# channel combinations for coherene

Jan Mathijs Schoffelen Jan.Schoffelen at FCDONDERS.RU.NL
Mon Jun 11 11:14:46 CEST 2007

```Dear Sameer,

I cannot cure memory problems for you. ;o) Even if you managed to achieve a
reduction in the amount of chncmbs, I think that you would still run into
problems.
Next to this, I feel that you should be a bit more specific about your
question. I assume that you would like to apply a kind of 'combineplanar' in
order to reduce the amount of chancmb's (in other words I guess you would
like to get rid of the _dV and _dH planar gradients, and collaps those into
one number). This is not at all trivial, since in a bivariate measure such
as coherence you are dealing with a cross-spectral density between 4
channels (which four and why?). In other words, you have a matrix which
looks like this:

Chn1_dh Chn1_dv Chn2_dh Chn2_dv
Chn1_dh      xx      xx       yx      yx
Chn1_dv      xx      xx       yx      yx
Chn2_dh      xy      xy       yy      yy
Chn2_dv      xy      xy       yy      yy

The xx and yy blocks contain info about the extent at which the activity
picked up by chn1 and chn2 respectively reflect a 'dipole' with fixed
orientation, the xy and yx blocks containt the cross-term information, and
are each other's conjugate (why was that again?).

If we consider coherence (or plv for the same argument) to be a measure
which quantifies the linear predictability of chn1 out of chn2 it might be
easy to see why actually we need to take into account the interaction
between the respective _dh and _dv gradiometers. If the _dh and _dv
component are linearly independent, then they explain independent parts of
the variance in the other channel. However, in practice this is of course
never the case, so the two planar gradients cannot be considered
independently. This means that it is generally not possible to sum the
coherence values in the xy blocks. If you want to summarize the sixteen
values in the matrix above, you have to come up with a clever strategy.

I could think of two strategies:

Either you reduce the amount of channels prior to doing the cross-spectral
density computation. This results in reducing the 4x4 csd-matrix back into a
2x2 matrix, in which the off-diagonal element gives you the chncmb csd
directly. This could for example be done by estimating the extent to which
the activity at a planar channel can be represented as a dipole with a fixed
orientation, and projecting the activity of the planar channel onto the
direction of the highest variance (basically doing a pca). This should be
applied to the fourier-data.
Another strategy could be to compute the frequency equivalent of canonical
correlation, which would yield the maximum of variance explained by an
optimal linear combination of the respective two planar gradient
combinations.

Yours,

Jan-Mathijs

-----Original Message-----
From: FieldTrip discussion list [mailto:FIELDTRIP at NIC.SURFNET.NL] On Behalf
Of Sameer Walawalkar
Sent: Sunday, June 10, 2007 7:58 PM
To: FIELDTRIP at NIC.SURFNET.NL
Subject: Re: [FIELDTRIP] channel combinations for coherene

Dear Jan,

{'MEG' 'MEG'} is too many channel combinations. I later run into memory
problems (I am trying to get Phase Lock Value and freqanalysis_mtmfft
needs a matrix of dimensions [number of trials X number of channel
combinations X number  of frequency points]). So I am trying to do only
that needs too much memory while computing phase lock values).

thanks,
sameer

On Sat, 9 Jun 2007, Jan Mathijs Schoffelen wrote:

> Dear Sameer,
>
> I am not sure whether I understood your question correctly, but couldn't
you just specify:
>
> cfg.channelcmb = {'MEG' 'MEG'} ?
>
> JM
>
> ----- Original Message -----
> From: Sameer Walawalkar <sameer at ANDREW.CMU.EDU>
> Date: Friday, June 8, 2007 10:31 pm
> Subject: [FIELDTRIP] channel combinations for coherene
>
>> Hello,
>>
>> how can I specify cfg.channelcmb for freqanalysis_mtmfft such that
>> it only
>> does planar-planar combinations or mag-mag combinations?
>>
>> thanks,
>> sameer
>>
>> ----------------------------------
>> The aim of this list is to facilitate the discussion between users
>> of the FieldTrip  toolbox, to share experiences and to discuss new
>> http://listserv.surfnet.nl/archives/fieldtrip.html and
>> http://www.ru.nl/fcdonders/fieldtrip.
>>
>
> ----------------------------------
> The aim of this list is to facilitate the discussion between users of the
FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG
http://listserv.surfnet.nl/archives/fieldtrip.html and
http://www.ru.nl/fcdonders/fieldtrip.
>
>

----------------------------------
The aim of this list is to facilitate the discussion between users of the
FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG