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@ARTICLE{Engemann:186311,
      author       = {Engemann, Denis and Gramfort, A.},
      title        = {{A}utomated model selection in covariance estimation and
                      spatial whitening of {MEG} and {EEG} signals.},
      journal      = {NeuroImage},
      volume       = {108},
      issn         = {1053-8119},
      address      = {Orlando, Fla.},
      publisher    = {Academic Press},
      reportid     = {FZJ-2015-00387},
      pages        = {328–342},
      year         = {2015},
      abstract     = {Magnetoencephalography and electroencephalography (M/EEG)
                      measure non-invasively the weak electromagnetic fields
                      induced by post-synaptic neural currents. The estimation of
                      the spatial covariance of the signals recorded on M/EEG
                      sensors is a building block of modern data analysis
                      pipelines. Such covariance estimates are used in
                      brain–computer interfaces (BCI) systems, in nearly all
                      source localization methods for spatial whitening as well as
                      for data covariance estimation in beamformers. The rationale
                      for such models is that the signals can be modeled by a zero
                      mean Gaussian distribution. While maximizing the Gaussian
                      likelihood seems natural, it leads to a covariance estimate
                      known as empirical covariance (EC). It turns out that the EC
                      is a poor estimate of the true covariance when the number of
                      samples is small. To address this issue the estimation needs
                      to be regularized. The most common approach downweights
                      off-diagonal coefficients, while more advanced
                      regularization methods are based on shrinkage techniques or
                      generative models with low rank assumptions: probabilistic
                      PCA (PPCA) and factor analysis (FA). Using cross-validation
                      all of these models can be tuned and compared based on
                      Gaussian likelihood computed on unseen data.We investigated
                      these models on simulations, one electroencephalography
                      (EEG) dataset as well as magnetoencephalography (MEG)
                      datasets from the most common MEG systems. First, our
                      results demonstrate that different models can be the best,
                      depending on the number of samples, heterogeneity of sensor
                      types and noise properties. Second, we show that the models
                      tuned by cross-validation are superior to models with
                      hand-selected regularization. Hence, we propose an automated
                      solution to the often overlooked problem of covariance
                      estimation of M/EEG signals. The relevance of the procedure
                      is demonstrated here for spatial whitening and source
                      localization of MEG signals.},
      cin          = {INM-3},
      ddc          = {610},
      cid          = {I:(DE-Juel1)INM-3-20090406},
      pnm          = {572 - (Dys-)function and Plasticity (POF3-572)},
      pid          = {G:(DE-HGF)POF3-572},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000349618600033},
      pubmed       = {pmid:25541187},
      doi          = {10.1016/j.neuroimage.2014.12.040},
      url          = {https://juser.fz-juelich.de/record/186311},
}