# [Eeglablist] A tentative issue in coherence calculation in EEGLAB for epoched data

Makoto Miyakoshi mmiyakoshi at ucsd.edu
Fri Jul 24 12:32:57 PDT 2015

```Dear Iman,

I finally tested it with the data.
First of all, the default 'type' option is 'phasecoher' (i.e. phase
coupling factor) and not 'coher' (which is linear coherence). Under this
condition, line 824 is executed, which is

coherres = sum( coherresout ./ abs(coherresout), 3) / g.trials;

where size(coherresout) is freq x time x trials. In this case,

mean(j1+j2+j3+j4+...+jn)

will produce the same results as

mean(mean(j1+j2)+mean(j3+j4)+...+mean(j(n-1)+jn))

I also tested 'coher' which you used. Under this condition, line 811 is
executed, which is

coherres = sum(alltfX .* conj(alltfY), 3) ./ sqrt( sum(abs(alltfX).^2,3) .*
sum(abs(alltfY).^2,3) );

where size(alltfX) is freq x time x trials, therefore same happens.

This concludes that you don't need to concern that '*calculate the
coherence for each trial first and then make the average across trials.'*

Iman, where does 'sum(fft(Y(i, :))/100' come from? newcrossf() does not use
Matlab fft().

Makoto

>  Hi,
>
> Suppose the data Y contains of 100 epochs and each epoch is 1000 points.
> Size Y is (100 x 1000). Now,  if we create X from Y and consider X as a (1
> , (100x1000) ) matrix then the fft(X) on the whole length of it is
> different that Sum(fft(Y(i, :))/100
>
> Best
>
> Iman
>
>
>
> *From:* Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
> *Sent:* Friday, July 24, 2015 10:53 AM
>
> *Cc:* EEGLAB List <eeglablist at sccn.ucsd.edu>; Loo, Sandra <
> SLoo at mednet.ucla.edu>; Scott Makeig <smakeig at ucsd.edu>; Chantelle C
> Kinzel <ckinzel at mednet.ucla.edu>; Michelini, Giorgia <
> giorgia.michelini at kcl.ac.uk>
> *Subject:* Re: A tentative issue in coherence calculation in EEGLAB for
> epoched data
>
>
>
> Dear Iman,
>
>
>
> If I understand the calculation correctly, you are comparing
>
>
>
> mean(j1+j2+j3+j4+...+jn)
>
>
>
> with
>
>
>
> mean(mean(j1+j2)+mean(j3+j4)+...+mean(j(n-1)+jn))
>
>
>
> They should produce the same results (if j is a data chunk, then they
> should have the same number of data points... which holds anyway)
>
>
>
> Do I understand the problem correctly?
>
>
>
> Makoto
>
>
>
> On Fri, Jul 24, 2015 at 10:43 AM, Iman Mohammad-Rezazadeh <
>
>  Hi Makoto ,
>
> It is about the stationarity of EEG signal and basically we cannot assume
> it is stationary for the long period of the concatenated data.
>
> Best,
>
> Iman
>
>
>
> *From:* Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
> *Sent:* Thursday, July 23, 2015 6:14 PM
>
>
> *Cc:* EEGLAB List <eeglablist at sccn.ucsd.edu>; Loo, Sandra <
> SLoo at mednet.ucla.edu>; Scott Makeig <smakeig at ucsd.edu>; Chantelle C
> Kinzel <ckinzel at mednet.ucla.edu>; Michelini, Giorgia <
> giorgia.michelini at kcl.ac.uk>
> *Subject:* Re: A tentative issue in coherence calculation in EEGLAB for
> epoched data
>
>
>
> Dear Iman,
>
>
>
> > coherres = sum(alltfX .* conj(alltfY), 3) ./ sqrt( sum(abs(alltfX).^2,3)
> .* sum(abs(alltfY).^2,3) );
>
>
>
> So 'sum(alltfX .* conj(alltfY), 3)' sums all data points? If so, as long
> as the number of data points distribute uniformly across all trials, the
> mean of the mean is the same as the grand mean. Am I wrong? Please correct
> me.
>
>
>
> Makoto
>
>
>
> On Thu, Jul 23, 2015 at 4:03 PM, Iman Mohammad-Rezazadeh <
>
>  Hi,
>
> The way the code scripted is to calculate the spectrum from the whole data
> at once
>
>
>
> [alltfX freqs timesout] = timefreq(X, g.srate, spectraloptions{:})
>
>
>
> Not each epoch separately and then make an average from them.  and yes in
> matters !
>
>
>
> Best,
>
> Iman
>
> *From:* Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
> *Sent:* Thursday, July 23, 2015 3:44 PM
> *Cc:* EEGLAB List <eeglablist at sccn.ucsd.edu>; Loo, Sandra <
> SLoo at mednet.ucla.edu>; Scott Makeig <smakeig at ucsd.edu>; Chantelle C
> Kinzel <ckinzel at mednet.ucla.edu>; Michelini, Giorgia <
> giorgia.michelini at kcl.ac.uk>
> *Subject:* Re: A tentative issue in coherence calculation in EEGLAB for
> epoched data
>
>
>
> Dear Iman,
>
>
>
> I ask you this without testing it, but does the order of the averaging
> process makes difference in results?
>
>
>
> Makoto
>
>
>
> On Mon, Jul 20, 2015 at 10:09 AM, Iman Mohammad-Rezazadeh <
>
>
>
> Hi EEGLABERs,
>
> I have been looking into ‘newcrossf’ function and the way it calculates
> coherence for epoched data. Basically, it uses the ‘timefreq’ function to
> calculate the time/frequency decomposition the data.  ‘timefreq’ function
> treats the epoched data as a continuous one:
>
>
>
> X = reshape(X, g.frame, g.trials);
>
> [alltfX freqs timesout] = timefreq(X, g.srate, spectraloptions{:});
>
>
>
> Y = reshape(Y, g.frame, g.trials);
>
> [alltfY] = timefreq(Y, g.srate, spectraloptions{:});
>
>
>
> and calculates the its spectrum using the whole data which is now
> concatenated version of all trials.  So, for each of channel’s pair (X and
> Y , for example) the spectrum is calculated as described above and then the
> joint time-freq decomposition is calculated for coherence value.
>
>
>
> coherres = sum(alltfX .* conj(alltfY), 3) ./ sqrt( sum(abs(alltfX).^2,3)
> .* sum(abs(alltfY).^2,3) );
>
>
>
> *However, similar to the ERSP concept, each trial/epoch might be different
> than others [because of perturbations in subjects’ mental status, mental
> fatigue, etc] and thus I think it is more appropriate to calculate the
> coherence for each trial first and then make the average across trials.*
>
>
>
> Any thoughts?
>
> Iman
>
>
>
>
>
>
>
>
>
> --
>
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>
>
>
>
>
> --
>
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>
>
>
>
>
> --
>
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>

--
Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego
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