@ARTICLE\{IMM2006-04031,
    author       = "M. M{\o}rup and L. K. Hansen and C. S. Hermann and J. Parnas and S. M. Arnfred",
    title        = "Parallel Factor Analysis as an exploratory tool for wavelet transformed event-related {EEG}",
    year         = "2006",
    month        = "feb",
    pages        = "938-947",
    journal      = "NeuroImage",
    volume       = "29",
    editor       = "",
    number       = "3",
    publisher    = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4031-full.html",
    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}."
}