# Coherence reference channel for statistical analysis

Stanley Klein sklein at BERKELEY.EDU
Tue Nov 9 10:17:35 CET 2010

```Rodolphe, one interesting option for dealing with the EEG problem of
reference electrode for coherence is to use Laplacians ("current sources")
for each electrode. You may be interested in the pair of papers Winter, et
al. J Neuroscience Methods 166 (2007) and Srinivasan, et al. (Statistics in
Medicine, 26 2007) that my colleague Jian Ding did with Winter, Srinivasan
and Nunez.  They compare Laplacian to regular reference for coherence.

I would think that a good approach would be to do it with several types of
very different references and compare the differences in coherence.

I'm going to be giving a talk on coherence next week at the Neuroscience
meeting in San Diego. I'm going to advocate measuring coherence on
unfiltered data, but using VERY broad-bandwidth Hilbert pair wavelets, very
local in time for doing the coherence. I have several questions on this:
1) Does anyone know whether very broad bandwidth Hilbert pair wavelets have
been used before? In my mind the locality in time is a useful complement to
alternative approaches.

2) Does anyone know whether it has been shown that Morlet and other usual
wavelets are not very pretty when only 1 to 1.5 cycles are present. We use
what we call Cauchy wavelets.

3) Is there a good reference for the connection of cross-correlation to
unnormalized coherence?
Let me define what I mean:
CC(e1, e2, del) = v(e1, t) v(e2,t-del)           (1)       (using Einstein
summation convention
Coh(e1, e2, f, n) = V(e1, t,  f, n) V*(e2, t, f, n) , (2) Einstein again
implying sum on t.
where v is the raw EEG, V is the wavelet transform
V(e, t, f, n) = v(e, t+del) * W(del, f, n),      (3)
where   W(t, f, n) = 1/(1+ i f t)^n               (4)  for complex, Cauchy
Hilbert pair wavelet
e1, e2 are the electrodes (unreferenced preferably with referencing to be
done at end)
t is t, and del is the time shift
f is the peak frequency of the wavelet
n specifies the bandwidth of the wavelet (sqrt(n) is the number of half
cycles)

The connection between CC and Coh would be:
Coh(e1, e2, f, n) = CC(e1, e2, t+del) *W(del, f', n')   (5)
where  f' and n' are simply connected to f and n but I'm still playing with
this to validate it all.

I'm very interested in learning whether Eq. 5 connecting unnormalized
coherence to cross-correlation is familiar, especially with a pretty closed
form time domain expression for the kernel W(del,f',n') in Eq. 5. The SfN
meeting is soon, which is why I'm eager to learn whether Eq. 5 is well
known. Pretty Hilbert pair filters like W are rare, so I'd be somewhat
surprised if Eq. 5 is commonly used. But I'm new to this coherence business
so I wouldn't be super surprised.

I'd be interested in any feedback. I'll also be happy to meet with anyone
interested in coherence at the SfN meeting or at the preceding
satellite meeting on "Resting State" before SfN.
Stan

On Mon, Nov 8, 2010 at 3:48 PM, Rodolphe <batrod at gmail.com> wrote:

> Dear Fieldtrip users,
>
> i take the liberty to ask again my question to you, as i still didnt find a
> solution.
> I used ft_connectivityanalysis fuction to get coherence values between
> every channels.
> I simply wonder how to select a reference channel to make statistical
> analysis , like when you can select a reference channel to make a
> Topographic plot on coherence values.
>
> Thanks a lot for your help,
>
> Rodolphe.
>
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