[Eeglablist] How phase is calculated in linear decomposition

[Makoto Miyakoshi]

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>
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_&
> _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.   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> 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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