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FSL  June 2007

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Subject:

Re: questions on PCA plot in MELODIC results report

From:

Xuelin Cui <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Fri, 22 Jun 2007 14:15:50 -1000

Content-Type:

text/plain

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Parts/Attachments

text/plain (176 lines)

Christian:

Thanks, I think I get it.

Xuelin

****************************************
Xuelin Cui
Department of Electrical Engineering
University of Hawaii-Manoa
Honolulu HI 96822

Tel: 1-808-349-0983
Email: [log in to unmask]
****************************************

----- Original Message -----
From: Christian Beckmann <[log in to unmask]>
Date: Friday, June 22, 2007 4:05 am
Subject: Re: [FSL] questions on PCA plot in MELODIC results report
To: [log in to unmask]

> Hi
> 
> On 22 Jun 2007, at 14:23, Xuelin Cui wrote:
> 
> > Christian:
> >
> > Thanks, that really helps
> >
> > First of all, in the last paragraph in your last Email, you  
> > mentioned "The green curve simply is
> > the sum of the leading Eigenvalues divided by their total sum", I 
> 
> > guess you actually meant to say "blue curve", right? Since the 
> blue  
> > curve looks more like the normalised eigenvalue solved from PCA.
> >
> 
> No, I don't. The blue curve is the normalised Eigenvalues, the 
> green  
> curve is the cumulative sum of the former, i.e.the sum of the 
> leading  
> Eigenvalues divided by the total sum.
> 
> > One more question:
> > In PCA, with the number of the more eigenvalue retained, there  
> > should be more eigenvectors as well, since eigenvalues and  
> > eigenvectors are 1-to-1 matching. But how come in the plot with 
> the  
> > number of the eigenvalue increases(going rightward along x-axis), 
> 
> > the red curve, which means the number of the dimentionality, drops?
> >
> 
> That's the entire point of the dim estimate - these are functions   
> (penalised likelihoods) which try to assess the likely number of  
> underlying sources which generated the observed data and hence the  
> observed Eigenspectrum. From the peak of the red curve onwards the  
> addition of more components becomes less likely since that part of  
> the Eigenspectrum is not very different from the expected  
> Eigenspectrum of Gaussian noise, i.e. you might as well assume that 
> 
> no further components exist and that the minor part of the  
> Eigenspectrum only corresponds to the noise.
> cheers
> christian
> 
> > Thanks
> >
> > Xuelin
> >
> > ****************************************
> > Xuelin Cui
> > Department of Electrical Engineering
> > University of Hawaii-Manoa
> > Honolulu HI 96822
> >
> > Tel: 1-808-349-0983
> > Email: [log in to unmask]
> > ****************************************
> >
> > ----- Original Message -----
> > From: Christian Beckmann <[log in to unmask]>
> > Date: Friday, June 22, 2007 7:51 pm
> > Subject: Re: [FSL] questions on PCA plot in MELODIC results report
> > To: [log in to unmask]
> >
> >> Hi
> >>
> >> On 19 Jun 2007, at 21:50, Xuelin Cui wrote:
> >>
> >>> Dear folk:
> >>>
> >>> I have some questions about the PCA plot in the MELODIC results
> >>> report. In the MELODIC report folder, there is a html file
> >> showing
> >>> the ICA analysis results. If opening the html file, one will see
> >> a
> >>> PCA plot report with 3 curves(red, green blue) on it.
> >>
> >>> First of all, is the x-axis and y-axis in the plot means the
> >> number
> >>> of eigenvalues and the value of eigenvalues respectively?
> >>
> >> Yes, though the x-axis will typically only be plotted up to the
> >> number of Eigenvalues which jointly explain the firs 99% of the
> >> veriation, i.e. your experiment might be 100 TRs long but the x-
> >> axis
> >> might only go from 1-56, say, because the final 44 Eigenvalues are
> >>
> >> <1% of the vraiance.
> >>
> >>> Also, as the plot says, the red curve means dimention estimate
> >> and
> >>> the green one means percentage of variance. I am just confused
> >> on
> >>> how to understanding the red and green curves in the plot.
> >>
> >> The y-scale is only meaningful for the green line - the other
> >> lines
> >> (the Eigenspectrum itself and the dim estimat) have been
> >> normalised
> >> to be in the range 0-1. It is plotted from 0-1.05 in order to
> >> avoid
> >> clipping of the curves at the top. The estimated dimensionality is
> >>
> >> the maximum of the red curve. From this point onwards the blue
> >> line
> >> (the Eigenspectrum) is not significantly different from the
> >> theoretical Eigenspectrum of random noise. The green curve simply
> >> is
> >> the sum of the leading Eigenvalues divided by their total sum,
> >> i.e.
> >> is the proportion of explained variance for any given dimension.
> >>
> >> cheers
> >> christian
> >>
> >>
> >>> For example: the maximum y-value on my PCA plot is 1.05, but my
> >>> projected subspace is 42-dimentional. Then, how should I explain
> >>
> >>> the red curve in the plot, as well as the green one?
> >>>
> >>> Thanks alot
> >>>
> >>> Xuelin
> >>> ****************************************
> >>> Xuelin Cui
> >>> Department of Electrical Engineering
> >>> University of Hawaii-Manoa
> >>> Honolulu HI 96822
> >>>
> >>> Tel: 1-808-349-0983
> >>> Email: [log in to unmask]
> >>> ****************************************
> >>
> >> ____
> >> Christian F. Beckmann
> >> University Research Lecturer
> >> Oxford University Centre for Functional MRI of the Brain (FMRIB)
> >> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
> >> [log in to unmask]	http://www.fmrib.ox.ac.uk/~beckmann
> >> tel: +44 1865 222551                	fax: +44 1865 222717
> >>
> 
> ____
> Christian F. Beckmann
> University Research Lecturer
> Oxford University Centre for Functional MRI of the Brain (FMRIB)
> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
> [log in to unmask]	http://www.fmrib.ox.ac.uk/~beckmann
> tel: +44 1865 222551                	fax: +44 1865 222717
> 

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