  Objective: The coupling between neuronal populations and its magnitude have
been shown to be informative for various clinical applications. One method to
estimate brain connectivity is with electroencephalography (EEG) from which the
cross-spectrum between different sensor locations is derived. We wish to test
the efficacy of tensor factorisation in the estimation of brain connectivity.
Methods: Complex tensor factorisation based on PARAFAC2 is used to decompose
the EEG into scalp components described by the spatial, spectral, and complex
trial profiles. An EEG model in the complex domain was derived that shows the
suitability of PARAFAC2. A connectivity metric was also derived on the complex
trial profiles of the extracted components. Results: Results on a benchmark EEG
dataset confirmed that PARAFAC2 can estimate connectivity better than
traditional tensor analysis such as PARAFAC within a range of signal-to-noise
ratios. The analysis of EEG from patients with mild cognitive impairment or
Alzheimer's disease showed that PARAFAC2 identifies loss of brain connectivity
better than traditional approaches and agreeing with prior pathological
knowledge. Conclusion: The complex PARAFAC2 algorithm is suitable for EEG
connectivity estimation since it allows to extract meaningful coupled sources
and provides better estimates than complex PARAFAC. Significance: A new
paradigm that employs complex tensor factorisation has demonstrated to be
successful in identifying brain connectivity and the location of couples
sources for both a benchmark and a real-world EEG dataset. This can enable
future applications and has the potential to solve some the issues that
deteriorate the performance of traditional connectivity metrics.
