[Eeglablist] backprojection after pca

[arno]

Dear Ralf,
> I am still in the process of working into EEGLAB and was trying to get 
> familiar with the ICA-variables. Especially I wanted to recover the 
> original data by multiplying the source activations with the mixing 
> matrix. As far as I understand things this should be
>  
>    test = EEG.icawinv * EEG.icaact;
>    comp = test - EEG.data                  %should be roughly zeros
>  
> With a 256/257 channel dataset and a ICA decomposition into 256 
> components this seems to work.
>  
> My question refers to the case when I - as I use to do in practice - 
> first reduce the dimensionality using pca. Then the results of " test 
> = EEG.icawinv * EEG.icaact" cannot be equal to EEG.data. Well, I got a 
> bit confused about all the ICA variables (icaweights, icawinv, 
> icasphere) and the reduction/expansion of dimensionality with pca. How 
> can I backproject the ica-source-activities from the commandline when 
> pca was done?
You can do the same thing

test = EEG.icawinv * EEG.icaact;
comp = test - EEG.data                  %should be roughly zeros

If you use PCA to reduce dimensionality to 150 (which we always do on 
our 256 channel data), EEG.icawinv will have a size of 257 x 150 (and 
EEG.icaact of 150 x ?). So the size of the result multiplication is 
identical to the non-PCA reduced case. It is correct though that "comp" 
will not be 0 because there is some data lost due to the dimension 
reduction. It should be fairly close though because you still have the 
first 150 PCA components that explain most of the data.
> P.S.:  i wonder why it seems to work with the 256/257 dataset, since 
> EEGLAB states during the ICA process that here too the dimensionality 
> is reduced by pca to 256 since the data are in average reference 
> (after referencing from cz-ref) and therefore have only rank 256 but 
> 257 channels. or is that a different case?
Yes this is different. In this case, there is no loss of information 
when we do the PCA (one channel is a linear combination of the others).
Hope this helps,

Best,

Arno

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://sccn.ucsd.edu/pipermail/eeglablist/attachments/20070118/998707dd/attachment.html>