got it, Thanks Christian, for your helps and patience
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 2:29 pm
Subject: Re: [FSL] questions on PCA plot in MELODIC results report
To: [log in to unmask]
> Hi
>
> On 23 Jun 2007, at 01:21, Xuelin Cui wrote:
>
> > The last questoiin:
> >
> > On my plot, the acme of the red curve corresponds to 39 on x-axis
> > (39 ICs). But for the green curve, at the same x value, 39, it
> only
> > reaches approximately 70%-75% on y-axis. Does that mean we throw
> > off too many eigenvalues?
>
> Nope, if these 25-30% of residual variance look like Gaussian noise
>
> then it's the right thing to do.
>
> > Since it seems that we just keep the eigenvectors that only match
>
> > 70%-75% of the eigenvalue. Is that reasonable/possible?
> >
>
> Yes
> cheers
> christian
>
> > Thank you
> >
> > 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
> >>
>
> ____
> 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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