<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:Helvetica;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:"Segoe UI";
panose-1:2 11 5 2 4 2 4 2 2 3;}
@font-face
{font-family:Georgia;
panose-1:2 4 5 2 5 4 5 2 3 3;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
p.ydpd8e298femsonormal, li.ydpd8e298femsonormal, div.ydpd8e298femsonormal
{mso-style-name:ydpd8e298femsonormal;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
p.ydp899ccae7yiv3573973499msonormal, li.ydp899ccae7yiv3573973499msonormal, div.ydp899ccae7yiv3573973499msonormal
{mso-style-name:ydp899ccae7yiv3573973499msonormal;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle20
{mso-style-type:personal;
font-family:"Calibri",sans-serif;
color:windowtext;}
span.EmailStyle22
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal">Hi Rob/Arno:<o:p></o:p></p>
<p class="MsoNormal">Let’s write down a paper and respond to his claim scientifically.
<o:p></o:p></p>
<p class="MsoNormal">-Iman<o:p></o:p></p>
<p class="MsoNormal"><a name="_MailEndCompose"><o:p> </o:p></a></p>
<span style="mso-bookmark:_MailEndCompose"></span>
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b>From:</b> eeglablist-bounces@sccn.ucsd.edu [mailto:eeglablist-bounces@sccn.ucsd.edu]
<b>On Behalf Of </b>Rob Coben<br>
<b>Sent:</b> Sunday, June 11, 2017 4:45 PM<br>
<b>To:</b> 'Arnaud Delorme' <arno@ucsd.edu><br>
<b>Cc:</b> 'eeglablist' <eeglablist@sccn.ucsd.edu><br>
<b>Subject:</b> Re: [Eeglablist] ICA misinformation<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Arno,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thanks for this message. Dr Thatcher has been saying this for a long time and has even published an article to this effect with no scientific basis of course.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Iman and myself have considered writing a response to the article but have not done so to date.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Would you be interested in publishing such a piece either on your own or with us? This could be included in our special issue in Frontiers in Neural Circuits:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><a href="http://journal.frontiersin.org/researchtopic/5265/computational-methodologies-in-brain-imaging-and-connectivity-eeg-and-meg-applications">http://journal.frontiersin.org/researchtopic/5265/computational-methodologies-in-brain-imaging-and-connectivity-eeg-and-meg-applications</a><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Rob Coben <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b>From:</b> <a href="mailto:eeglablist-bounces@sccn.ucsd.edu">
eeglablist-bounces@sccn.ucsd.edu</a> [<a href="mailto:eeglablist-bounces@sccn.ucsd.edu">mailto:eeglablist-bounces@sccn.ucsd.edu</a>]
<b>On Behalf Of </b>Arnaud Delorme<br>
<b>Sent:</b> Saturday, June 10, 2017 8:18 PM<br>
<b>To:</b> Robert Thatcher <<a href="mailto:rwthatcher2@yahoo.com">rwthatcher2@yahoo.com</a>><br>
<b>Cc:</b> eeglablist <<a href="mailto:eeglablist@sccn.ucsd.edu">eeglablist@sccn.ucsd.edu</a>>; Georges Otte <<a href="mailto:georges.otte@telenet.be">georges.otte@telenet.be</a>>; rwthatcher <<a href="mailto:robert@appliedneuroscience.com">robert@appliedneuroscience.com</a>><br>
<b>Subject:</b> Re: [Eeglablist] ICA misinformation<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Dear Robert,<o:p></o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">My comment posted 8 months ago does not appear in the video comments . It does appear for me when I am logged in on my Google account. It was likely marked as spam. There is now a new comment that reads.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">"<span style="font-size:10.0pt;font-family:"Arial",sans-serif">Somebody by the name of Arnaud is making false claims that a post he did that I have not even seen was "suppressed" by me. Does any one know when and where this person made
a post? Infact I do not think that it is oossible to "suppress" another person's post and I would certainly not suppress anyone even if I could? Robert Thatcher, Ph.D.</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif"></span><span style="font-size:10.0pt;font-family:"Arial",sans-serif">”</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">I apologize if </span><span style="font-size:12.0pt;font-family:"Arial",sans-serif">I wrongly claimed that you suppressed the post and </span><span style="font-size:10.0pt;font-family:"Arial",sans-serif">somehow
