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Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments

Published online by Cambridge University Press:  01 January 2025

Ji Yeh Choi ,
Heungsun Hwang  and
Marieke E. Timmerman
Ji Yeh Choi*
Affiliation:
McGill University
Heungsun Hwang
Affiliation:
McGill University
Marieke E. Timmerman
Affiliation:
University of Groningen
*
Correspondence should be made to JiYeh Choi andHeungsunHwang, Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, QC H3A 1B1 Canada. Email: [email protected]
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Abstract

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Keywords

three-way dataparallel factor analysisfunctional data analysisspatial and temporal variation
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 1 , March 2018 , pp. 1 - 20
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

The authors wish to thank Jelena Ristic for her constructive comments on the analysis of EEG data.

The MATLAB code used in this paper is available upon request from the author Ji Yeh Choi.

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