findings

Performs as well or better than existing methods

Orders of magnitude faster than current approaches

Scales well with large datasets

Abstract

We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2) fitting local random intercept generalized linear mixed models in every bin to obtain the initial estimates of the person-specific functional linear predictors; (3) using fast functional principal component analysis to smooth the linear predictors and obtain their eigenfunctions; and (4) estimating the global model conditional on the eigenfunctions of the linear predictors. An extensive simulation study shows that fast-GFPCA performs as well or better than existing state-of-the-art approaches, it is orders of magnitude faster than existing general purpose GFPCA methods, and scales up well with both the number of observed curves and observations per curve. Methods were motivated by and applied to a study of active/inactive physical activity profiles obtained from wearable accelerometers in the NHANES 2011-2014 study. The method can be implemented by any user familiar with mixed model software, though the R package fastGFPCA is provided for convenience.