# [FieldTrip] ft_connectivityanalysis and PLV formula

jan-mathijs schoffelen jan.schoffelen at donders.ru.nl
Mon Jul 15 10:43:07 CEST 2013

```Hi Manuel,

The first formula is correct, the second isn't.
Hint: when working with the complex representation in the second formula you should use a multiplication, rather than a subtraction, and take the negative angle for the second signal.

In other words

exp(1i.*angle(x)) .* exp(-1i.*angle(y)).

This is the same as:

exp(1i.*(angle(x)-angle(y))).

Hope this helps,

Jan-Mathijs

On Jul 8, 2013, at 3:32 PM, Manuel Mercier wrote:

> Dear Fieldtrip Community
> I am still stuck with the implementation of PLV. To be sure that I understand properly the principle of Phase Locking Value, I wrote a code to compute it. That code (see below) gave me the same results as ft_connectivityanalysis.
> plv = squeeze(abs(mean(exp(1i*(angle(data.fourierspctrm(:,electrodes_1,:,:)) -angle(data.fourierspctrm(:,electrode_2,:,:)))),1)));
> (data.fourierspctrm being produced by ft_freqanalysis).
>
> However, I then realized that the subtraction between the two angles should be done in the complex plane as in:
> plv = squeeze(abs(mean(exp(1i*(angle(exp(1i*(angle(data.fourierspctrm(:,electrodes_1,:,:)))) - exp(1i*(angle(data.fourierspctrm(:,electrode_2,:,:))))))),1)));
>
> I doubt that PLV computed through FT is wrong, but then I am circumspect since the first formula is somewhat no correct and give the same results a as ft_connectivityanalysis.
> I went to FT code and got confused by the way ft_connectivity_corr use the cross spectrum to compute PLV.
> I would greatly appreciate if someone could tell me where I am missing/misunderstanding something.
> Thanks you for your help,
>
> Manuel
>
>
>
> Manuel Mercier, PhD
> Research Fellow
>
> Cognitive Neurophysiology Laboratory,
> Childrenâ€™s Evaluation and Rehabilitation Center (CERC),
> Departments of Pediatrics and Neuroscience
> Albert Einstein College of Medicine,
> 1225 Morris Park Avenue
> Bronx , NY 10461
>
> phone: +1 (718) 862 1859
> fax: +1 (718) 862 1807
> From: fieldtrip-bounces at science.ru.nl [fieldtrip-bounces at science.ru.nl] on behalf of Manuel Mercier [manuel.mercier at einstein.yu.edu]
> Sent: Friday, June 28, 2013 4:43 PM
> To: fieldtrip at science.ru.nl
> Subject: [FieldTrip] PLV formula
>
> Dear Fieldtripers
> Sometime ago I wrote for myself a function that was computing PLV and some related non parametric statistics.
> (Phase Locking Value as define as the mean across trials of the phase angle difference recorded at two loci ; based on Lachaux et al., 1999, HBM).
> I implemented PLV in matlab using the following formula:
> plv = squeeze(abs(mean(exp(1i*(angle(data.fourierspctrm(:,cmb(1),:,:)) ...
>                                                 -angle(data.fourierspctrm(:,cmb(2),:,:)))),1)));
> with cmb(1) and cmb(2) being the indices of the electrodes of interest (between which PLV is computed).
> I compared my results with the ft_connectivityanalysis function from Fieldtrip and the results were exactly the same.
> So far so good.
>
> But I recently went back to my code, and I was a little bit confused.
> Since I was dealing with angles, I though that the best way to do the subtraction should be done in the complex plane
> Like:
> plv = squeeze(abs(mean(exp(1i*(angle(exp(1i*(angle(data.fourierspctrm(:,cmb(1),:,:)))) ...
>                                                         - exp(1i*(angle(data.fourierspctrm(:,cmb(2),:,:))))))),1)));
> (for instance if the two angles: pi/2 and -pi/2 the direct subtraction will give pi,
> whereas in the complex plan it will be pi/2 - with the norm x2).
>
> The result I got with this code is obviously different from the previous one, and what I got from Fieldtrip.
> I went back to the archive of the mailing list but didn't find a clear answer to my point. Does anyone can enlighten me ?
> Thanks !
>
> Manuel
>
>
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> fieldtrip at donders.ru.nl
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Jan-Mathijs Schoffelen, MD PhD

Donders Institute for Brain, Cognition and Behaviour,
Centre for Cognitive Neuroimaging,

Max Planck Institute for Psycholinguistics,
Nijmegen, The Netherlands

J.Schoffelen at donders.ru.nl
Telephone: +31-24-3614793

http://www.hettaligebrein.nl

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