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A multi‐dimensional functional principal components analysis of EEG data
Author(s) -
Hasenstab Kyle,
Scheffler Aaron,
Telesca Donatello,
Sugar Catherine A.,
Jeste Shafali,
DiStefano Charlotte,
Şentürk Damla
Publication year - 2017
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12635
Subject(s) - computer science , electroencephalography , principal component analysis , pattern recognition (psychology) , artificial intelligence , autism spectrum disorder , functional principal component analysis , event related potential , autism , machine learning , psychology , neuroscience , developmental psychology
Summary The electroencephalography (EEG) data created in event‐related potential (ERP) experiments have a complex high‐dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functional data. The experiments are made up of sequences of multiple trials, resulting in longitudinal functional data and moreover, responses are recorded at multiple electrodes on the scalp, adding an electrode dimension. Traditional EEG analyses involve multiple simplifications of this structure to increase the signal‐to‐noise ratio, effectively collapsing the functional and longitudinal components by identifying key features of the ERPs and averaging them across trials. Motivated by an implicit learning paradigm used in autism research in which the functional, longitudinal, and electrode components all have critical interpretations, we propose a multidimensional functional principal components analysis (MD‐FPCA) technique which does not collapse any of the dimensions of the ERP data. The proposed decomposition is based on separation of the total variation into subject and subunit level variation which are further decomposed in a two‐stage functional principal components analysis. The proposed methodology is shown to be useful for modeling longitudinal trends in the ERP functions, leading to novel insights into the learning patterns of children with Autism Spectrum Disorder (ASD) and their typically developing peers as well as comparisons between the two groups. Finite sample properties of MD‐FPCA are further studied via extensive simulations.