[gmx-users] What is an acceptable cosine content values?

[Tsjerk Wassenaar]

Hi Catherine,

I did explain this already:

>> >  1 0.602921

Cosine content for first pc

>> >  2 0.011185

Cosine content for second pc

>> >  3 0.0659901

Cosine content for third pc

>> >  4 0.425943

...

>> >  5 0.204306

...

>> >  6 0.439315

...

>> >  7 0.0288551

...

>> >  8 0.0830944

Cosine content for eighth pc

>
> Do you mean I should only look at the first row?

If you care to know only the cosine content of the projection on the
first pc, yes, then only look at the first row.

> When you said I should perform the analysis per component, do you mean I
> should also consider row 2-8 above?  If yes, could you teach me how to
> interpret it too?

Berk Hess showed that random diffusion yields a specific pattern in
terms of the cosine contents of projections on the first few
eigenvectors. But in more general terms, just like a high cosine
content on the first pc may indicate unidirectional motion from one
region in conformational space to another, so may a high cosine
content on subsequent pc's. However, in line with Hess' findings, the
cosine content for the i'th pc is fitting against a i/2 period cosine,
while one should be especially cautious of nonconvergence if any pc
fits nicely to a half cosine, indicating a unidirectional motion along
the eigenvector.

If it starts to be less clear now than it seemed, I'm sorry, but PCA
is not one of the easiest methods of analysis, and there is a lot of
misconception around regarding the interpretation...

Cheers,

Tsjerk

>
> Sorry to have so many questions, hope you don't mind.
>
> Best regards & many many thanks in advanced,
>
> Catherine
>
>
>
>
>
>
>
>
>> Date: Thu, 12 Apr 2012 11:53:25 +0200
>> Subject: Re: [gmx-users] What is an acceptable cosine content values?
>> From: tsjerkw at gmail.com
>> To: gmx-users at gromacs.org
>
>>
>> Hi Catherine,
>>
>> > When we use cosine content to determine if our simulation are converged
>> > or
>> > not, should I
>>
>> You can't use the cosine content to determine if a simulation is
>> converged. You can only use it to determine whether the simulation is
>> not converged, which is quite a different thing.
>>
>> > (1) sum all the first three principal components together or examine
>> > individually?
>>
>> Determination of the cosine content is done by means of fitting, and
>> the cosine content can be regarded a correlation coefficient, which is
>> one for a perfect fit and 0 for no fit. That only makes sense for one
>> pc. The analysis is thus performed per component.
>>
>> > (2) If I expect the first 10 ns is the equilbrium period, while the
>> > other 20
>> > ns as the production period.  Should I include all 30 ns of trajectory
>> > to
>> > the analys is or should I just include the last 20 ns trajectory to the
>
>> > analysis?
>>
>> No, you should perform the analysis on the part you intend to use for
>> all analysis.
>>
>> > (3) Let's if I got the PC1 as low as 0.3, can I still claim the
>> > trajectories
>> > are converged?
>>
>> No. You can claim that the cosine content is low, but that is not the
>> same as being converged.
>>
>> > (4) Did you comes across that when you increase the simulation time, the
>> > cosine content values of the first three principal components did not
>> > goes
>> > down but increased?
>>
>> May very well happen. Especially if the system tips over to a
>> previously unexplored region of conformational space due to a
>> conformational change or internal rearrangement.
>>
>> Cheers,
>>
>> Tsjerk
>>
>> --
>> 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
>> --
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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