[gmx-users] Re: Eigenvalue values from PCA (a general question)

[Tsjerk Wassenaar]

Hi Michiel,

You're right there. The OP may have assumed that the numbers were
percentages, whereas they are the eigenvalues, which remain to be
divided by the total variance to get the cumulative fraction of
variance explained. The variance explained by the first ten pc's in
this case is approximately 32 / (trace of covariance matrix). I
naively assumed that the 30% referred to by the OP corresponded to the
fraction.

Cheers,

Tsjerk

On Fri, Dec 16, 2011 at 7:37 AM, Niesen, Michiel <mniesen at coh.org> wrote:
>>Hi Michiel,
>>
>>I disagree, and so does semantics. The cumulative variance of a pc is the
>>variance of it plus the sum of the preceding ones. You're talking about the
>>cumulative fraction of the total variance.
>
> You are right about the proper word usage. It seemed to me from his question, the use of a % mark when discussing the variance covered by the first 10 PCs, and the conclusions drawn from the value he calculated, that Vijayan meant the cumulative fraction of the total variance. I should name it properly, but I still believe that cumulative fraction of the total variance is the property Vijayan would be interested in.
>
> Regards,
>  Michiel
>
>
>>
>>Cheers,
>>
>>Tajerk
>>
>>On Dec 16, 2011 12:07 AM, "Niesen, Michiel" <mniesen at coh.org> wrote:
>>
>>>Date: Thu, 15 Dec 2011 15:11:12 -0500
>>>From: "R.S.K.Vijayan" <biovijayan at gmail.com>
>>>Subject: [gmx-users] Eigenvalue values from PCA (a general question)
>>>To: gmx-users at gromacs.org
>>>Message-ID:
>>>       <CAMM9PAWRYMQrgzHEriarvOVk7QwuzpfWRm_oWC_0+ceMeZmwsA at mail.gmail.com>
>>>Content-Type: text/plain; charset="iso-8859-1"
>>
>>> >Hi all > >I have a query about the eigenvalue values obtained from
>>g_covar and >g_anaeig > >I pe...
>>
>>>What i infer from this is that the cumulative variance experienced by the
>>>top 10 PC is hardly ~ ...
>>The cumulative variance described by a set of PCs is not the sum of their
>>eigenvalues. You have to take the sum of the first x eigenvalues as a
>>percentage of the sum of all eigenvalues to get the cumulative variance.
>>
>>>a) does this imply inadequate sampling by MD or a limited conformational
>>>change happening in the...
>>
>>>b) is it wise to consider the Nucleic acid during essential dynamics or
>>>should it be discared and ...
>>
>>>Thanking you in advance for your suggestions. My apologies since it sound
>>>to be a very general que...
>
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-- 
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
* Groningen Institute for Biomolecular Research and Biotechnology
* Zernike Institute for Advanced Materials
University of Groningen
The Netherlands