Google machinery automatically marked my post as spam. Or it might be that you did not approve the post and did not explicitly reject it. </span><span style="font-size:12.0pt;font-family:"Arial",sans-serif">I have submitted my post a second time, so hopefully
this time it will appear. I think multiple opinions should be represented.</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif">The denial and dismissal of the facts based on the possibility of a deep source is irrelevant. No matter what the sources of phase differences between the original time
series the fact is that the ICA reconstructed time series is not the same as the phase differences in the original time series.<o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">This is right. The reconstructed data after removing spurious ICA components differs from the original time series, and because of that there are phase differences. However, I would argue the original phase is wrong because it is contaminated
by artifacts.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">If you have process (brain source) with signal at phase A and another process (artifact) with signal at phase B both oscillating at the same frequency and projecting equally to a given channel. Then the resulting oscillation when recorded
at a scalp channel represent the mixture of A and B and has a different phase than A and B. The snippet of code below illustrates the process.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">figure; <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">subplot(3,1,1); plot(sin([0:0.1:3*pi])); title('A'); <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">subplot(3,1,2); plot(sin([0:0.1:3*pi]+pi)); title('B'); <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">subplot(3,1,3); plot(sin([0:0.1:3*pi]+sin([0:0.1:3*pi]+pi))); title('Mixture of A and B'); <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">So if ICA tease A and B apart from the mixed signal recorded at the channel level, then we remove B (which could for example be an artifact), then yes the phase of the signal at the channel level is changed (it is now equal to the phase
of A since we removed B contribution). However, this does not mean that ICA has corrupted the phase. <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">With respect to the analysis you present on the video, I would claim that phase coherence at the scalp channel level are misleading (even partial directed coherence that compute coherence on all channels simultaneously) because single<span style="font-family:"Helvetica",sans-serif;color:#26282A"> EEG
source can project to distant channels and create spurious coherence. If one really wants to compute coherence at the channel level, I would recommend using the EEGLAB plugin </span><a href="http://www.erpwavelab.org/">http://www.erpwavelab.org/</a> that was
takes into account non-0 phase coherence (non-0 phase coherence cannot be due to a single deep source). However, my take is that brain dynamics needs to be performed at the source level, not a the channel level.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Note that I would not say it is impossible that ICA distorts the phase. In theory one could imagine that the EEG signal contains time-delayed version of the same signal and then it might be possible that the linear combination achieved
by ICA would be equivalent to a time domain filter (that would distort the phase). It is a stretch though, and contrary to what we know about ICA applied to EEG so far, so I would not favor this as a likely explanation.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Solving this question might prove very hard. What is the correct phase? Is it the channel phase, is it the ICA phase, is the phase of the intracranial underlying signal (and if yes, at what location because neighboring locations within
the brain might exhibit different phases and the scalp average is just a global representation of the multitude of local signals).<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">In any case, thank you for bringing the discussion here. It is important for people to see this topic discussed.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Best wishes,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Arno<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif">The facts are the facts and are easily replicated. I recommend that readers do not bother with abstract theory or invented assumptions - simply do the empirical test yourself.
