# [FieldTrip] What is the data present in the covariance matrix after using ft_timelockanalysis

Nakhnikian, Alexander Alexander_Nakhnikian at hms.harvard.edu
Thu Jun 16 17:00:02 CEST 2016

```Hi Soujatta,

I hope I understand your question.

For demeaned data, the covariance is the expected value of sum(xy).  For data with finite mean, we have to get the expected value of sum(x-mu(x))*sum(y-mu(y)).  Removing the mean and trend doesn't have any impact on the denominators used to compute the unbiased estimate of E{sum(xy)}.  The unbiased covariance estimated between x and y for a given trial is sum(xy)/(N_times-1), where N _times is the number of time points in an epoch.  When averaging covariance matrices over multiple trials the denominator becomes N_trs-1.  I hope that helps.

Best,

Alexander

________________________________
From: fieldtrip-bounces at science.ru.nl <fieldtrip-bounces at science.ru.nl> on behalf of Soujata Borbaruah <s.borbaruah at student.utwente.nl>
Sent: Thursday, June 16, 2016 10:19:12 AM
To: fieldtrip, donders
Subject: [FieldTrip] What is the data present in the covariance matrix after using ft_timelockanalysis

Hello,

I want to calculate the covariance of the data I provide. In the function ft_timelockanalysis there is a portion where the covariance is being normalised over all trials by the total number of samples in all trials.

% normalize the covariance over all trials by the total number of samples in all trials
if strcmp(cfg.covariance, 'yes')
if strcmp(cfg.keeptrials,'yes')
for i=1:ntrial
if strcmp(cfg.removemean, 'yes')
covsig(i,:,:) = covsig(i,:,:) / (numcovsigsamples(i)-1);
else
covsig(i,:,:) = covsig(i,:,:) / numcovsigsamples(i);
end
end
else
if strcmp(cfg.removemean, 'yes')
covsig = squeeze(nansum(covsig, 1)) / (sum(numcovsigsamples)-ntrial);
else
covsig = squeeze(nansum(covsig, 1)) / sum(numcovsigsamples);

end
end
end

Please note that the cfg.removemean was selected as yes.

Can someone please explain what is the final data present in my covariance matrix?

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