hi Steve:
Thanks for reply
But could you please forward my email to Christian? I am reading the technique report. Those questions are exactly the questions on the technique report.
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: Steve Smith <[log in to unmask]>
Date: Monday, March 12, 2007 7:34 am
Subject: Re: [FSL] some theoretical questions on MELODIC
To: [log in to unmask]
> Hi,
>
> As well as Christian's main techrep, you should read the basic
> intro
> to ICA at:
> http://www.fmrib.ox.ac.uk/analysis/techrep/tr01mj2/tr01mj2.pdf
>
>
> On 12 Mar 2007, at 09:34, Xuelin Cui wrote:
>
> > hi Christian:
> >
> > I have a question on equation 5 in you technique report 2.
> >
> > Equation 5 seems to be the maximum likelihood estimation of
> mixing
> > matrix. It is:
> > A_ml=U_q*(lamda_q-sigma^2*I)^1/2*Qt
> > Is U_q the eigenvector matrix directly solved from the 2D fMRI
> data
> > by PCA?
>
> Nearly: it is the top q eigenvectors from the initial data PCA.
>
> > If so, should each of the column vector in U_q be orthogonal?
>
> Yes.
>
> > Also, I dont really figure out that where does the Q matrix come
> > from. Since it is a rotational matrix, each column of it should
> be
> > orthogonal too, right? Why we need Q here?
>
> Q is the final ICA rotation within the space produced by the PCA.
> WIthout Q you would just have PCA.
>
> Steve.
>
>
> >
> > Thanks a lot in advance
> >
> > 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: Tuesday, March 6, 2007 5:06 pm
> > Subject: Re: [FSL] some theoretical questions on MELODIC
> > To: [log in to unmask]
> >
> >> Xuelin,
> >>
> >> all of these questions are readily answered in the technical
> >> report
> >> http://www.fmrib.ox.ac.uk/analysis/techrep/tr02cb1/tr02cb1.pdf
> >>
> >>> 1. Is PCA applied to the data before ICA is applied? (to
> >> decrease
> >>> the dimentionality)
> >> Yes, the maximum likelihood estimate is given by a rotated PCA
> >> solution (equation 5 in the TR)
> >>
> >>> 2. If PCA is applied as a preprocessing, where are those
> >> principal
> >>> components fed into?(put it in this way: After PCA applied, we
> >> have
> >>> a matrix E of some eigenvectors, is E same with X? where X=MS,
> >> X:
> >>> mixed information, M: mixing matrix, S: source)
> >> Nope, PCA uses the Eigenvectors of the data covariance matrix of
> >> X,
> >> see text after equation 5
> >>
> >>> 3: What criterion is used to extract those ICs by MELODIC?
> >>> (minimize the negentropy?)
> >> Approximations to neg-entropy, see text and equation 12
> >>
> >>> 4. What on earth are those ICs, which are extracted by MELODIC?
> >> Projections of the data which are maximally non-Gaussianity - see
> >> text and equation 12. You might find the section on 'uniqueness'
> >> interesting, too
> >>
> >> hope this helps
> >> Christian
> >>
> >>> Thanks a lot in advance
> >>>
> >>> 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
> >> Oxford University Centre for Functional
> >> Magnetic Resonance Imaging of the Brain,
> >> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
> >> Email: [log in to unmask] -
> >> http://www.fmrib.ox.ac.uk/~beckmann/ Phone: +44(0)1865 222551
> >> Fax: +44(0)1865 222717
> >>
>
>
> --------------------------------------------------------------------
> ----
> ---
> Stephen M. Smith, Professor of Biomedical Engineering
> Associate Director, Oxford University FMRIB Centre
>
> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> +44 (0) 1865 222726 (fax 222717)
> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> --------------------------------------------------------------------
> ----
> ---
>
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