[Mne_analysis] tf_mixed_norm and PCA option?

[Alexandre Gramfort]

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