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Psychometrika

, Volume 82, Issue 2, pp 427–441 | Cite as

A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation

  • Ji Yeh ChoiEmail author
  • Heungsun Hwang
  • Michio Yamamoto
  • Kwanghee Jung
  • Todd S. Woodward
Article
  • 385 Downloads

Abstract

Functional principal component analysis (FPCA) and functional multiple-set canonical correlation analysis (FMCCA) are data reduction techniques for functional data that are collected in the form of smooth curves or functions over a continuum such as time or space. In FPCA, low-dimensional components are extracted from a single functional dataset such that they explain the most variance of the dataset, whereas in FMCCA, low-dimensional components are obtained from each of multiple functional datasets in such a way that the associations among the components are maximized across the different sets. In this paper, we propose a unified approach to FPCA and FMCCA. The proposed approach subsumes both techniques as special cases. Furthermore, it permits a compromise between the techniques, such that components are obtained from each set of functional data to maximize their associations across different datasets, while accounting for the variance of the data well. We propose a single optimization criterion for the proposed approach, and develop an alternating regularized least squares algorithm to minimize the criterion in combination with basis function approximations to functions. We conduct a simulation study to investigate the performance of the proposed approach based on synthetic data. We also apply the approach for the analysis of multiple-subject functional magnetic resonance imaging data to obtain low-dimensional components of blood-oxygen level-dependent signal changes of the brain over time, which are highly correlated across the subjects as well as representative of the data. The extracted components are used to identify networks of neural activity that are commonly activated across the subjects while carrying out a working memory task.

Keywords

functional data functional principal component analysis functional multiple-set canonical correlation analysis  alternating regularized least squares algorithm 

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Copyright information

© The Psychometric Society 2016

Authors and Affiliations

  • Ji Yeh Choi
    • 1
    Email author
  • Heungsun Hwang
    • 1
  • Michio Yamamoto
    • 2
  • Kwanghee Jung
    • 3
  • Todd S. Woodward
    • 4
  1. 1.Department of PsychologyMcGill UniversityMontrealCanada
  2. 2.Kyoto UniversityKyotoJapan
  3. 3.University of Texas Health Science CenterSan AntonioUSA
  4. 4.University of British Columbia and British Columbia Mental Health and Addiction Research InstituteVancouverCanada

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