Compare the phase differences and coherence in the original time series to the phase differences and coherence in the ICA reconstructed time series and post your results.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif">Thank you again,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif">Robert Thatcher, Ph.D.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div>
<p class="ydpd8e298femsonormal" style="margin-bottom:12.0pt;line-height:11.9pt"><b><i><span style="font-size:10.0pt;font-family:"Georgia",serif">“There is a principle which is a bar against all information, which is proof against all argument, and which cannot
fail to keep a man in everlasting ignorance. This principle is: contempt prior to investigation.” </span></i></b><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p></o:p></span></p>
<p class="MsoNormal"><b><i><span style="font-size:10.0pt;font-family:"Georgia",serif;color:#55208D">– Herbert Spencer </span></i></b><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"> <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:16.0pt;font-family:"Segoe UI",sans-serif">“For those who believe, no proof is necessary. For those who don't believe, no proof is possible.”</span><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p></o:p></span></p>
</div>
<p class="ydp899ccae7yiv3573973499msonormal" style="margin:0in;margin-bottom:.0001pt">
<span style="font-size:16.0pt;font-family:"Segoe UI",sans-serif"> </span><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:16.0pt;font-family:"Segoe UI",sans-serif">― Stuart Chase</span><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p></o:p></span></p>
</div>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Helvetica",sans-serif"><o:p> </o:p></span></p>
</div>
<div id="ydpf5aa456yahoo_quoted_8070059572">
<div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">On Saturday, June 10, 2017, 2:44:59 PM EDT, Georges Otte <<a href="mailto:georges.otte@telenet.be">georges.otte@telenet.be</a>> wrote:<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<div id="ydpf5aa456yiv1666281484">
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">---------- Forwarded message ----------<br>
From: Arnaud Delorme <<a href="mailto:arno@ucsd.edu">arno@ucsd.edu</a>><br>
Date: Jun 10, 2017 19:00<br>
Subject: [Eeglablist] ICA misinformation<br>
To: eeglablist <<a href="mailto:eeglablist@sccn.ucsd.edu">eeglablist@sccn.ucsd.edu</a>><br>
Cc: <o:p></o:p></span></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt">
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">We get asked repetitively about the video below which claims that ICA adulterates EEG Phase & Coherence<o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><a href="https://www.youtube.com/watch?v=BfqCh2UeJik&feature=youtu.be" target="_blank">https://www.youtube.com/watch?v=BfqCh2UeJik&feature=youtu.be</a><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">I posted a comment on this video which was suppressed by the author. Please repost that message again if you can and vote down this video which is basically
misleading people.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">Thanks,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">Arno<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">------<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">My response to this video:<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">The measure of FFT coherence and phase lag between hemisphere that is being used in this video has no physiological basis to my knowledge (because inter-hemispheric
FFT coherence and change in phase lag may be due to a single deep EEG source, so it does not reflect inter-hemispheric communication), so I do not think that ICA makes it better or worse. It just makes it different.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">ICA applies a spatial filter to extract artifacts activity which can be then removed from the data. One needs to be mindful of which artefacts are being removed
and also if ICA was successful at isolating such artifacts.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">Arnaud Delorme, PhD - Main developer of EEGLAB, the ICA/EEG software<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">This is a more technical response from Jason Palmer who is a mathematician at UCSD and ICA expert<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">"My take: ordinary ICA can’t change the phase of any oscillations because it is just an “instantaneous” linear combination of the channels without any time
shifts. Just as the channel EEG is a linear combination of the sources in the brain, each IC is a certain linear sum of all the channels, so it contains all the oscillations except that ICA is formulated to separate sources in different ICs.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">The only way to distort phase is to do some kind of filtering, or convolution, of the data. E.g. using a normal FIR filter will change the phase, ideally just
adding a constant delay to each oscillation (linear phase). Typically to do high-pass filtering, we use filtfilt, which runs the filter first in the forward direction, adding a constant phase, and then in the reverse direction subtracting the phase, to leave
all oscillations with zero phase shift.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">But each ICs is just an instantaneous combination of the channels, with no filtering. So all oscillations (in the fourier decomposition) have the same phase,
it’s just that oscillations may be separated into different ICs.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A">There may be some confusion if you use phase to refer to the temporal shift of a general waveform, for example the peak latency of an ERP which is itself the
combination of a number of oscillations (frequencies and phases). ICA may separate an apparent peak into the sum of two independent nearby peaks, but the argument which is testable is that the sources are statistically independent (distinct) and the decomposition
gives more information about the nature of the ERP. And again, the separation is done just by an instantaneous combination of the non-delayed channels. This is completely different from doing a time-domain PCA or other time of decomposition of the waveform.
In ICA we are basically trying to design (instantaneous) spatial filters such that the output signals have distributions that are statistically independent.”</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:#26282A"></span><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p></o:p></span></p>
</div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Helvetica",sans-serif;color:#26282A"><o:p> </o:p></span></p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</div>
</body>
</html>