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
StatePublished - Jan 1 2019

Fingerprint

Functional Principal Component Analysis
Principal Components
Penalized Splines
Thin-plate Spline
Trivariate
Statistical Software
Functional Data
Accelerometer
Principal Component Analysis
Covariance matrix
Principal component analysis
Proportion
Flexibility
Decompose
Estimate
Principal components

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

Cite this

Variable-Domain Functional Principal Component Analysis. / Johns, Jordan T.; Crainiceanu, Ciprian M; Zipunnikov, Vadim; Gellar, Jonathan.

In: Journal of Computational and Graphical Statistics, 01.01.2019.

Research output: Contribution to journalArticle

@article{882d18ab76a6496e9008e11418568b50,
title = "Variable-Domain Functional Principal Component Analysis",
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.",
keywords = "Dimension reduction, Functional data analysis, Longitudinal data, Nonparametric statistics",
author = "Johns, {Jordan T.} and Crainiceanu, {Ciprian M} and Vadim Zipunnikov and Jonathan Gellar",
year = "2019",
month = "1",
day = "1",
doi = "10.1080/10618600.2019.1604373",
language = "English (US)",
journal = "Journal of Computational and Graphical Statistics",
issn = "1061-8600",
publisher = "American Statistical Association",

}

TY - JOUR

T1 - Variable-Domain Functional Principal Component Analysis

AU - Johns, Jordan T.

AU - Crainiceanu, Ciprian M

AU - Zipunnikov, Vadim

AU - Gellar, Jonathan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Dimension reduction

KW - Functional data analysis

KW - Longitudinal data

KW - Nonparametric statistics

UR - http://www.scopus.com/inward/record.url?scp=85067546442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067546442&partnerID=8YFLogxK

U2 - 10.1080/10618600.2019.1604373

DO - 10.1080/10618600.2019.1604373

M3 - Article

AN - SCOPUS:85067546442

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

ER -