title: A multi-dimensional functional principal components analysis of EEG data.
abstract: 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.
authors.affiliation: Department of Statistics, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Kyle
authors.initials: K
authors.lastname: Hasenstab
authors.affiliation: Department of Biostatistics, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Aaron
authors.initials: A
authors.lastname: Scheffler
authors.affiliation: Department of Biostatistics, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Donatello
authors.initials: D
authors.lastname: Telesca
authors.affiliation: Department of Statistics, University of California, Los Angeles, California 90095, U.S.A.|Department of Biostatistics, University of California, Los Angeles, California 90095, U.S.A.|Department of Psychiatry and Biobehavioral Sciences, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Catherine A
authors.initials: CA
authors.lastname: Sugar
authors.affiliation: Department of Psychiatry and Biobehavioral Sciences, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Shafali
authors.initials: S
authors.lastname: Jeste
authors.affiliation: Department of Psychiatry and Biobehavioral Sciences, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Charlotte
authors.initials: C
authors.lastname: DiStefano
authors.affiliation: Department of Statistics, University of California, Los Angeles, California 90095, U.S.A.|Department of Biostatistics, University of California, Los Angeles, California 90095, U.S.A.
authors.forename: Damla
authors.initials: D
authors.lastname: Şentürk
mesh_terms: D000067877:Autism Spectrum Disorder; D004569:Electroencephalography; D005071:Evoked Potentials; D006801:Humans; D025341:Principal Component Analysis; D059629:Signal-To-Noise Ratio
keywords: Electroencephalography; Event-related potentials data; Functional data analysis; Multilevel functional principal components