title: A multivariate method for estimating cross-frequency neuronal interactions and correcting linear mixing in MEG data, using canonical correlations.
abstract: Cross-frequency interactions between distinct brain areas have been observed in connection with a variety of cognitive tasks. With electro- and magnetoencephalography (EEG/MEG) data, typical connectivity measures between two brain regions analyze a single quantity from each region within a specific frequency band; given the wideband nature of EEG/MEG signals, many statistical tests may be required to identify true coupling. Furthermore, because of the poor spatial resolution of activity reconstructed from EEG/MEG, some interactions may actually be due to the linear mixing of brain sources.
  
  
  
  In the present work, a method for the detection of cross-frequency functional connectivity in MEG data using canonical correlation analysis (CCA) is described. We demonstrate that CCA identifies correlated signals and also the frequencies that cause the correlation. We also implement a procedure to deal with linear mixing based on symmetry properties of cross-covariance matrices.
  
  
  
  Our tests with both simulated and real MEG data demonstrate that CCA is able to detect interacting locations and the frequencies that cause them, while accurately discarding spurious coupling.
  
  
  
  Recent techniques look at time delays in the activity between two locations to discard spurious interactions, while we propose a linear mixing model and demonstrate its relationship with symmetry aspects of cross-covariance matrices.
  
  
  
  Our tests indicate the benefits of the CCA approach in connectivity studies, as it allows the simultaneous evaluation of several possible combinations of cross-frequency interactions in a single statistical test.
authors.affiliation: Department of Telecommunications and Control Engineering, University of São Paulo, São Paulo, Brazil. Electronic address: juan@lcs.poli.usp.br.
authors.forename: Juan L P
authors.initials: JL
authors.lastname: Soto
authors.affiliation: Brain Dynamics and Cognition Team, Lyon Neuroscience Research Center, INSERM U1028 - CNRS UMR5292 - Lyon University, Lyon, France.
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Lachaux
authors.affiliation: McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University, Montreal, Canada.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Baillet
authors.affiliation: Department of Psychology, University of Montreal, Montreal, Canada.
authors.forename: Karim
authors.initials: K
authors.lastname: Jerbi
mesh_terms: D001921:Brain / Q000502:physiology; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D015225:Magnetoencephalography / Q000379:methods*; D015999:Multivariate Analysis; D009434:Neural Pathways / Q000502:physiology; D012372:ROC Curve; D012815:Signal Processing, Computer-Assisted
keywords: Canonical correlation analysis; Cross-frequency coupling; Functional connectivity; Linear mixing correction; Magnetoencephalography (MEG); Multivariate analysis