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</o:shapelayout></xml><![endif]--></head><body lang=NL link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=NL-BE style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>Dear Robert<o:p></o:p></span></p><p class=MsoNormal><span lang=NL-BE style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>Thank You for Your mail and positive suggestions. I personally think that ICA may be a valuable technique but needs more fundamental research (such as the type you propose) before deploying it in the clinical theatre. The fact that we still have debates and discussions going on (what I think is positive) suggests that more academic research is indeed necessary.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>Had I been working in an academic setting this would have been a real interesting topic for a doctorate. Unfortunately, in a private clinical practice that is hardly possible but discussions like this might inspire younger colleagues to move on this path. As EEGLab is free and Neuroguide has a wonderful demo version (also free) where all algorithms can be tested a galore (and where a EEG signal generator is included so that all hypotheses and phase effects can be tested) there are far less barriers then in our days. Moreover, opensource software (fi Python or “R” based) gives access to different ICA and BS implementations. This is important as discussions about ICA often seem to neglect the fact that it is not some monolytic object but that different implementations (especially in neural networks based versions) will come up with different solutions. They often yield good but not necessarily “best” components. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>After all I find ICA and BSS a fascinating topic but we must stay aware of its limitations and possible side-effects and the conditional framework in which to operate. My reactions are not against ICA as such but inspired by the fear that some producers and clinicians will put blind faith on black box type implementations and unwise use could take an epidemiological spread.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>We have seen that happen with fMRI and with many other stuff (especially in psychiatry).<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>Sincerely<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'>Georges<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><b>From:</b> robert lawson [mailto:robert@sherab.net] <br><b>Sent:</b> Thursday, July 27, 2017 10:49 PM<br><b>To:</b> otte georges <georges.otte@pandora.be><br><b>Subject:</b> Re: [Eeglablist] How phase is calculated in linear decomposition<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Hi George, <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>I talked to Phil Zeman last year about 19 channel data, ICA, and phase. He had come up with a method to remove artifact from data that does not distort phase and does not use ICA. There were many postings about this in the Neuroguide list a few years ago. <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Zeman suggested what you just wrote. With 19 channel data and 19 components there is likely to be some EEG in artifact components. With 256 channels and components, it is more likely to have artifact components with little or no EEG. I am not going to do it but I would love to see someone pull out the 19 10-20 channels from a 256 channel recording and compare the phase from the reconstructed datasets when artifact components are removed from each of them. This test could convince me that ICA does not distort phase and I would be happy to be considered convinced. <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>I tested coherence after Marco Congedo coded an ICA artifact removal progrm 15 or so years ago and found it was different from the same data when manually edited. Marco tried to fix this coherence phase change and could not do it. I wish he had participated in this discussion as he has had the most experience with ICA and phase. <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>After all this back and forth, I still don't believe 19 channel reconstructed ICA data would be valid in neuroguide or any of the other normative databases. <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>You probably remember a previous EEG controversy that said EEG recorded with physically linked ears would have different asymmetry from data with mathematically linked ears. I tested this empirically and found it was not so. I talked to Roberto Pascal Marqui about and he said he had done the same thing with the same results. I will not believe that ICA artifact removal produces valid phase until it is done empirically with real EEG datasets. <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Regards, <o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Robert Lawson<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>From: otte georges<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Sent: Thursday, July 27, 11:48 AM<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Subject: Re: [Eeglablist] How phase is calculated in linear decomposition<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>To: </span><span style='font-family:"Arial",sans-serif;color:black'><a href="mailto:mmiyakoshi@ucsd.edu"><span lang=EN-US>mmiyakoshi@ucsd.edu</span></a></span><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>, Robert Thatcher<o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Cc: EEGLAB List, Georges Otte<br><br><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Dear Makoto<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>These are wise words born from scientific humbleness and relentless search for a deeper truth. I look forward to hear your further views on ICA as I am to very worried about phase contortion in reconstruction of signals from a limited set of components. I am aware that most researchers on the EEGLab list are working with 256 or more high density channel EEG recordings but we must also be aware that in the clinical scene 19 channels are conventionally used and reconstruction after rejection of 4-5 components is of course quite a different story than rejecting one component in a 256 ch recording. New techniques will at the end of the day pop up in the clinical theater and I think it is wise that controversies are straightened out or at least be documented and discussed so that the necessary caveats can be drawn. