[FieldTrip] Different way of calculating the covariance for LCM
Yuval Harpaz
yuvharpaz at gmail.com
Thu Mar 24 10:41:02 CET 2011
Dear Michael, Jean-Michel and FieldTrip users.
To my experience and understanding it does matter if you first asses the
covariance and then average or the other way around.
First, as far as my understanding goes, if we have some brain activity such
as alpha, which is not phase locked to the event then in the covariance will
not 'catch' too much covariability there after averaging, compared to
unaveraged data where it should. if the process of calculating covariance
and averaging id linear then I must be wrong here.
anyway, beamforming on averaged and unaveraged base covariance matrices give
different results in fieldtrip. this is because the covariance matrices are
not the same with or without averaging.
I ran the following test to check it all. I took the same structure as in
the example above, and I tested the covariance matrix after
1. running it with cfg.keeptrials='yes'; then I averaged (across trials)
the 3d matrix to get 2d matrix.
2. running it without keeping trials; it gives a 2d covariance matrix.
3. averaging the data with this command: mD1st=ft_timelockanalysis([],D1st).
no filters baseline correction or anything.
then I ran timelockanalysis again to compute the covariance (no keeptrials
of course).
the result is that 1. and 2. gave the same result but not 3.
It seems to me that the process is not linear, at least in fieldtrip, and
that one doesn't need to specify keeptrials for unaveraged data because it
calculates the covariance for every trial and then averages the cov
matrices.
If I am wrong here I will appreciate further help with this issue.
thanks
yuval
On 23 March 2011 21:27, Michael Wibral <michael.wibral at web.de> wrote:
>
> 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
>
>
>
>
>
> _______________________________________________
> 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
>
>
>
>
> _______________________________________________ fieldtrip mailing list [
> fieldtrip at donders.ru.nl] [
> http://mailman.science.ru.nl/mailman/listinfo/fieldtrip]
>
>
>
>
>
>
>
>
>
>
> _______________________________________________
> 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
>
>
>
> _______________________________________________ fieldtrip mailing list [
> fieldtrip at donders.ru.nl] [
> http://mailman.science.ru.nl/mailman/listinfo/fieldtrip]
>
>
>
> --
>
>
>
> <!--
> @page { size: 21cm 29.7cm; margin: 2cm }
> P { margin-bottom: 0.21cm }
> -->
> 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
>
>
>
>
>
>
> _______________________________________________
> 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*
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20110324/6227d85a/attachment-0002.html>
More information about the fieldtrip
mailing list