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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