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

Loukianos Spyrou, Mario Parra, Javier Escudero

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8 Citations (Scopus)
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Objective: The coupling between neuronal populations and its magnitude have been shown to be informative for various clinical applications. One method to estimate functional 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: An EEG model in the complex domain is derived that shows the suitability of the PARAFAC2 model. Complex tensor factorisation based on PARAFAC2 is used to decompose the EEG into scalp components described by the spatial, spectral, and complex trial profiles. A connectivity metric is 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-tonoise ratios. MVAR-ICA outperformed PARAFAC2 for very low signal-to-noise ratios while being inferior in most of the range, and in contrast to our method MVAR-ICA does not allow the estimation of trial to trial information. The analysis of EEG from patients with mild cognitive impairment or Alzheimer’s disease showed that PARAFAC2 identifies loss of brain connectivity 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 and MVAR-ICA. 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.
Original languageEnglish
Number of pages13
JournalIEEE Transactions on Neural Systems and Rehabilitation Engineering
Early online date28 Nov 2018
Publication statusE-pub ahead of print - 28 Nov 2018


  • complex tensor factorisation
  • connectivity
  • EEG


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