[FieldTrip] fieldtrip Digest, Vol 119, Issue 14
RICHARDS, JOHN
RICHARDS at mailbox.sc.edu
Thu Oct 15 16:17:58 CEST 2020
Jan-Mathijs
Thanks for the explanation. That is helpful.
John
***********************************************
John E. Richards
Carolina Distinguished Professor
Department of Psychology
University of South Carolina
Columbia, SC 29208
Dept Phone: 803 777 2079
Fax: 803 777 9558
Email: richards-john at sc.edu
https://jerlab.sc.edu
*************************************************
-----Original Message-----
From: Schoffelen, J.M. (Jan Mathijs) <jan.schoffelen at donders.ru.nl>
Sent: Thursday, October 15, 2020 9:31 AM
To: FieldTrip discussion list <fieldtrip at science.ru.nl>
Cc: CONTE, STEFANIA <CONTES at mailbox.sc.edu>; Santiago Morales Pamplona <moraless at umd.edu>; Marco Mcsweeney <mmcsw1 at umd.edu>; RICHARDS, JOHN <RICHARDS at mailbox.sc.edu>
Subject: Re: fieldtrip Digest, Vol 119, Issue 14
Dear John,
Let’s consider the COV to actually be the matrix product of some data matrix X, multiplied by itself, transposed X'.
In that case (which is in general true), the quantity filt*COV*filt’ can be also thought of as (filt*X)*(filt*X)’.
In other words, when we do an svd on filt*COV*filt’ we get the same left singular vectors (u matrix) as when we would do an svd on filt*X. For a dipole at a given location, the product filt*X reflects the dipole moment as a function of time, expressed as a 3-by-Ntimepoint matrix (which can be ‘unaveraged data’, an ERP, or something else). Rotating these data with the u’ matrix will align this matrix to a coordinate system that has the variance (over time) maximized in the first row, and has progressively less variance in the second and third rows. In other words, sandwiching the COV between the filter, before doing the svd, and subsequently taking the first component, estimates the orientation of the dipole that maximizes the variance over time for that dipole. In an ERP setting, I could imagine that one is interested in maximizing the variance of the average-across-trials, rather than maximizing the average variance across the individual trials. Thus, one could use as a covariance matrix the covariance computed on the grand mean ERP, estimate the orientation, and then use the source time courses projected onto that orientation to compare the ERPs across experimental conditions. In a ‘continuous setting’, e.g. a situation where one wants to post-process the reconstructed time series in terms of band-limited power dynamics, I could imagine that it makes more sense to use as a covariance matrix the covariance of the unaveraged (band-limited) data.
So, more specifically tapping into what you wrote, I’d not recommend to use a prestimulus cov to estimate optimal dipole orientation, because you are then optimizing the orientation for the variance in the ’noise’.
Best wishes,
Jan-Mathijs
> On 15 Oct 2020, at 14:48, RICHARDS, JOHN <RICHARDS at mailbox.sc.edu> wrote:
>
> Jan-Mathijs (or others)
>
> Thanks for your answers. I still have one question to be answered.
>
> If we use the method where we do the SVD step on the filter, then calculating the source elements from any dataset will use the same projection orientation.
>
> What is the rationale for including the COV in the filter*COV*filter'? Does this intend to modify the orientation by the directionality of the noise? This makes sense to me if this is an ERP experiment. I have used this in various FT functions by choosing the prestimulus as a baseline for noise and the COV is from the prestimulus; then use the resulting filter (filter * COVprestimulus * filter') for the source analysis of the stimulus data. However, in the current analysis we are doing we have a continuous EEG context--don't really have a baseline for estimation the noise. We also have several conditions and different transformations of the data before the source calculation. What would we be gaining by adding the svd(filter*COV*filter') step to the SVD, over just using the svd(filter)? I think the crux of my question is what is being accomplished by using the COV in the projection calculation?
>
> Thanks for your help.
>
> John
>
> ***********************************************
> John E. Richards
> Carolina Distinguished Professor
> Department of Psychology
> University of South Carolina
> Columbia, SC 29208
> Dept Phone: 803 777 2079
> Fax: 803 777 9558
> Email: richards-john at sc.edu
> https://jerlab.sc.edu
> *************************************************
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