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Objective: The coupling between neuronal populations and its magnitude havebeen shown to be informative for various clinical applications. One method toestimate brain connectivity is with electroencephalography (EEG) from which thecross-spectrum between different sensor locations is derived. We wish to testthe efficacy of tensor factorisation in the estimation of brain connectivity.Methods: Complex tensor factorisation based on PARAFAC2 is used to decomposethe EEG into scalp components described by the spatial, spectral, and complextrial profiles. An EEG model in the complex domain was derived that shows thesuitability of PARAFAC2. A connectivity metric was also derived on the complextrial profiles of the extracted components. Results: Results on a benchmark EEGdataset confirmed that PARAFAC2 can estimate connectivity better thantraditional tensor analysis such as PARAFAC within a range of signal-to-noiseratios. The analysis of EEG from patients with mild cognitive impairment orAlzheimer's disease showed that PARAFAC2 identifies loss of brain connectivitybetter than traditional approaches and agreeing with prior pathologicalknowledge. Conclusion: The complex PARAFAC2 algorithm is suitable for EEGconnectivity estimation since it allows to extract meaningful coupled sourcesand provides better estimates than complex PARAFAC. Significance: A newparadigm that employs complex tensor factorisation has demonstrated to besuccessful in identifying brain connectivity and the location of couplessources for both a benchmark and a real-world EEG dataset. This can enablefuture applications and has the potential to solve some the issues thatdeteriorate the performance of traditional connectivity metrics.

Complex tensor factorisation with PARAFAC2 for the estimation of brain connectivity from the EEG