[gmx-users] g_covar -ref

vijaya subramanian vijaya65 at hotmail.com
Thu Mar 18 21:11:57 CET 2010 

Hi
Thanks for your input, what are the few specific cases where 
a reference structure might be used?
Vijaya

> Date: Thu, 18 Mar 2010 20:42:36 +0100
> Subject: Re: [gmx-users] g_covar -ref
> From: tsjerkw at gmail.com
> To: gmx-users at gromacs.org
> 
> Hi Vijaya,
> 
> > Your answer truly eludes me, unless -ref is an useless option.
> 
> Well, that's pretty close to the conclusion. The use is limited to a
> few very specific cases and it might be better to hide the option from
> the view of casual users.
> 
> But apparently you didn't catch the why yet. If you imagine a pendulum
> going back and forth, the principal components will be commonly
> determined by taking the deviations from the mean position. Then you
> get two components, one for the direction of the motion and one for
> the deflection from linearity, right? But now, you calculate  the
> deviations not with respect to the average position, but you take the
> deviations with respect to a position that is away from the mean, say
> halfway to the left. Now you can follow the same procedure,
> calculating a matrix of cross products for these deviations, and
> diagonalizing it. But what do these results then mean? This is a neat
> example to run with pen and paper... You should even be able to solve
> it analytically :)
> 
> Have fun,
> 
> Tsjerk
> 
> 
> > In any case it isn't particularly important.
> > Vijaya
> >
> >
> >
> >> Date: Thu, 18 Mar 2010 19:37:40 +0100
> >> Subject: Re: [gmx-users] g_covar -ref
> >> From: tsjerkw at gmail.com
> >> To: gmx-users at gromacs.org
> >>
> >> Hi Vijaya,
> >>
> >> I'm sorry if I didn't quite get that first sentence of yours. Did you
> >> meant to start it with "I thought that ..."? Or were you trying to
> >> explain me something you thought I missed?
> >>
> >> PCA stands for 'principal component analysis', not 'covariance
> >> analysis'. For instance, PCA can be applied to correlations, and then
> >> is 'correlation analysis'. SVD is a particular flavour of PCA and here
> >> yields the same results as traditional PCA because the covariance
> >> matrix is symmetric, but otherwise they're not strictly the same. That
> >> is to say, the SVD is obtained by extracting the eigenvectors from the
> >> matrices transpose(S) x S and S x transpose(S). Which are quite
> >> obviously identical if S is a symmetric matrix.
> >>
> >> By the way, was your question regarding the -ref option answered, or
> >> did the answer elude you? If the latter is the case, maybe if now you
> >> feel sufficiently confident that I know a bit about PCA, you can go
> >> through the answer again.
> >>
> >> Cheers,
> >>
> >> Tsjerk
> >>
> >> On Thu, Mar 18, 2010 at 7:01 PM, vijaya subramanian
> >> <vijaya65 at hotmail.com> wrote:
> >> > PCA refers to covariance analysis (though SVD gives the same results).
> >> > Principal components are obtained by projecting the trajectory onto
> >> >  the eigenvectors of the covariance matrix.
> >> > I just wanted to know why the option -ref was offered and if it had any
> >> > significance.
> >> > Thanks
> >> > Vijaya
> >> >
> >> >> Date: Thu, 18 Mar 2010 17:51:04 +0100
> >> >> Subject: Re: [gmx-users] g_covar -ref
> >> >> From: tsjerkw at gmail.com
> >> >> To: gmx-users at gromacs.org
> >> >>
> >> >> Hi Vijaya,
> >> >>
> >> >> Well, to start with that will be something as calculating the
> >> >> 'fluctuation' as sum((xi-ri)^2)/N, with xi and ri denoting the ith
> >> >> atom of the conformation x and the reference structure r and the sum
> >> >> is over time/observations. In the case of no variation in xi, the
> >> >> value you get will still be finite, in stead of zero, as would
> >> >> probably be most meaningful.
> >> >> Now for the covariances, there's a bit more to it. The covariance is
> >> >> the product moment of the deviations: sum((xi-ri)(xj-rj))/N. When
> >> >> there is no correlation, the deviations about the mean are random and
> >> >> average out to zero. But with the deviations against a reference, that
> >> >> is not the case. So the results should be regarded meaningless, unless
> >> >> you have a good reason for doing so, and come with a solid
> >> >> justification. Okay, there may be a purpose, but I'll leave that to
> >> >> your imagination :)
> >> >>
> >> >> Hope it helps,
> >> >>
> >> >> Tsjerk
> >> >>
> >> >> On Thu, Mar 18, 2010 at 5:33 PM, vijaya subramanian
> >> >> <vijaya65 at hotmail.com> wrote:
> >> >> > Hi
> >> >> > Has anyone studied the effect of using different reference
> >> >> > structures,
> >> >> > not the average structure, when carrying out PCA.  Does it make sense
> >> >> > to
> >> >> > use
> >> >> > a structure besides the average to calculate the covariance matrix?
> >> >> > Thanks
> >> >> > Vijaya
> >> >> >
> >> >> >
> >> >> >
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> >> >>
> >> >>
> >> >>
> >> >> --
> >> >> Tsjerk A. Wassenaar, Ph.D.
> >> >>
> >> >> post-doctoral researcher
> >> >> Molecular Dynamics Group
> >> >> Groningen Institute for Biomolecular Research and Biotechnology
> >> >> 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
> >> 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
> University of Groningen
> The Netherlands
> -- 
> gmx-users mailing list    gmx-users at gromacs.org
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