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Dear Ralf,<br>
<blockquote cite="mid004101c736ab$8dc390a0$0201a8c0@R" type="cite">
<div><font face="Arial" size="2">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 </font></div>
<div> </div>
<div><font face="Arial" size="2"> test = EEG.icawinv * EEG.icaact;</font></div>
<div><font face="Arial" size="2"> comp = test -
EEG.data %should be roughly zeros </font></div>
<div> </div>
<div><font face="Arial" size="2">With a 256/257 channel dataset and a
ICA decomposition into 256 components this seems to work. </font></div>
<div> </div>
<div><font face="Arial" size="2">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. </font><font face="Arial" size="2">How can
I backproject the ica-source-activities from the commandline when pca
was done?</font></div>
</blockquote>
You can do the same thing <br>
<br>
<font face="Arial" size="2">test = EEG.icawinv * EEG.icaact;</font>
<div><font face="Arial" size="2">comp = test -
EEG.data %should be roughly zeros </font></div>
<br>
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.<br>
<blockquote cite="mid004101c736ab$8dc390a0$0201a8c0@R" type="cite">
<div><font face="Arial" size="2">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?</font></div>
</blockquote>
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).
<br>
Hope this helps,<br>
<br>
Best,<br>
<br>
Arno<br>
<br>
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