Thank you very much for your prompt response and your suggestion. As a matter of fact, that was exactly how I did my comparison. I have passed xY.y to princomp.m of matlab (see the attached screenshot of my code), and compared the first principal component score with the "Y" in the mat file saved by spm_regions.m, which is the "eigenvariate" plotted on the gui. Therefore, the filtering was not the reason for the difference between the two results. 

I did an additional comparison to test whether the difference between the two results are indeed due to the mean subtraction. I modified my local copy of spm_regions.m to subtract the mean of each column of y before passing y’y to the svd routine. The result of the modified spm_regions.m is the same as that of princomp.m of matlab after scaling with the square root of the number of columns in the data matrix. 

I am attaching the figure depicting my comparison. As you will see, the first PC score of the modified spm_regions.m (labeled as “spm_demeaned”) is the same as the scaled result of princomp.m of matlab (labeled as “matlab/sqrt(#columns)”), while it is very different from the “eigenvariate” of the original spm_regions.m (labeled as “spm”). The variance of the first PC score computed after mean subtraction is greater than that of the original “eigenvariate”. 

My comparison indicates that the “eigenvariate” computed by spm_regions.m would have been the same as the scaled first principal component score (of the filtered time series data) if the the mean of each column (from the filtered data matrix) had been subtracted before passing y’y to the SVD routine. 
Is there an explicit rationale for SPM’s decision to NOT demean the columns prior to passing the matrix to the SVD routine?  

Can you clarify whether the first eigenvariate estimate you have implemented in the gPPI software uses the SPM approach (omitting demeaning step) or the matlab princomp.m approach (i.e., where columns are demeaned)?

Is one approach more “correct” in terms of the goal of extracting the first eigenvariate from a group of voxels?
 
Thanks again,

Taihao


-----Original Message-----
From: "MCLAREN, Donald" <[log in to unmask]>
Sent: Friday, May 15, 2015 1:12pm
To: "Taihao Jin" <[log in to unmask]>
Cc: "SPM" <[log in to unmask]>
Subject: Re: [SPM] Mean subtraction for computing eigenvariate?

One main difference between your approach in matlab and SPM is that SPM has
filtered the data. The variance difference you are seeing are because the
two graphs are plotted on different axis. SPM also scales the values. I'd
start with xY.y to start with the filtered data for princomp/pca.


Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Postdoctoral Research Fellow, GRECC, Bedford VA
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Thu, May 14, 2015 at 4:55 PM, Taihao Jin <[log in to unmask]> wrote:

> Dear experts,
>
> I am writing to ask you a question regarding to the computation of
> "eigenvariate" in spm_regions.m of SPM8.
>
> I have compared the first eigenvariate returned by spm_regions.m with the
> first principal component score returned by matlab's princomp.m for a mask
> ROI applied to the time series data from a single subject.  The time series
> of these two first principal component scores are different, as are the
> eigenimages depicting the spatial map of the component weights.  In trying
> to understand the basis for the difference, it appears that matlab's
> princomp.m function demeans the columns of the data matrix (rows are time
> points, columns are voxels) before passing the data matrix y to the
> singular value decomposition routine in matlab (svd.m).  In contrast, SPM's
> spm_regions.m does not demean the columns of the data matrix before passing
> matrix y'y to the svd routine.
>
> I am attaching the comparison (see the attached screenshot) of the first
> principal component score computed by the matlab built in routine
> princomp.m  (labeled as "matlab") and the output of spm_regions.m (labeled
> as "spm"). It is obvious that the one computed by princomp.m has much
> greater temporal variance than the one computed with spm. The eigenimages
> are also different.
>
> Could you please explain why the first "eigenvariate" calculated by SPM
> does not correspond to the first principal component score returned by
> matlab's princomp.m function, and also why the SPM routine does not appear
> to mean-correct the columns of the time x voxels data matrix?
>
> Thank you very much.
>
> Taihao
>
>
>