Beamforming across trials not time

[Robert Oostenveld]

Hi Marie

On 27 Feb 2007, at 17:07, Marie Smith wrote:
> Just to be clear, the covariance is always computed for single
> trials and then either averaged across trials (keeptrials = 'no')
> or kept separate (keeptrials = 'yes') to be averaged in the
> beamforming step?

correct. The averaging in the beamforming step is optional, you can
also beam single-trial (rawtrials=yes in sourceanalysis). Or you can
beam the single trial ERF timecourses using a filter constructed from
the average covariance (requires a first run of sourceanalysis with
rawtrials=no and keepfilters=yes, and a second run with
cfg.grid=previous_source and rawtrials=yes).

> At no time is the data averaged and then the covariance computed on
> this one average trial?

correct. There is no averaging of the ERFs over trials prior to
computing the covariance. It is possible to "average" over time
within a single trial by boxcar smoothing.

>> Regarding your 2 -> that can be done with step "a". The smoothing
>> can be done with a boxcar, and the selection of samples of
>> interest is done in our step "e".
>
> I'm not sure that this is the same thing. I am smoothing the data
> across trials at each time point, where i think time lock analysis
> is smoothing the data in each trial across time points.

Oh, I thought you smoothed over time. Then indeed it is quite
different. Averaging (smoothing) over a subset of M trials prior to
computing the covariance in the most extreme case (M=Ntrials)
corresponds to taking the covariance of the ERF, right? And in the
other most extreme case (M=1) it resembles to the approach
implemented in timelockanalysis. Am I correct?

In the M=Ntrials case, the covariance matrix probably would be rather
rank deficient (if the time window is short), and the data covariance
would include little or no noise structure (data covariance = signal
covariance + noise covariance). But the same applies to induced
activity, i.e. that would also not be present in your covariance, so
it stresses the effect of the evoked at the expense of the induced
activity. I can't tell whether that is good or bad, that depends on
your data and research question.

>> That means that in the current implementation, the data within
>> each trial is baseline subtracted (over the whole timewindow)
>> prior to computing the covariance within that trial.
>
> So, if I were to look at only one time point across trials,
> implementing things in fieldtrip would always result in a zero
> value (as the mean == the data value here)?

yes, that is correct.

So I would phrase the approach that you suggest as a "resampling
approach", in which you compute the covarioance over M subsets of
trials, in which each subset is averaged (c.f. bootstraping). You
mentioned in your previous mail that "it has  been suggested". Could
you give a reference? And how does it behave in your data?

best regards,
Robert

PS we can discuss it in detail during my visit