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<p>Hi All - <br>
</p>
<p>I think Bob is right that the relative phase will be changed by
deleting 1 or 2 artifact components. Any artifact is broad-band
and hence has components in each frequency bin. When
reconstructing the (in this example, 19) channels, the relative
phases will change because some of the signal in each frequency
bin has been removed when using only 17 or 18 components. <br>
</p>
<p>The open question is whether the original relative phase or the
ICA-corrected relative phase is the better estimate of the
relative phase between the populations that contributed to each
electrode. It's not obvious to me to prefer the original relative
phase with the artifact components. <br>
</p>
<p>Part of the problem for me (and I do use EEGLAB's ica) about
identifying components as artifact in the ICA is that I don't
think they contain just the artifact, they also contain some
genuine brain activity that we are removing. This bothers me, but
I don't know a better solution. Even the case of the eye-movement
artifact components is likely a mixture. <br>
</p>
<p>I'd like to see this discussion move away from algorithm to this
harder question about artifact removal. <br>
</p>
<p>ramesh <br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 06/14/2017 10:43 AM, Robert Thatcher
wrote:<br>
</div>
<blockquote cite="mid:8508200.2362016.1497462199093@mail.yahoo.com"
type="cite">
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<p class="ydp76ba64cbMsoNormal"><span>Iman,</span></p>
<p class="ydp76ba64cbMsoNormal"><span> Thank
you for the information. I could only find a power point
attachment of a simulation in your post. I did not
find a scientific publication where you compared the phase
differences changes
between an original EEG recording and a ICA reconstruction
after removing one
or more components. Please re-send your
study. Also please give the citation to
any of your publications or other’s publications where
phase differences were
compared between the original EEG recording and post ICA
reconstruction. It will be interesting to see if you
found
similar changes like in the study by Montefusco-Siegmund
et al or by Georges
Otte or even in the example pre vs post data files that
you can download from
the internet. I am assuming that you
have downloaded the EEG data and then used a JTFA like the
Hilbert transform or
even the FFT cross-spectrum to prove to yourself that the
phase differences between
the original and the ICA reconstruction have not been
preserved.</span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>As for the mathematics
concerning reconstruction from a
lower dimensional matrix to a higher dimensional matrix
where there are no
simple linear transforms I refer you to Taken’s theorem
where “<span>The reconstruction preserves the
properties of the dynamical system that do not change
under smooth coordinate
changes, but it does not preserve the geometric shape of
structures in phase
space.</span>” Also, in standard
differential geometry math courses the issue of lower
dimensional manifold mapping
to higher dimensional manifolds shows a loss of
information in all cases. Also, commonsense operates here
where one tries
to reconstruct 19 channels of EEG using only 15 or 16 or
17 ICA components
hence a loss of information.</span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>Finally, the brain is
not a total chaotic organ. As
demonstrated by many scientists (e.g., Nunez; Walter
Freeman; Roberto-Pascual
Marqui; E. Roy John; Joel Lubar; etc) coherence and phase
differences are well behaved
and highly reproducible within and between subjects.
Coherence and phase are dependent on the
number and strength of connections between groups of
neurons. Here is a URL to a study that tested Paul
Nunez’s two-compartmental model of Coherence and Phase
Differences and found
that these measures vary as a function of distance and
packing density:</span></p>
<p class="ydp76ba64cbMsoNormal"><span><a
moz-do-not-send="true"
href="http://www.appliedneuroscience.com/TWO-COMPARTMENTAL_MODEL_EEG_COHERENCE.pdf"
rel="nofollow" target="_blank">http://www.appliedneuroscience.com/TWO-COMPARTMENTAL_MODEL_EEG_COHERENCE.pdf</a></span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>Here is a url to a
study that used EEG LORETA correlations to replicate
Diffusion Tensor Imaging
measures of connectivity in the brain:</span></p>
<p class="ydp76ba64cbMsoNormal"><span><a
moz-do-not-send="true"
href="http://www.appliedneuroscience.com/DTI-ThatcherHumanBrainmapping.pdf"
rel="nofollow" target="_blank">http://www.appliedneuroscience.com/DTI-ThatcherHumanBrainmapping.pdf</a></span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>Here is a url to a
study that measured phase lock and phase shift duration
from birth to about 16
years of age in 458 and where phase differences were
stable and well
behaved:
<a class="moz-txt-link-freetext" href="http://www.appliedneuroscience.com/PhaseresetDevelopment.pdf">http://www.appliedneuroscience.com/PhaseresetDevelopment.pdf</a></span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>If you do a search of
the National Library of Medicine database (Pubmed) using
the search terms “EEG coherence”
you will find 2,874 citations. There is
huge consistency in this vast literature which would be
impossible if the brain
was totally chaotic.</span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>Best regards,</span></p>
<p class="ydp76ba64cbMsoNormal"><span> </span></p>
<p class="ydp76ba64cbMsoNormal"><span>Robert</span></p>
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