[FieldTrip] Different way of calculating the covariance for LCM
Michael Wibral
michael.wibral at web.de
Wed Mar 23 20:27:07 CET 2011
Dear Fieldtrip users interested in covariance computation,
dear Yuval,
I would like to my opinion on covariance computation up for discussion here.
Covariance is a (bi-)linear measure (like an inner (scalar) product) and should in principle be commutative mathematically with other linear procedures as long as you respect the distributative law from elementary math. Hence,
(1) averaging single trial covariances or computing the covariance of concatenated trials should give the same result if a am not mistaken. In these two approaches samples from your two time course are in the end multiplied with each other one by one. Whichever route of these two you take does not matter at all.
This holds as long as you treat baseline correction and filtering (!) exactly the same way in both cases - otherwise you'll additionally get the baseline covariance over trials as a term in the covariance matrix or filtering related differences. This latter point maybe important if you post hoc decide on a band width to confine your beamformer analysis to and do not go back to the raw data for the band pass filtering.
(2) In contrast, when you compute covariance from a precomputed trial average then every sample at time t in one trial on channel A will in the course of the calculations be implicitely multiplied with samples at time t at EVERY other trial on channel B. So this covariances focuses on covariance structures that are consistent irrespective of the correct pairings of trials.
It's a little bit like first computing the power spectrum and averaging to get total activity (induced+evoked) - this would correspond to procedure (1) , or first averaging and then computing spectral power in order to get the power of evoked activity alone - this would correspond to procedure (2).
This said, when you're interested in the sources of all task related oscillatory activity - not only the activity phase locked to a stimulus you should pick option (1).
Please let me know If I overlooked something important.
Michael
---------------------
Von: "Jean-Michel Badier" <jean-michel.badier at univmed.fr>
Gesendet: Mar 23, 2011 9:42:53 AM
An: "Email discussion list for the FieldTrip project" <fieldtrip at donders.ru.nl>
Betreff: Re: [FieldTrip] Different way of calculating the covariance for LCM
Thanks Yuval,
Le 22/03/11 10:55, Yuval Harpaz a écrit :
So just run the commands on an unaveraged dataset.
Yes but that would be correct if there was only one trial in the data set (see the message from Luisa).
Another option to consider is the one used by Dr. Robinson when performing SAMerf (we have his tool [here], works for our 4D machine).
Thanks for it I will test it.
The idea is to calculate the covariance on all trials, calculate weights by this covariance (keep filter in LCMV) and then apply these weights on the averaged data. I found it useful because the covariance is better for longer datasets, and the averaging in the end increases the signal to noise ratio. I do not know exactly how to do it in fieldtrip.
On 22 March 2011 10:43, Jean-Michel Badier <[jean-michel.badier at univmed.fr]> wrote:
Dear Yuval,
I have to admit that I did not look at the matlab routines.
In item 2 I suppose that the covariance is calculated for each trial then averaged. In item 3 I would like to calculate the covariance from all the signal (the trials being concatenated).
Jean-Michel
Le 22/03/11 05:47, Yuval Harpaz a écrit :
Dear Jean Michel
As far as I know you can do it on an averaged data structure (item 1) or do the same with the data structure before averaging (3). I did not understand what you meant by 2.
Yuval
On 21 March 2011 22:58, Jean-Michel Badier <[jean-michel.badier at univmed.fr]> wrote:
Dear fieldtrip users,
There are different ways of estimating the covariance for LCMV calculation.
If I am correct:
1. As suggested in one of the tutorial one can apply the calculation of the covariance directly on the average data (for the different periods of interest that are at least a base line and the period of interest).
2. Estimate the covariance from the average of the covariance rather than the covariance of the average using cfg.keeptrials = "yes"
3. Estimate the covariance from the whole trials concatenated together.
Is there an easy way to do that in fieldtrip (beside create a new data set of one trial constituted of all the trials)?
Thanks
Jean-Michel
-- Jean-Michel Badier PhD
Laboratoire de MagnétoEncéphaloGraphie INSERM U751. Aix Marseille Université 33 (0)4 91 38 55 62 [jean-michel.badier at univmed.fr]
Service de Neurophysiologie Clinique. CHU Timone 264 Rue Saint-Pierre, 13005 Marseille-France
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Y.Harpaz
a link to the BIU MEG lab:
[http://faculty.biu.ac.il/~goldsa/index.html]
" Why, Dan," ask the people in Artificial Intelligence, "do you waste your time conferring with those neuroscientists? They wave their hands about information processing and worry about where it happens, and which neurotransmitters are involved, and all those boring facts, but they haven't a clue about the computational requirements of higher cognitive functions." "Why," ask the neuroscientists, "do you waste your time on the fantasies of Artificial Intelligence? They just invent whatever machinery they want, and say unpardonably ignorant things about the brain." The cognitive psychologists, meanwhile, are accused of concocting models with neither biological plausibility nor proven computational powers; the anthropologists wouldn't know a model if they saw one, and the philosophers, as we all know, just take in each other's laundry, warning about confusions they themselves have created, in an arena bereft of both data and empirically testable theories. With so many idiots working on the problem, no wonder consciousness is still a mystery. Philosopher Daniel Dennet, consciousness explained, pp. 225
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_______________________________________________
fieldtrip mailing list
[fieldtrip at donders.ru.nl]
[http://mailman.science.ru.nl/mailman/listinfo/fieldtrip]
--
Y.Harpaz
a link to the BIU MEG lab:
[http://faculty.biu.ac.il/~goldsa/index.html]
" Why, Dan," ask the people in Artificial Intelligence, "do you waste your time conferring with those neuroscientists? They wave their hands about information processing and worry about where it happens, and which neurotransmitters are involved, and all those boring facts, but they haven't a clue about the computational requirements of higher cognitive functions." "Why," ask the neuroscientists, "do you waste your time on the fantasies of Artificial Intelligence? They just invent whatever machinery they want, and say unpardonably ignorant things about the brain." The cognitive psychologists, meanwhile, are accused of concocting models with neither biological plausibility nor proven computational powers; the anthropologists wouldn't know a model if they saw one, and the philosophers, as we all know, just take in each other's laundry, warning about confusions they themselves have created, in an arena bereft of both data and empirically testable theories. With so many idiots working on the problem, no wonder consciousness is still a mystery. Philosopher Daniel Dennet, consciousness explained, pp. 225
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Jean-Michel Badier
Laboratoire de MagnétoEncéphaloGraphie
INSERM U751. Aix Marseille Université
33 (0)4 91 38 55 62
[jean-michel.badier at univmed.fr]
Service de Neurophysiologie Clinique. CHU Timone
264 Rue Saint-Pierre, 13005 Marseille-France
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