Hi -
Christian is away at the moment I'm afraid. He is off email, but did
you see that steve answered your questions as well as pointing you to
the tech report.
T
On 12 Mar 2007, at 21:36, Xuelin Cui wrote:
> 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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