# [Eeglablist] Two step source connectivity analysis (as implemented in SIFT)

Thu Feb 20 11:33:27 PST 2014

```Hi,

Sorry for using vague terms:) .Phase space and strange attractors are terms
use in non-linear signal processing. Basically if you plot x(t) vs y(t+M) it
is called phase space and the shape of that is called strange attractor. The
extension or contraction of strange attractor could should some nature of
event that is studied ( like how chaotic or non-linear or non-predictable is
that event).

Suppose x(t)=Sin(2*pi*t/T) and y(t)=Cos(2*pi*t/T).  x(t) and y(t) are
perpendicular to each other, in other words they are
independent/uncorrelated and their autocorrelation in ideal case is not a
pure impulse function at zero - they are not noise- . Now, you can find a
time lag T0 in which x(t) and Y(t+T0) are correlated - for simplicity if
T0=T/4 then Cos will change to Sin.

~Iman

From: Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
Sent: Thursday, February 20, 2014 9:54 AM
Cc: Andrei Medvedev; EEGLAB List
Subject: Re: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

Dear Iman,

I did not understand your explanation. I don't know convenient terms to
discuss it (I don't have an engineering background), so please use plain
words.

My point is that neural signal has predictive patterns, which is what I
meant auto-correlation. This means X(t) and X(t+1) are correlated, so are
Y(t) and Y(t+1). If this holds, then it seems impossible to assume that
although X'(t) and Y'(t) are independent X'(t) and Y'(t+1) are dependent.

Dear Andrei,

I have a question about Nolte's claim.

**********

The imaginary part of coherency is only sensitive to synchronizations of two
processes which are time-lagged to each other. If volume conduction does not

cause a time-lag, the imaginary part of coherency is hence insensitive to
artifactual 'self-interaction'.

**********

I understand it. The assumption here is that source activity should be
observed at different channels with the same phase. Am I correct? However,
ERP researchers have observed inverted visual potentials in frontal
channels, and also inverted N170 at vertex (Cz), and so on. Why these ERP
components change phases depending on recording sites? I thought these are
simple volume conduction.

'zero-delay' interaction is very interesting as you point. ICA is not good
at capturing gamma (in my opinion) unless it is coupled with theta or other
low-frequency activities. Our lab also reported broadband gamma (Onton and
Makeig 2009) which is a different form of gamma from well-known gamma burst
evoked by Kanitza illusions or moony faces.

It's a great opportunity for learning. Maybe my questions are naive and
possibly based on wrong understanding. If I'm wrong I would appreciate if
you tell me how I failed. Thank you very much.

Makoto

Thanks Andrei for elaborating this in more details. Also in  my former post,

I forgot to mentioned the imaginary coherence method as suggested on Nolte
et al. work and I agree with you on this as well.

-Iman

From: eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu>
[mailto:eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu> ] On Behalf Of Andrei Medvedev
Sent: Wednesday, February 19, 2014 12:18 PM
To: eeglablist at sccn.ucsd.edu <mailto:eeglablist at sccn.ucsd.edu>

Subject: Re: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

Hi All,

I believe Iman gave an important point for the discussion. Let me reiterate
it. Causality (Granger or any other causality algorithm for that matter)
implies that there is a TIME DELAY between the first signal (the source of
influence) and the second signal (the recipient of influence). While, on the
other hand, ICA is essentially tries to eliminate INSTANTANEOUS dependence
between signals i.e, at each CURRENT time point. Therefore, causality and
ICA do not contradict (at least, conceptually). Any source reconstruction
algorithm is also conceptually similar to ICA b/c it minimizes this
instantaneous dependence between signals. The most important issue here is
that this way we minimize a possible artefactual component present in both
signals such as 'influence' simply due to volume conductance. It makes sense
b/c (usually) 'real' influence is NOT instantaneous and takes some time to
occur (but see below for the important exception).

So, if one does ICA and then calculates Granger (or any other type of
autoregressive (AR) modeling) between components x(t) and y(t), the expected
(and ideal) result would be that the influence between x(t) and y(t) should
be close to zero (thanks to ICA) but there may be a non-zero influence at
time shifts >0 (at t and t-1 etc). All seems to be fine (I am putting aside
the fact that 'no algorithm is perfect' and small delays may still result in
some amount of instantaneous correlation b/c signals may not be perfect
Poisson processes and thus have some 'memory' i.e., their autocorrelation
functions are not delta-functions).

