[Eeglablist] How phase is calculated in linear decomposition
otte georges
georges.otte at pandora.be
Wed Jul 26 00:08:42 PDT 2017
Dear Makoto
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.
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.
What is missing? (or what am I missing?)
Sincerely
Georges
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?
From: Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
Sent: Wednesday, July 26, 2017 3:01 AM
To: Robert Thatcher <rwthatcher2 at yahoo.com>
Cc: EEGLAB List <eeglablist at sccn.ucsd.edu>; Georges Otte <georges.otte at telenet.be>
Subject: Re: How phase is calculated in linear decomposition
Dear Robert,
Sorry for belated response.
I updated my wiki page to explain how phase is synthesized and split when components are rejected.
https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition
As I explained above, you are calling the difference between 18 Bitcoins and 19 Bitcoins 'distortion'.
> 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.
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.
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 ground truth 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!
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.
Makoto
On Fri, Jul 7, 2017 at 11:07 AM, Robert Thatcher <rwthatcher2 at yahoo.com <mailto:rwthatcher2 at yahoo.com> > wrote:
Dear Makoto,
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.
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).
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.
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.
https://youtu.be/Q36ojib5OZE
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.
http://www.appliedneuroscience.com/Phase_Differences-between-Original_ <http://www.appliedneuroscience.com/Phase_Differences-between-Original_&_Delorme-Post-ICA.pptx> &_Delorme-Post-ICA.pptx
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.
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 qeeg at appliedneuroscience.com <mailto:qeeg at appliedneuroscience.com> . Here is the download url:
http://www.appliedneuroscience.com/Download_NeuroGuide.htm
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.
This is important because if the primary level of measurement is distorted then all subsequent analyses are invalid as a matter of verifiable fact.
Best wishes,
Robert
On Thursday, July 6, 2017, 2:31:56 PM PDT, Makoto Miyakoshi <mmiyakoshi at ucsd.edu <mailto:mmiyakoshi at ucsd.edu> > wrote:
Dear Robert and list,
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.
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.
https://sccn.ucsd.edu/wiki/How_phase_is_calculated_in_linear_decomposition
Robert, if you do not agree, please show the right process in a form of math.
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.
Makoto
--
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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