[Mne_analysis] tf_mixed_norm and PCA option?

[Per Arnold Lysne]

Hi Alex,

    I think I misunderstand your response because it seems like two different items arise here:

    First, as your publications mention, the model requires that the noise terms be Gaussian white noise. The whitening process is based on the noise covariance matrix and is designed to decorrelate the noise between different sensor channels and then to standardize the variance of these noise distributions. The noise covariance matrix itself is derived from either empty room measurements or combined periods of pre-stimulus measurement with the subject. In either case, these are resting states where we can assume the state of the system is stable and therefore can estimate these covariances over time. 

    Second is my question about the pca flag to tf_mixed_norm: is this doing a spatial pca on the post-stimulus data itself, or is this transformation also estimated from the pre-stimulus data? In the former case, I am concerned about stationarity (because the brain network is in a transient, dynamic state), but in the later it makes sense.

    Thanks for your patience with these questions,

-Per
________________________________________
From: mne_analysis-bounces at nmr.mgh.harvard.edu <mne_analysis-bounces at nmr.mgh.harvard.edu> on behalf of Alexandre Gramfort <alexandre.gramfort at telecom-paristech.fr>
Sent: Friday, October 3, 2014 3:14 AM
To: Discussion and support forum for the users of MNE Software
Subject: Re: [Mne_analysis] tf_mixed_norm and PCA option?

hi Per,

>     If I understand you correctly, the PCA is being used in a data reduction capacity across the sensors, or the spatial dimension. In which case the sensor values at each sample represent the variables (204 in your example), and the samples in time represent the observations.

yes

> The outcome of this are the component scores (80) at each sample which become the new timecourses.

yes. You can see this step as a signal space projection ie. projection
onto the dimensions
which contain the most signal in the evoked data.

>     The motivation for tf-mxne is do avoid assuming temporal stationarity of the neural sources. By performing the PCA solution over time, i.e. assuming that all of the observations come from the same population, do we not make the same error? This seems very similar to the traditional method of estimating the parameters of an MVAR system over time?

this spatial projection is applied to the data and the gain matrix. If
the data was full rank it would be a rotation and the solution of
TF-MxNE would be exactly the same and the L2 data fit term is
invariant by rotation.

clearer?

Alex

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