Re: [AMBER] PCA variance using Freq = 108.587 * sqrt( 0.6 / Eigenvalue )

From: Daniel Roe <daniel.r.roe.gmail.com>
Date: Wed, 28 Jan 2015 08:26:03 -0700

Hi,

On Sun, Jan 25, 2015 at 10:40 PM, Muthukumaran R <kumaran.bicpu.edu.in> wrote:
> To calculate variance, it is necessary to obtain all the eigen values of a
> system. This can be obtained using 'thermo' keyword and 'thermo' runs only
> with mass-weighted covariance matrix.
> Hence mass-weighted covariance matrix was used.
>
> Is there any other way to calculate variance without using mass-weighted
> covariance matrix ?

I'm not clear on what you mean by 'variance' here. It's not necessary
to mass-weight a coordinate covariance matrix to obtain eigenvalues,
but it does change the units (when mass-weighted eigenvalues are
converted to frequencies to enable quasi-harmonic analysis). In your
original email you mention PCA, which implies (to me at least) using
the non-mass-weighted coordinate covariance matrix. Maybe if you
provide some more details on the analysis you're trying to perform I
can try to give more specific advice.

-Dan

>
>
>
>
> On Sun, Jan 25, 2015 at 9:53 PM, Daniel Roe <daniel.r.roe.gmail.com> wrote:
>
>> Hi,
>>
>> The actual formula is:
>>
>> Freq. = TO_CM1 * sqrt( KT / Eigenvalue)
>>
>> where TO_CM1 is a constant for converting from original eigenvalue
>> units to units of frequency (was 108.587 in ptraj but has much higher
>> precision in cpptraj) and KT is Boltzmann's constant time temperature
>> in Kelvin (originally in ptraj this was hardcoded to 0.6 kcal/mol, but
>> in recent versions of cpptraj you can specify the temperature during
>> 'diagmatrix'). So according to this, the conversion the other way is:
>>
>> Eigenvalue = KT / (Freq. / TO_CM1)^2
>>
>> If I plug your first frequency (0.48444 cm^-1) into this (using
>> 108.587 and 0.6 for TO_CM1 and KT respectively) I get ~30145 Ang.^2 *
>> amu.
>>
>> However, is there a reason you chose to mass-weight your covariance
>> matrix in the first place? If all you want to do is PCA you should
>> just use the coordinate covariance matrix (i.e. 'matrix covar'). I
>> think the only real reason you'd want to mass-weight your covariance
>> matrix is if you want to perform quasi-harmonic analysis.
>>
>> Hope this helps,
>>
>> -Dan
>>
>> On Sun, Jan 25, 2015 at 8:42 AM, Muthukumaran R <kumaran.bicpu.edu.in>
>> wrote:
>> > Dear Amber users,
>> >
>> > I am performing PCA calculations using cpptraj in ambertools 14.
>> > There are 630 C-alpha atoms in my protein and the mass-weighted
>> covariance
>> > matrix is 1890 x 1890.
>> >
>> > I extracted the eigenvalues and the first 5 are given below.
>> >
>> > 1 0.48444
>> > 2 0.58309
>> > 3 1.08605
>> > 4 1.58621
>> > 5 1.98272
>> >
>> > I want to calculate the percentage of variance for each eigenvector.
>> >
>> > According to the suggestions given in the mailing list, I understand that
>> > these are frequencies and should be converted to eigenvalues for
>> > calculating variance.
>> >
>> > I tried to convert them using the conversion formula,
>> > Freq = 108.587 * sqrt( 0.6 / Eigenvalue )
>> >
>> > (http://archive.ambermd.org/201307/0678.html)
>> >
>> > But, the first frequency gave a very small eigenvalue (in the range of
>> e-06)
>> >
>> > Am I proceeding in the right direction?
>> >
>> > I need your valuable suggestions in calculating the percentage variance
>> of
>> > each eigenvector.
>> >
>> >
>> > _______________________________________________
>> > AMBER mailing list
>> > AMBER.ambermd.org
>> > http://lists.ambermd.org/mailman/listinfo/amber
>>
>>
>>
>> --
>> -------------------------
>> Daniel R. Roe, PhD
>> Department of Medicinal Chemistry
>> University of Utah
>> 30 South 2000 East, Room 307
>> Salt Lake City, UT 84112-5820
>> http://home.chpc.utah.edu/~cheatham/
>> (801) 587-9652
>> (801) 585-6208 (Fax)
>>
>> _______________________________________________
>> AMBER mailing list
>> AMBER.ambermd.org
>> http://lists.ambermd.org/mailman/listinfo/amber
>>
> _______________________________________________
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> http://lists.ambermd.org/mailman/listinfo/amber

```--
-------------------------
Daniel R. Roe, PhD
Department of Medicinal Chemistry
University of Utah
30 South 2000 East, Room 307
Salt Lake City, UT 84112-5820
http://home.chpc.utah.edu/~cheatham/
(801) 587-9652
(801) 585-6208 (Fax)
_______________________________________________
AMBER mailing list
AMBER.ambermd.org
http://lists.ambermd.org/mailman/listinfo/amber
```
Received on Wed Jan 28 2015 - 07:30:04 PST
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