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
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