[gmx-users] g_covar -ref

Thu Mar 18 19:44:37 CET 2010

Hi
Your answer truly eludes me, unless -ref is an useless option.
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
> -- 
> gmx-users mailing list    gmx-users at gromacs.org
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