title: Parallel Factor Analysis as an exploratory tool for wavelet transformed event-related EEG.
abstract: In the decomposition of multi-channel EEG signals, principal component analysis (PCA) and independent component analysis (ICA) have widely been used. However, as both methods are based on handling two-way data, i.e. two-dimensional matrices, multi-way methods might improve the interpretation of frequency transformed multi-channel EEG of channel x frequency x time data. The multi-way decomposition method Parallel Factor (PARAFAC), also named Canonical Decomposition (CANDECOMP), was recently used to decompose the wavelet transformed ongoing EEG of channel x frequency x time (Miwakeichi, F., Martinez-Montes, E., Valdes-Sosa, P.A., Nishiyama, N., Mizuhara, H., Yamaguchi, Y., 2004. Decomposing EEG data into space-time-frequency components using parallel factor analysis. Neuroimage 22, 1035-1045). In this article, PARAFAC is used for the first time to decompose wavelet transformed event-related EEG given by the inter-trial phase coherence (ITPC) encompassing ANOVA analysis of differences between conditions and 5-way analysis of channel x frequency x time x subject x condition. A flow chart is presented on how to perform data exploration using the PARAFAC decomposition on multi-way arrays. This includes (A) channel x frequency x time 3-way arrays of F test values from a repeated measures analysis of variance (ANOVA) between two stimulus conditions; (B) subject-specific 3-way analyses; and (C) an overall 5-way analysis of channel x frequency x time x subject x condition. The PARAFAC decompositions were able to extract the expected features of a previously reported ERP paradigm: namely, a quantitative difference of coherent occipital gamma activity between conditions of a visual paradigm. Furthermore, the method revealed a qualitative difference which has not previously been reported. The PARAFAC decomposition of the 3-way array of ANOVA F test values clearly showed the difference of regions of interest across modalities, while the 5-way analysis enabled visualization of both quantitative and qualitative differences. Consequently, PARAFAC is a promising data exploratory tool in the analysis of the wavelets transformed event-related EEG.
authors.affiliation: Informatics and Mathematical Modelling, IMM, Technical University of Denmark, Richard Petersens Plads, Building 321, DK-2800 Kongens Lyngby, Denmark. mm@imm.dtu.dk
authors.forename: Morten
authors.initials: M
authors.lastname: Mørup
authors.forename: Lars Kai
authors.initials: LK
authors.lastname: Hansen
authors.forename: Christoph S
authors.initials: CS
authors.lastname: Herrmann
authors.forename: Josef
authors.initials: J
authors.lastname: Parnas
authors.forename: Sidse M
authors.initials: SM
authors.lastname: Arnfred
mesh_terms: D000328:Adult; D000465:Algorithms; D003627:Data Interpretation, Statistical; D004569:Electroencephalography / Q000706:statistics & numerical data*; D005071:Evoked Potentials / Q000502:physiology; D005074:Evoked Potentials, Visual / Q000502:physiology; D005163:Factor Analysis, Statistical; D006801:Humans; D008297:Male; D009778:Occipital Lobe / Q000502:physiology; D010775:Photic Stimulation