Variable-Domain Functional Principal Component Analysis

Jordan T. Johns, Ciprian M Crainiceanu, Vadim Zipunnikov, Jonathan Gellar

Research output: Contribution to journalArticle

Abstract

We introduce a novel method of principal component analysis for data with varying domain lengths for each functional observation. We refer to this technique as variable-domain functional principal component analysis, or vd-FPCA. We fit a trivariate smoother using penalized thin plate splines to estimate the covariance as a function of the domain length. Principal components are then calculated through eigen-decomposition of the estimated covariance matrix, conditional on the domain length. We apply vd-FPCA in two functional data settings, first to daily measures of patient wellness during a stay in the ICU, and second, to accelerometer recordings of repeated in-lab movements. In each example, vd-FPCA uses fewer principal components than typical FPCA methods to explain a greater proportion of the variation in the data. We also find the principal components provide greater flexibility in interpretation with respect to domain length than traditional approaches. These methods are easily implementable through standard statistical software and applicable to a wide variety of datasets involving continuous observations over a variable domain. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalJournal of Computational and Graphical Statistics
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Dimension reduction
  • Functional data analysis
  • Longitudinal data
  • Nonparametric statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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