[Eeglablist] A non-EEGLAB question: What to do with small eigenvalues when performing data whitening in EEG artifact removal.

[Seyed Mohammad Reza Shahshahni]

Dear Makoto

Thanks for your attention. You're right. But what should I do then?
Imagine I have 10 channels of data and I want to perform ICA, find the
artifactual components, eliminate them and get back to the signal space.
This is what I know: Based on the eigenvalue decomposition of the
covariance matrix, I find the eigenvalues. I ignore small eigenvalues based
on threshold. Then what? Is it correct to ignore the corresponding channels
and go on? What if we want to check how well the algorithm works? My
problem is that in papers who have talked about artifact rejection, to my
knowledge, they have assumed full rank and have not considered such a case.

Could you please guide me through this?

Best,
Reza

On Tue, Nov 8, 2016 at 7:04 AM, Makoto Miyakoshi <mmiyakoshi at ucsd.edu>
wrote:

> Dear Reza,
>
> > But I don't one to compress my data at this point because I want to have
> the same number of signals after artifact removal.
>
> I would say this motivation is wrong. You should count the rank of the
> data, not the number of the channels. What if your data are severely rank
> deficient due to channel bridging etc? You don't want to let your ICA fail
> in that way.
>
> Makoto
>
>
>
> On Fri, Oct 28, 2016 at 2:26 AM, Seyed Mohammad Reza Shahshahni <
> smr.shahshahani at gmail.com> wrote:
>
>> Dear all
>>
>> I'm trying to implement on-line artifact removal based on ICA. As known,
>> in and ICA algorithm like FastICA or SOBI we need to perform data whitening
>> to lessen the complexity.
>> I have encountered a case where some eigenvalues I have computed are very
>> small (in order of 1e-7) which are literally zeros. How should I deal with
>> them. I know one solution is do as in PCA. But I don't one to compress my
>> data at this point because I want to have the same number of signals after
>> artifact removal.
>>
>> Any suggestions?
>>
>> Thanks,
>>
>> Regards,
>> Reza M. Shahshahani
>> PhD Candidate of Electical Engineering,
>> Shahid Beheshti University,
>> Tehran,Iran.
>>
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>
>
>
> --
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>
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