Coherence calculation results

changki000 · December 9, 2019, 8:29pm

Hello,

I have a question regarding 'zero' coherence result for pairs that have different signals.
The way I calculated coherence is...

Connectivity - coherence N x N - time window (-1~6s (entire trial duration)) - use scouts (desikan-Killiany) and selected a total of 6 scouts - scout function (Mean) - scout function applied (Before) - Measure (Imaginary) - Max freq resolution (2Hz) - highest freq of interest (30 Hz)

Coherence results have 15 x 21 (15 = frequencies, 21 = all pairs ([scout1,scout1].....[scout6, scout6])

in self coherence calculations (for example [scout1,scout1], it gave zero coherence value.
but there are multi pairs that have '0's, not in self coherence results.

Can you explain whether different scout coherence calculation can be zero? and if so why?

Thank you,

Chang

Francois · December 10, 2019, 11:28am

The coherence of a signal with itself is one, and we don't care about this result. We set the diagonal to zero for making the visualization easier (colormap scales to the maximum value instead of always 1).

For the non-diagonal zeros, it means that the number of data points you used to estimate it is too low to assess that the coherence value obtained is meaningful. Check the code of function bst_cohn.m for more information about this parametric estimation:

github.com

brainstorm-tools/brainstorm3/blob/7d878aa7a9ebb44b03520cdbb169e84651669853/toolbox/connectivity/bst_cohn.m#L25


%    - waitMax       : Increase of the progress bar during the execution of this function

%

% Definitions:

%     Gxy:  cross-spectral density between x and y

%     Gxx:  autospectral density of x

%     Gyy:  autospectral density of y

%     Coherence function (C)            : Gxy/sqrt(Gxx*Gyy)

%     Magnitude-squared Coherence (MSC) : |C|^2 = |Gxy|^2/(Gxx*Gyy) = Gxy*conj(Gxy)/(Gxx*Gyy) 

%     Imaginary Coherence (IC)          : imag(C)^2 / (1-real(C)^2)

%

% Parametric significance estimation:  

%     When overlap=0%   [Syed Ashrafulla]

%        Kuramaswamy's CDF using using Goodman's formula from [1], simplified by the null hypothesis as in [2]

%        => pValues = (1 - MSC) .^ floor(signalLength / windowLength)

%     

%     When overlap=50%   [Ester Florin]

%        dof = 2.8 * nSamples * (1.28/(nFFT+1));   % According to Welch 1976

%        pValues = (1 - MSC) .^ ((dof-2)/2);       % Schelter [3] and Bloomfield [4]

%        While Matlab defines the coherence as the square of the cross sepctra divided by the product of the spectra, Bokil (2007)

%        and Schelter (2006) work with the square root within the correction and significance determination

%

changki000 · December 10, 2019, 12:34pm

Thank you for your response Francois.