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

Wed Feb 19 12:48:03 PST 2014

Hi,

Think about this : 

X(t=t1)=[x1(t1) x2(t1)]; 

Y(t=t1)=[y1(t1) y2(t1)];

These two vectors at t=t1 can be uncorrelated/independent/..

Now, X(t=t2) =[ x1(t2) x2(t2)] can be correlated/dependent/. to X(t=t1) or
Y(t=t2). A simple experiment could be to sketch the phase/state space of
variable X, Y and also joint phase space ( Y(t+m) vs. X(t) ).  my though is
if X and Y are not noise/random - they are not if you are considering two
"neural" sources -  then the joint strange attractor should be limited to a
region in the phase space  and on can find an m which leads to more condense
strange attractor.

P.S.: I do not get your point when you say  "  given that X(t) has
auto-correlation?"

~Iman

From: Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu] 
Sent: Wednesday, February 19, 2014 12:27 PM
To: Iman M.Rezazadeh
Cc: Aleksandra Vuckovic; EEGLAB List
Subject: Re: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

Dear Iman,

Is it possible that X(t) and Y(t) are independent but X(t) and Y(t+1) are
dependent, given that X(t) has auto-correlation?

Makoto

2014-02-19 11:44 GMT-08:00 Iman M.Rezazadeh <irezazadeh at ucdavis.edu
<mailto:irezazadeh at ucdavis.edu> >:

Hi Makoto and all, 

Actually I am thinking about ICA and GC without considering their
applications in ERP/EEG. What I said is the IC sources are "independent' at
time point t but ICA does not guarantee to remove any dependency between
event X and Y at different time points like X(t) and (Y+1) 

~Iman

From: Aleksandra Vuckovic [mailto:Aleksandra.Vuckovic at glasgow.ac.uk
<mailto:Aleksandra.Vuckovic at glasgow.ac.uk> ] 
Sent: Wednesday, February 19, 2014 11:31 AM
To: mmiyakoshi at ucsd.edu <mailto:mmiyakoshi at ucsd.edu> ; Iman M.Rezazadeh
Cc: EEGLAB List
Subject: RE: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

Hi

we've looked at Granger causality of ICAs during motor imagery task, yes you
can definitively see that some sources 'speak' to each other at certain
points of time, related to the event while some other seem to be there
always (in mu rhythm) independent on the event.

Regards,

Alex

  _____  

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 Makoto Miyakoshi
[mmiyakoshi at ucsd.edu <mailto:mmiyakoshi at ucsd.edu> ]
Sent: 19 February 2014 18:18
To: Iman M.Rezazadeh
Cc: EEGLAB List
Subject: Re: [Eeglablist] Two step source connectivity analysis (as
implemented in SIFT)

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 

2014-02-19 0:53 GMT-08:00 Iman M.Rezazadeh <irezazadeh at ucdavis.edu
<mailto:irezazadeh at ucdavis.edu> >:

I would like step in and add more comments which may be helpful (hopefully):

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 

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

Iman M.Rezazadeh, Ph.D

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
contradicts the
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>

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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

-- 

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

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