This approach is similar to the imaginary coherence which is insensitive to
instantaneous effects of volume conductance (Nolte et al 2004).

But to add more to the discussion, this approach means that when we minimize
instantaneous effects, we may overlook a real 'zero-delay' interaction when
two signals are synchronized at phase delay =0. The good example of such
zero-delay interaction is gamma-band synchrony. Here, the zero-phase is
achieved through the emergent property of the network itself (due to mutual
inhibitory and excitatory connections). To reveal this zero-delay
interaction in the presence of volume conductance seems to be a hard
problem. But I would still argue in favor of removal instantaneous effects
simply because they are huge in scalp EEG. Also, 'physiological'/'real'
zero-phase synchrony is likely to be 'not perfect' giving rise to small
deviations from zero from time to time, which would then be 'detected' by
Granger/AR/imag coh).

I also agree that going to the source space instead of the channel space
(through ICA or other source reconstruction algorithms) is not free of its
own limitations. Perhaps, applying Granger/AR (with 'instantaneous'
coefficients ignored) or imaginary coh to the channel data could be a method
of choice as well.

Best,
Andrei Medvedev

--
Andrei Medvedev, PhD
Assistant Professor,
Center for Functional and Molecular Imaging
Georgetown University
4000 Reservoir Rd, NW
Washington DC, 20057

On 2/19/2014 1:18 PM, Makoto Miyakoshi wrote:

Dear Iman and all,

So are you saying independent sources can Granger cause each other?

I agree with Joe and you. I'm not a specialist, but I would imagine (correct
me if I'm wrong) that ICs are usually independent except when they are
perturbed event-relatedly. In such moments independence are transiently lost
and ICs start to Granger cause each other... I tend to think in this way
because stationarity depends on time scale. So in the sense it's correct to
say ICs are not always independent, because its independency changes from
timepoint to timepoint. You can see this visualization with one of AMICA
tools. However I haven't seen a log likelihood drop around the event, which
contradicts my explanation above, so I could be wrong somewhere. Multiple
model AMICA does extract peri-event-onset periods as a different model
though.

Note also that there is an issue of IC subspace within which ICs are always
intra-dependent.

Makoto

The assumption of ICA is : The observed data is the sum of a set of inputs
which have been mixed together in an unknown fashion and the aim of ICA is
to discover both the inputs and how they were mixed. So, after ICA we have
some sources which are temporally independent. In other words, they are
independent at time t  McKeown, et al. (1998)

However and based on Clive Granger talk at 2003 Nobel Laureate in Economics
"The basic "Granger Causality" definition is quite simple. Suppose that we
have three terms, Xt, Yt, and Wt, and that we first attempt to forecast Xt+1
using past terms of Yt and Wt. We then try to forecast Xt+1 using past terms
of Xt, Yt, and Wt. If the second forecast is found to be more successful,
according to standard cost functions, then the past of Y appears to contain
information helping in forecasting Xt+1 that is not in past Xt or Wt. .
Thus, Yt would "Granger cause" Xt+1 if (a) Yt occurs before Xt+1 ; and (b)
it contains information useful in forecasting Xt+1 that is not found in a
group of other appropriate variables."  So, in Granger causality we try to
relate time t+1 to t.

So, ICA and Granger causality are not contradicting each other and finding
causality btw sources would not have anything to do with source space or
channel space data. In my point of view, using ICA and source signal for
Granger causality is good because you do not have to worry about the volume
conductance problem. However, one can apply Granger causality in the channel
space as well since the dipole localization has its own limitations. One
clue code be transforming the channel space data to  current source density
(CSD) format and then applying any causality/connectivity analysis you would
like to study.

