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Data may now be recorded concurrently from EEG and functional MRI, using the Simultaneous Imaging for Tomographic Electrophysiology (SITE) method. As yet, there is no established means to integrate the analysis of the combined data set. Recognizing that the hemodynamically convolved time-varying EEG spectrum, S, is intrinsically multidimensional in space, frequency, and time motivated us to use multiway Partial Least-Squares (N-PLS) analysis to decompose EEG (independent variable) and fMRI (dependent variable) data uniquely as a sum of “atoms”. Each EEG atom is the outer product of spatial, spectral, and temporal signatures and each fMRI atom the product of spatial and temporal signatures. The decomposition was constrained to maximize the covariance between corresponding temporal signatures of the EEG and fMRI. On all data sets, three components whose spectral peaks were in the theta …