[Eeglablist] References on ICA algorighm; mixing matrix?

[Arnaud Delorme]

Dear Jim,

> Hello.  We wish to know more about the algorithm used by EEGLAB to do 
> ICA.  Looking at the reference list for "EEGLAB: an open source 
> toolbox for analysis of single-trial EEG dynamics including 
> independent component analysis," it seems the best sources are the 
> chapters in "Advances in Neural Information Processing Systems," which 
> we unfortunately don't have immediate access to. 

There are a number of ressources on the Internet about ICA (some of them 
listed below).

http://sccn.ucsd.edu/~arno/indexica.html (no equations)
http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/ (good reference)
http://www.ph.tn.tudelft.nl/~dick/cvonline/ica/ica.html
http://www.fmrib.ox.ac.uk/analysis/research/melodic/tr02cb1/node1.html 
(technical but very detailed for application to fMRI)

> So, we wonder what references would be recommended to understand the 
> algorithm for ICA, as well as the Matlab implementation of it.

About Infomax ICA implemented in EEGLAB, the best reference is probably 
Tony Bell paper

Bell AJ, Sejnowski TJ.
An information-maximization approach to blind separation and blind 
deconvolution.
Neural Comput. 1995 Nov;7(6):1129-59.

For the Matlab implementation, the best is probably to look at the 
Matlab code itself (runica.m). There are other implementation of Infomax 
(Natural Gradient) in the ICALAB toolbox (which is automatically 
detected by EEGLAB).

> Particularly, we wonder if a mixing matrix that maps components to 
> electrodes is computed during the calculations, whether it is 
> separately computed for each "trial," and how we can access this 
> matrix in Matlab.

Yes, the mixing matrix is computed at each time step. It is not computed 
separately for each trial. All data points from all trials are shuffled 
at each time step. Infomax ICA does not use the fact that neighboring 
time points have similar activities (other ICA algorithms like SOBI do, 
but it does not mean that they are returning better results).

Best,

Arno

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