[FieldTrip] sloreta doest not get unity source variance

Tue Oct 11 09:37:58 CEST 2022

Dear Jan-Mathjis,

Thank you very much for your quick reply.

I really appreciate your technical comment. I think that I had some confusion of some terms. I think the equation(15) refers the prior variance-covariance matrix of the source, which was set to be an identity matrix. Then it was estimated scalp covariance matrix taking into account this consideration (eq 16). Then Then it was reformulated the estimated ‘prior’ variance-covariance matrix (eq 17). I thought that the estimated ‘prior’ variance-covariance matrix should be identity matrix, but I found that this term in eq17 does not meet the criteria regardless of the hypothesis eq15. 

My question if the estimated ‘prior’ variance-covariance matrix in eq 17 should be identity matrix from theoretical point of view.

Best regards

*******************

Yiyao Ye Lin

C/Camino de Vera SN

Universidad Politècnica de València

Departamento de Ingeniería Electrónica, Ed. 7F

46022, València

València

Ext. 76026 

De: fieldtrip <fieldtrip-bounces at science.ru.nl> En nombre de Schoffelen, J.M. (Jan Mathijs) via fieldtrip
Enviado el: martes, 11 de octubre de 2022 8:39
Para: FieldTrip discussion list <fieldtrip at science.ru.nl>
CC: Schoffelen, J.M. (Jan Mathijs) <janmathijs.schoffelen at donders.ru.nl>
Asunto: Re: [FieldTrip] sloreta doest not get unity source variance

Hi Yiyao, 

Thank you for your attempts at clarifying your doubts. I still don’t understand what the confusion is. I doubt whether many people have made the effort of opening the word document, but I did so, and cannot make much out of it. It’s a bit too confusing to me to try and map all the different variable name conventions (paper versus code) onto each other. In general, however, I don’t understand why you think that the ’source covariance matrix’ should be an identity matrix, which source covariance matrix you are referring to, and which combination of variables in the code you would expect to yield an identity matrix. 

As in any distributed source model, the source reconstructed variance-covariance matrix (i.e. filter * C * filter’) surely will not be an identity matrix. This would namely imply that the variance of each of the reconstructed sources is the same (and has a value of 1). On the other hand, it could be that there’s some confusion with respect to the ‘prior’ that is used for the computations, i.e. the (implicit) identity matrix that is used for the computation of the Gram-matrix (lf * lf’) -> this can be thought of as (lf * S * lf’), with S being the prior variance-covariance matrix of the sources, which is often conveniently set to be an identity matrix. 

Note that the FieldTrip code for the sloreta implementation has originally been contributed by Sarang Dalal, and this is based on the formulation as described in the Sekihara & Nagarajan book (adaptive spatial filters for electromagnetic brain imaging). It would therefore be better to check the code against the description in the book, rather than to the paper that you attached to the e-mail. And subsequently you might want to check the exposition in the book, with the paper.

Good luck and best wishes,

Jan-Mathijs

On 8 Oct 2022, at 16:56, Yiyao Ye Lin via fieldtrip <fieldtrip at science.ru.nl <mailto:fieldtrip at science.ru.nl> > wrote:

Dear researchers,

I am sorry to not formulate correctly the question. In the attached file I attempted to explain my doubt. Hope that you can understand my question this time and can help me to better understand sLortea. 

What I can not understand is that sLoreta is standardized minimum norm solution, the source covariance matrix should be identity matrix. However, I could not check this. I think that there be something that I did not understand correctly.

Thank you very much for your attention

Best regards

*******************

Yiyao Ye Lin

C/Camino de Vera SN

Universidad Politècnica de València

Departamento de Ingeniería Electrónica, Ed. 7F

46022, València

València

Ext. 76026 

De: fieldtrip <fieldtrip-bounces at science.ru.nl <mailto:fieldtrip-bounces at science.ru.nl> > En nombre de Schoffelen, J.M. (Jan Mathijs) via fieldtrip
Enviado el: jueves, 6 de octubre de 2022 8:09
Para: FieldTrip discussion list <fieldtrip at science.ru.nl <mailto:fieldtrip at science.ru.nl> >
CC: Schoffelen, J.M. (Jan Mathijs) <janmathijs.schoffelen at donders.ru.nl <mailto:janmathijs.schoffelen at donders.ru.nl> >
Asunto: Re: [FieldTrip] sloreta doest not get unity source variance

Hi Yiyao, 

To be honest, I don’t understand your question. And it is not clear what the problem is. 

Can you please have a look at the documentation below and reformulate your question, so that the readership of the list can constructively think along?

 <https://www.fieldtriptoolbox.org/faq/how_to_ask_good_questions_to_the_community/> https://www.fieldtriptoolbox.org/faq/how_to_ask_good_questions_to_the_community/

 <https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002202> https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002202

 <http://www.catb.org/esr/faqs/smart-questions.html> http://www.catb.org/esr/faqs/smart-questions.html

Best wishes,

Jan-Mathijs

On 5 Oct 2022, at 18:49, Yiyao Ye Lin via fieldtrip < <mailto:fieldtrip at science.ru.nl> fieldtrip at science.ru.nl> wrote:

Dear researchers,

After reading the sLoreta theory, I attempted to understand the sloreta implementation detail. I attempted to obtain the source covariance matrix, and I could not get the expected unit variance. To do this, I attempted to calculate by two ways:

a)       lf'*invG*lf after line 268 of ft_inverse_sloreta

b)      lf(:,ii)'*invG*lf(:,ii) at line 267 of ft_inverse_sloreta

For this, I used EEG signal with average reference. 

What's wrong? How can the unity variance of source variance matrix? 

Best regards

*******************

Yiyao Ye Lin

C/Camino de Vera SN

Universidad Politècnica de València

Departamento de Ingeniería Electrónica, Ed. 7F

46022, València

València

Ext. 76026 

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