TY - JOUR
T1 - A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation
AU - Choi, Ji Yeh
AU - Hwang, Heungsun
AU - Yamamoto, Michio
AU - Jung, Kwanghee
AU - Woodward, Todd S.
N1 - Publisher Copyright:
© 2016, The Psychometric Society.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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.
AB - 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.
KW - alternating regularized least squares algorithm
KW - functional data
KW - functional multiple-set canonical correlation analysis
KW - functional principal component analysis
UR - http://www.scopus.com/inward/record.url?scp=84957679894&partnerID=8YFLogxK
U2 - 10.1007/s11336-015-9478-5
DO - 10.1007/s11336-015-9478-5
M3 - Article
C2 - 26856725
AN - SCOPUS:84957679894
SN - 0033-3123
VL - 82
SP - 427
EP - 441
JO - Psychometrika
JF - Psychometrika
IS - 2
ER -