[Eeglablist] ICA after PCA

Thu Apr 21 12:10:04 PDT 2016

Thanks Makoto. I think I understand that if you apply PCA and picked the first 30 components from it then your K-factor is increased , since you have 30 PCA signals – instead of 100ch.
However:

1)      Picking up the first 30 PCA components would not let you to reconstruct the data perfectly!

2)      If you apply ICA to those 30 PCA signals ( not the original 100ch data) then you will have 30 ICA sources. But what is the relationship btw each ICA source and original recording? In other words, how can you back-project each ICA source to the original recording montage ( ie , 100ch) ? After performing PCA and later ICA , the (un)mixing matrix dimension is 30 x 30 not 100 x 100. Thus, I am still confused how the outcome IC maps after PCA+ICA would be meaningful !

Iman

From: Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
Sent: Thursday, April 21, 2016 10:04 AM
To: Iman Mohammad-Rezazadeh <irezazadeh at UCDAVIS.EDU>
Cc: EEGLAB List <eeglablist at sccn.ucsd.edu>; Arnaud Delorme <arno at ucsd.edu>; Loo, Sandra <SLoo at mednet.ucla.edu>; Jeste, Shafali M.D. <SJeste at mednet.ucla.edu>; ADickinson at mednet.ucla.edu; Scott Makeig <smakeig at ucsd.edu>
Subject: Re: ICA after PCA

Dear Iman,

It does not increase K directly, but effectively it does.
If you have 100ch and K==30 (fixed), you need (100^2) * 30 data points.
But if you apply PCA on it and reduce it to 10 PCs, you need only (10^2) * 30 data points. In this case, your K is effectively multiplied by 100^2/10^2 ==100.

Note that the value K should increase exponentially as the number of channels increases. K==30 is for the case of 32ch. There is no good study on the question how many data points are necessary for stable ICA results, but Jason says 1 million datapoints for 100ch is a rule of thumb (in this case, K==100).

Makoto

On Thu, Apr 21, 2016 at 12:22 AM, Iman Mohammad-Rezazadeh <irezazadeh at ucdavis.edu<mailto:irezazadeh at ucdavis.edu>> wrote:
Hi Makoto,
My question is : does doing PCA before ICA helps for increasing K or in other words the quality of ICA output? Could you please describe it in a simple language ☺
Thanks
Iman
From: Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu<mailto:mmiyakoshi at ucsd.edu>]
Sent: Wednesday, April 20, 2016 7:01 PM
To: Iman Mohammad-Rezazadeh <irezazadeh at UCDAVIS.EDU<mailto:irezazadeh at UCDAVIS.EDU>>
Cc: EEGLAB List <eeglablist at sccn.ucsd.edu<mailto:eeglablist at sccn.ucsd.edu>>; Arnaud Delorme <arno at ucsd.edu<mailto:arno at ucsd.edu>>; Loo, Sandra <SLoo at mednet.ucla.edu<mailto:SLoo at mednet.ucla.edu>>; Jeste, Shafali M.D. <SJeste at mednet.ucla.edu<mailto:SJeste at mednet.ucla.edu>>; ADickinson at mednet.ucla.edu<mailto:ADickinson at mednet.ucla.edu>; Scott Makeig <smakeig at ucsd.edu<mailto:smakeig at ucsd.edu>>
Subject: Re: ICA after PCA

Dear Iman,

> I have found few papers and discussions about doing PCA and then ICA for increasing the K-factor and dimensionality reduction.

K-factor you mean is the term you see in the equation?

minimumDataPointsToRunICA = ((number of channels)^2) * K

> However, I cannot completely understand what is the meaning of the ICA outputs?

ICA output rotates PCA-dimension-reduced data. You can reconstruct full-channel (but now rank-deficient) data using PCA output.

Actually there is another rotation, sphering, as a preprocess for ICA. So you rotate data three times to find unmixing matrix using PCA rank-reduction option. That's why you feel dizzy :-)

Makoto

On Wed, Apr 13, 2016 at 11:59 PM, Iman Mohammad-Rezazadeh <irezazadeh at ucdavis.edu<mailto:irezazadeh at ucdavis.edu>> wrote:
Hi EEGLABers,
I have found few papers and discussions about doing PCA and then ICA for increasing the K-factor and dimensionality reduction. The (un)mixing matrix would be m x m which m is the number of PCA. Each row (column) is the weights for ICA sources.
However, I cannot completely understand what is the meaning of the ICA outputs? How are the IC maps (topo maps) constructed since we need the location of PCA components (similar to  the channels locations) to plot the spatial filters/IC maps.
In other words,  how can we plot the IC maps given the fact that we don’t have the spatial information about PCA components?
Best
Iman

============================================
Iman M.Rezazadeh, Ph.D
UCLA David Geffen School of Medicine
Semel Institute for Neuroscience and Human Behavior
760 Westwood Plaza, Ste 47-448
Los Angeles, CA  90095
http://www.linkedin.com/pub/iman-m-rezazadeh/10/859/840/

--
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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