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>That being said I wonder a bit about your remark on EEG models. Are you not a bit too pessimistic? As a clinician and neurologist, I had the impression that after all this time and basic scientific work we do have quite clear ideas about the generating mechanisms in pyramidal cells embedded in cortical columns, synaptic channel dynamics and its equations, dendritic and axonal conduction and its correlation with the electrical activity recorded at the scalp. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>What is missing? (or what am I missing?) <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Sincerely<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Georges<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>PS My latest mail to this list (dated start of July) concerning the transit from EEG (or MEG) channel recordings to network parameters in a graph theory model was not published. Was something wrong with it?<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>From:</span></b><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'> Makoto Miyakoshi [</span><span style='font-family:"Arial",sans-serif;color:black'><a href="mailto:mmiyakoshi@ucsd.edu"><span lang=EN-US>mailto:mmiyakoshi@ucsd.edu</span></a></span><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>] <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-family:"Arial",sans-serif;color:black'>Sent:</span></b><span style='font-family:"Arial",sans-serif;color:black'> Wednesday, July 26, 2017 3:01 AM<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>To:</span></b><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'> Robert Thatcher <</span><span style='font-family:"Arial",sans-serif;color:black'><a href="mailto:rwthatcher2@yahoo.com"><span lang=EN-US>rwthatcher2@yahoo.com</span></a></span><span lang=EN-US style='font-family:"Arial",sans-serif;color:black'>><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-family:"Arial",sans-serif;color:black'>Cc:</span></b><span style='font-family:"Arial",sans-serif;color:black'> EEGLAB List <<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>><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-family:"Arial",sans-serif;color:black'>Subject:</span></b><span style='font-family:"Arial",sans-serif;color:black'> Re: How phase is calculated in linear decomposition<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Dear Robert,<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Sorry for belated response.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>I updated my wiki page to explain how phase is synthesized and split when components are rejected.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'><a href="https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition">https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition</a><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>As I explained above, you are calling the difference between 18 Bitcoins and 19 Bitcoins 'distortion'.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>> In addition to mathematics, there is empirical proof of “distortion” or “adulteration” that has been repeated over and over again on this forum and accepted to be true by Arnaud and Stephan and Georges and Robert Larson and Ramesh but apparently not yet by you.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>I don't think Arno and Stefan accepted 'the proof' because they will write a rebuttal paper with me. It's a good opportunity for us anyways to refute the Montefucso-Siegmunt paper.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>By the way Robert, I like your claim that people tend to be trapped by their own dogma and make errors in circular logic. That's a good point. I believe that this criticism actually applies to the entire EEG research field, since we do not have a <i>ground truth</i> in generative model of EEG signals; and do we not tend to compensate the lack of the ground truth by using fancy signal processings? All computational EEG analysts need a good introspection on this issue. We also need to know the difference between engineering and science, models and truth, etc; Good engineering is not necessarily a good science!<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>I also enjoy and sympathize your criticism against dogmatic people. However, your criticism against ICA is invalid and unsatisfactory to me. Let me invite you to the next thread to share my real criticisms against ICA. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Makoto<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>On Fri, Jul 7, 2017 at 11:07 AM, Robert Thatcher <<a href="mailto:rwthatcher2@yahoo.com">rwthatcher2@yahoo.com</a>> wrote:<o:p></o:p></span></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Dear Makoto,<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> It is correct that a linear decomposition where one decomposes a 19 channel time series into 19 ICA components then, like the inverse Fourier transform, one can recover the phase information if one uses all 19 ICA components. However, one cannot recover the phase information in 19 channels if one uses 18 or 17 or 16 or any number less than 19 components to reconstruct a new 19 channel time series. