[Eeglablist] Some basic questions about ICA

[Benedikt Ehinger]

Hi Chen

These are inherent limitation of ICA.
If you look at the mixing formular:
     x = As (with x mixed data, A mixing matrix and s sources)

and you add a scaling of k

x = B(k*s)

you can match the scaling with B = (A/k)

x = (A/k)(k*s)
any arbitrary scaling factor k of the sources can be matched by the 
mixing matrix. As both s and the mixing matrix are unknown, you will 
never be able to recover the original amplitude. This of course is also 
the case if you scale only a single source.

For the Permutation of the signal it is similar, if you permute the 
order of the sources, you can as well permute the order of the Mixing 
matrix to match the mixed signal again. It is impossible to do in this 
method. That is why usually ICA orders the components with decreasing 
variance.

If you want to read more about ICA I recommend:
http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/
Or directly the limitations:
http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/node4.html

Also interesting: Why gaussian variables are forbidden:
http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/node9.html


Hope this explanation helps.
Best,
Benedikt

Am 06.02.2014 14:09, schrieb Chen Chen:
> Hi.
>
> I also have some questions about ICA, I wanna someone can help.
>
> I generated four orignal signals and mixed them with a random matrix 
> and add some noise, then I used ICA to remove artifacts/noise and 
> restore orignial signals, then I found, after using ICA, the amplitude 
> of orignial signals reduced and the order of the orignial signals are 
> changed.
>
> How can I to sovle those two problems?
>
> Thank you for your kindly responses.
>
> CHEN
>
>
>
> On Wed, Jan 29, 2014 at 10:10 AM, Kristoffer Aberg <kc.aberg at gmail.com 
> <mailto:kc.aberg at gmail.com>> wrote:
>
>     Hi,
>     thanks for a wonderful toolbox!
>
>     I will try to use ICA to remove blinks / eye-movement / ECG
>     artifacts, but i have some questions i would be very happy if
>     someone could address:
>
>     1. For the ICA decomposition, does it matter if the electrode
>     locations are correct? That is, would the decomposition work even
>     if the locations would be completely randomized? I ask because i
>     dont know where to place the eye / ecg electrodes exactly.
>
>     2. Is it a good idea to always include the eye / ecg channels in
>     the ICA decomposition? I ask because i thought to decompose data
>     based on scalp electrodes only and then verify blink / pulse
>     components by comparing them to the eye / ecg channels. When
>     should i not include the eye / ecg channels in the ICA decomposition?
>
>     Thanks for your time and your responses!
>
>     Kris
>
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