[Eeglablist] Two step source connectivity analysis (as implemented in SIFT)
jdien07 at mac.com
Mon Feb 10 15:20:15 PST 2014
This is a really great question that highlights some widespread ambiguities in how ICA tends to be discussed in the EEG field.
To bullet point it:
1) ICA (specifically thinking about Infomax here) separates components using an algorithm that maximizes non-normality of the variables (Central Limit Theorem says a mix should be more normal so non-normal variables are more likely to not be a mix) and also to minimize the degree to which one variable or its higher powers can predict another variable (independence).
2) While this makes sense in principle, in practice the second order moments (correlations) tend to swamp the algorithm, making it not work, so it is common practice to desphere the variables (remove the correlations), run the ICA, and then sphere them again (put the correlations back in).
3) So although the ICA algorithm maximizes independence, the EEG variables resulting from a typical ICA procedure are NOT independent. They are correlated. This is a good thing since it does not make sense for brain processes to always be orthogonal to each other. Clearly they should in fact be able to influence each other. A mathematical procedure that imposed such an artificial constraint would be unlikely to yield accurate results. So we get the benefit of separated components as well as flexibility for them to be correlated. This means that ICA-derived measures of sources can absolutely reflect influences on each other (in principle, without addressing the specifics of SIFT).
Of course, there are subtleties here about the nature of how one source might influence another and so for this to work the nature of the influence would need to be more apparent in the second-order moments than the higher order moments, but I think this is not an unreasonable assumption. Of course, this discussion only applies if you did indeed desphere/sphere in your ICA procedure.
I go into some discussion of how ICA is applied to ERPs and how it compares to PCA rotations in my 2007 paper, where I also demonstrate that in the temporal domain (time points), Promax (an oblique rotation that also allows for correlated components) yields better results with a simulated dataset, although ICA (Infomax) does a better job in the spatial domain (channels).
Dien, J., Khoe, W., & Mangun, G. R. (2007). Evaluation of PCA and ICA of simulated ERPs: Promax versus Infomax rotations. Human Brain Mapping, 28(8), 742-763.
Interestingly, a similar conclusion (Langers, 2009) has been made for fMRI datasets (although here ICA works better for temporal and Promax works better for spatial, for reasons that make sense in view of the discussion in my 2007 paper).
On Feb 10, 2014, at 7:57 AM, Bethel Osuagwu <b.osuagwu.1 at research.gla.ac.uk> wrote:
> 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!
> From: eeglablist-bounces at sccn.ucsd.edu [eeglablist-bounces at sccn.ucsd.edu] On Behalf Of IMALI THANUJA HETTIARACHCHI [ith at deakin.edu.au]
> Sent: 07 February 2014 01:27
> To: mullen.tim at gmail.com
> Cc: 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
> Dr. Imali Thanuja Hettiarachchi
> Centre for Intelligent Systems research
> Deakin University, Geelong 3217, Australia.
> Mobile : +61430321972
> Email: ith at deakin.edu.au<mailto:ith at deakin.edu.au>
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Senior Research Scientist
Maryland Neuroimaging Center
University of Maryland
E-mail: jdien07 at mac.com
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