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>The mathematics proving “distortion” by ICA reconstruction with a small number of components is explained by Taken’s Theorem (& other theorems in differential geometry, e.g. Shannon's) where a lower dimensional time series does not preserve phase when used to reconstruct a higher dimensional time series. Therefore mathematically (including the inverse Fourier transform) there is always a loss of information when using a smaller number of components to reconstruct a larger number of channels. Also, commonsense tells one that it is not possible to create something out of nothing, e.g., if I give you 18 Bitcoins will you give me 19 Bitcoins? (credit to Georges for asking this question).<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>In addition to mathematics, there is empirical proof of “distortion” or “adulteration” that has been repeated over and over again on this forum and accepted to be true by Arnaud and Stephan and Georges and Robert Larson and Ramesh but apparently not yet by you. The empirical proof can be demonstrated by yourself if you compute the phase differences between all channel combinations in the original EEG time series vs the ICA reconstructed time series using a smaller number of ICA components. Anyone can demonstrate the phase difference “distortion” for themselves using the Hilbert transform for instantaneous phase differences (i.e., each time point) or the FFT for an average. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Here is a URL of a You Tube Video that provides additional empirical proof that ICA reconstruction distorts or adulterates the physiologically based phase differences in the original EEG recording.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'><a href="https://youtu.be/Q36ojib5OZE">https://youtu.be/Q36ojib5OZE</a><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Here is a url to four power points of two different time points that compares the phase difference before and after Arnaud’s ICA reconstruction. <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'><a href="http://www.appliedneuroscience.com/Phase_Differences-between-Original_&_Delorme-Post-ICA.pptx">http://www.appliedneuroscience.com/Phase_Differences-between-Original_&_Delorme-Post-ICA.pptx</a><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Please download and expand the power points so that you can verify for yourself that the phase differences in the original recording have been distorted or altered. I would be happy to issue a temporary license to Neuroguide so that you can launch two Neuroguides and import and compare the original time series and Arnaud’s ICA reconstructed time series to verify for yourself that phase differences for all channel combinations for each and every time point have been distorted by ICA reconstruction.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>I offer this same opportunity to all of the members of this forum. Download, install and launch NG-2.9.4 and paste the key A to <a href="mailto:qeeg@appliedneuroscience.com">qeeg@appliedneuroscience.com</a>. Here is the download url:<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'><a href="http://www.appliedneuroscience.com/Download_NeuroGuide.htm">http://www.appliedneuroscience.com/Download_NeuroGuide.htm</a><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>I will mail step by step mouse instructions so that anyone interested can verify for themselves that ICA reconstruction distorts the phase differences for all channel combinations and all time points.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>This is important because if the primary level of measurement is distorted then all subsequent analyses are invalid as a matter of verifiable fact.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Best wishes,<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Robert<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>On Thursday, July 6, 2017, 2:31:56 PM PDT, Makoto Miyakoshi <<a href="mailto:mmiyakoshi@ucsd.edu">mmiyakoshi@ucsd.edu</a>> wrote:<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Dear Robert and list,<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>If I remember correctly, one of the critical issue was how phase changes in 'channel data' after removing independent components. Let me focus on this point only.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>1. To show my rebuttal and mathematical proof, I prepared a wiki page. In this page. I described how a phase is split/synthesized before and after linear decomposition. Note that this applies to any linear decomposition and not specific to ICA. In doing so, made it nice and educational to show my respect to Arno's effort. Hopefully this mathematical clarification helps.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <a href="https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition">https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition</a><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Robert, if you do not agree,<b> please show the right process in a form of math</b>.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>2. Apart from this scientific/mathematical dispute, I insist that one should not use the word 'distortion' in this context because it includes subjective judgement.<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Makoto<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>-- <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Makoto Miyakoshi<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Swartz Center for Computational Neuroscience<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Institute for Neural Computation, University of California San Diego<o:p></o:p></span></p></div></blockquote><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>-- <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Makoto Miyakoshi<o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:black'>Swartz Center for Computational Neuroscience<o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Institute for Neural Computation, University of California San Diego<br><br><o:p></o:p></span></p></div></div></body></html>