# [FieldTrip] SVD and projectmom

RICHARDS, JOHN RICHARDS at mailbox.sc.edu
Tue Oct 13 21:06:20 CEST 2020

```I have a question about using “svd” to get a projection along the maximum variance in the filter.  The output of the leadfield matrix and eloreta, or other types of procedures, is a 3 x nvoxel x nchannels filter.  This can be multiplied by data to get the 3 x nvoxel x time data in source analysis.  To restrict the dipole direction to the max direction of the filter coefficients, the svd function is used.  For example, in ft_sloreta

%  'projectmom'       = project the dipole moment timecourse on the direction of maximal power, yes/no

[u, s, v] = svd(filt * Cy * ctranspose(filt));
mom = u(:,1); % dominant dipole direction
filt = (mom') * filt;

% estimate the instantaneous dipole moment at the current position
dipout.mom{i,1} = filt * dat;

in this case filter is 1 (maximal orientation) x nvoxel by channels, data is nchannels x time, so the output is nvoxel x time.

So I have a couple of questions.

1—What is the function of the covariance matrix in the following:
[u, s, v] = svd(filt * Cy * ctranspose(filt));

I understand in some of the source computations the covariance of the prestimulus ERP is used and this gives source output relative to the prestimulus covariance.  We usually have ERP data and use the covariance of the prestimulus period.  We also have EEG data rather than ERP data, and the data are not timelocked, so we have been using the entire interval of the data for the covariance matrix. I don’t understand the function of the covariance matrix in this formula, and if it is appropriate to use the entire interval for the covariance matrix.

We also make some transformations on the original data (sum over trials; or time-freq computations).  In these cases should we use the COV matrix from the original data, or recompute a new COV matrix for derivative data?

2—What about using this instead—which I have seen in a couple of place.  I think in the leadfield step one can use the maximum orientation rather than the 3-d orientation during the leadfield calculation, In this case the Cy would not be present, so this would be done instead

[u, s, v] = svd(filt);filter=u(:,1)’*filter;

Then later in the program doing the source analysis
dipout.mom{i,1} = filter * dat;
This would result in a 1 (max orientation) X nvoxel x time data.

Any suggestions or information would be helpful.

John

```