Best

Iman

-------------------------------------------------------------

Research Fellow

Semel Intitute, UCLA , Los Angeles

& Center for Mind and Brain, UC DAVIS, Davis

From: eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu>
[mailto:eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu> ] On Behalf Of Makoto Miyakoshi
Sent: Tuesday, February 18, 2014 3:54 PM
To: mullen.tim at gmail.com <mailto:mullen.tim at gmail.com>
Cc: eeglablist at sccn.ucsd.edu <mailto:eeglablist at sccn.ucsd.edu>
Subject: Re: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

Dear Tim,

Why don't you comment on the following question: If independent components
are truly independent, how do causality analyses work?

Dear Joe,

Your inputs are too difficult for me to understand. In short, are you saying
causality analysis works on independent components because they are not
completely independent?

Makoto

2014-02-18 15:46 GMT-08:00 Makoto Miyakoshi <mmiyakoshi at ucsd.edu
<mailto:mmiyakoshi at ucsd.edu> >:

Dear Bethel,

> say A=sunrise and B=ice-cream-sale, then the ICA in EEGLAB should find
that A is maximally  temporaly independent from B.

ICA would find a correlation between sunrise and ice-cream-sale.

Makoto

2014-02-10 4:57 GMT-08:00 Bethel Osuagwu <b.osuagwu.1 at research.gla.ac.uk
<mailto:b.osuagwu.1 at research.gla.ac.uk> >:

Hi
I am not an expert but I just want to give my own opinion!

I do not think that temporal independence of two variables (A and B) violets
causality between them as implemented in SIFT. In fact if  say A=sunrise and
B=ice-cream-sale, then the ICA in EEGLAB should find that A is maximally
temporaly independent from B. However we know there is causal flow from A to
B.

This is what I think, but I wait to be corrected so that I can learn!

Thanks
Bethel
________________________________________
From: eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu>  [eeglablist-bounces at sccn.ucsd.edu
<mailto:eeglablist-bounces at sccn.ucsd.edu> ] On Behalf Of IMALI THANUJA
HETTIARACHCHI [ith at deakin.edu.au <mailto:ith at deakin.edu.au> ]
Sent: 07 February 2014 01:27
To: mullen.tim at gmail.com <mailto:mullen.tim at gmail.com>
Cc: eeglablist at sccn.ucsd.edu <mailto:eeglablist at sccn.ucsd.edu>
Subject: [Eeglablist] Two step source connectivity analysis (as implemented
in SIFT)

Hi Tim and the list,

I am just in need of a clarification regarding the ICA source reconstruction
and the subsequent MVAR -based effective connectivity analysis using the
components, which is the basis of the SIFT toolbox. I was trying to use this
approach in my work but was questioned on the validity using ICA and
subsequent MVAR analysis by my colleagues.

"When using independent component analysis (ICA), we assume the mutual
independence
of underlying sources, however when we try to estimate connectivity between
EEG sources,
we implicitly assume that the sources may be  influenced by each other. This
fundamental assumption of mutual independence between sources in ICA [Cheung
et al., 2010, Chiang et al., 2012, Haufe et al., 2009 ]. "

So due to this reason different approaches such as MVARICA,
CICAAR(convolution ICA+MVAR),  SCSA and state space-based methods have been
proposed as ICA+MVAR based source connectivity analysis techniques.

.         So, how would you support the valid use of SIFT ( ICA+MVAR as a
two-step procedure) for the source connectivity analysis?

.         If I argue that I do not assume independent sources but rely on
the fact that ICA will decompose the EEG signals and output 'maximally
independent' sources and then, I subsequently model for the dependency, will
you agree with me? How valid would my argument be?

It would be really great to see different thoughts and opinions.

Kind regards

Imali

Dr. Imali Thanuja Hettiarachchi
Researcher
Centre for Intelligent Systems research
Deakin University, Geelong 3217, Australia.

Mobile : +61430321972 <tel:%2B61430321972>

Email: ith at deakin.edu.au <mailto:ith at deakin.edu.au>
<mailto:ith at deakin.edu.au <mailto:ith at deakin.edu.au> >
Web :www.deakin.edu.au/cisr <http://www.deakin.edu.au/cisr>
<http://www.deakin.edu.au/cisr>

[cid:image001.jpg at 01CF23FF.F8259940]

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--

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

--

Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego

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--

Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego

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