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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