Re: Request for information on ICA-Maximum likelihood approach

[Bryan Paton <bryan.paton@xxxxxxxxxxxxxxxxxx>]

Brian Gygi wrote:
> Doesn't that kind of negate the whole purpose of ICA?  

Not quite. PCA enforces the rule that components must contain the 
maximal amount of variance not accounted for by previous components. 
Where as ICA returns (depending on the ICA algorithm) maximally 
temporally (or spatially) independent sources. There is no restriction 
on how much variance (usually) the components must account for only that 
they are independent.


> It's supposed to 
> find the dimensions that PCA might miss.  But if you do a PCA first, all 
> you will get out are subsets of the dimensions the PCA finds in the 
> first place.

There are also good reasons why you should run PCA (for big data sets) 
where the number of channels might approach (or be larger than) the 
square root of the number of sample points. This has the effect of 
having a "better" number of data points for the ICA weight matrix:

http://sccn.ucsd.edu/pipermail/eeglablist/2006/001481.html
http://sccn.ucsd.edu/pipermail/eeglablist/2006/001485.html
http://sccn.ucsd.edu/wiki/Chapter_09:_Decomposing_Data_Using_ICA

Although again this might depend on the ICA algorithm being used.

Thanks.

Bryan.

--
Bryan Paton

PhD candidate
Philosophy Program, SOPHIS / School of Psychology & Psychiatry

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