[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

I see. But I have checked the data. It's full rank. But still the ratio of
maximum eigenvalue of the covariance matrix to minimum eigenvalue is around
10^5 (max is of order 10^7, min is of order of 10^2). Is such a difference
acceptable?

Best,
Reza

On Fri, Nov 11, 2016 at 11:04 AM, Seyed Mohammad Reza Shahshahni <
smr.shahshahani at gmail.com> wrote:

> Dear Makoto
>
> I see. But I have checked the data. It's full rank. But still the ratio of
> maximum eigenvalue of the covariance matrix to minimum eigenvalue is around
> 10^5 (max is of order 10^7, min is of order of 10^2). Is such a difference
> acceptable?
>
> Best,
> Reza
>
> On Wed, Nov 9, 2016 at 5:42 AM, Makoto Miyakoshi <mmiyakoshi at ucsd.edu>
> wrote:
>
>> Dear Reza,
>>
>> > I ignore small eigenvalues based on threshold. Then what? Is it correct
>> to ignore the corresponding channels and go on?
>>
>> What do you mean by corresponding channel? Eigenvalues and channels are
>> not one to one, but usually all to all.
>>
>> After all, if you want to make your data full-ranked, you need to reject
>> channels. If you have 10 channels and rank(data) returns 8 (or your
>> eigenvalue decomposition says the two smallest values are zero/near-zero),
>> discard ANY two channels. See OLD description of this for this explanation:
>> https://sccn.ucsd.edu/wiki/Makoto's_preprocessing_pipeline#
>> Re-reference_the_data_to_average
>>
>> Makoto
>>
>> On Mon, Nov 7, 2016 at 10:02 PM, Seyed Mohammad Reza Shahshahni <
>> smr.shahshahani at gmail.com> wrote:
>>
>>> 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.
>>>>>
>>>>> _______________________________________________
>>>>> Eeglablist page: http://sccn.ucsd.edu/eeglab/eeglabmail.html
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>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Makoto Miyakoshi
>>>> Swartz Center for Computational Neuroscience
>>>> Institute for Neural Computation, University of California San Diego
>>>>
>>>
>>>
>>
>>
>> --
>> Makoto Miyakoshi
>> Swartz Center for Computational Neuroscience
>> Institute for Neural Computation, University of California San Diego
>>
>
>
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