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Hi<br>Thanks for your input, what are the few specific cases where <br>a reference structure might be used?<br>Vijaya<br><br>> Date: Thu, 18 Mar 2010 20:42:36 +0100<br>> Subject: Re: [gmx-users] g_covar -ref<br>> From: tsjerkw@gmail.com<br>> To: gmx-users@gromacs.org<br>> <br>> Hi Vijaya,<br>> <br>> > Your answer truly eludes me, unless -ref is an useless option.<br>> <br>> Well, that's pretty close to the conclusion. The use is limited to a<br>> few very specific cases and it might be better to hide the option from<br>> the view of casual users.<br>> <br>> But apparently you didn't catch the why yet. If you imagine a pendulum<br>> going back and forth, the principal components will be commonly<br>> determined by taking the deviations from the mean position. Then you<br>> get two components, one for the direction of the motion and one for<br>> the deflection from linearity, right? But now, you calculate the<br>> deviations not with respect to the average position, but you take the<br>> deviations with respect to a position that is away from the mean, say<br>> halfway to the left. Now you can follow the same procedure,<br>> calculating a matrix of cross products for these deviations, and<br>> diagonalizing it. But what do these results then mean? This is a neat<br>> example to run with pen and paper... You should even be able to solve<br>> it analytically :)<br>> <br>> Have fun,<br>> <br>> Tsjerk<br>> <br>> <br>> > In any case it isn't particularly important.<br>> > Vijaya<br>> ><br>> ><br>> ><br>> >> Date: Thu, 18 Mar 2010 19:37:40 +0100<br>> >> Subject: Re: [gmx-users] g_covar -ref<br>> >> From: tsjerkw@gmail.com<br>> >> To: gmx-users@gromacs.org<br>> >><br>> >> Hi Vijaya,<br>> >><br>> >> I'm sorry if I didn't quite get that first sentence of yours. Did you<br>> >> meant to start it with "I thought that ..."? Or were you trying to<br>> >> explain me something you thought I missed?<br>> >><br>> >> PCA stands for 'principal component analysis', not 'covariance<br>> >> analysis'. For instance, PCA can be applied to correlations, and then<br>> >> is 'correlation analysis'. SVD is a particular flavour of PCA and here<br>> >> yields the same results as traditional PCA because the covariance<br>> >> matrix is symmetric, but otherwise they're not strictly the same. That<br>> >> is to say, the SVD is obtained by extracting the eigenvectors from the<br>> >> matrices transpose(S) x S and S x transpose(S). Which are quite<br>> >> obviously identical if S is a symmetric matrix.<br>> >><br>> >> By the way, was your question regarding the -ref option answered, or<br>> >> did the answer elude you? If the latter is the case, maybe if now you<br>> >> feel sufficiently confident that I know a bit about PCA, you can go<br>> >> through the answer again.<br>> >><br>> >> Cheers,<br>> >><br>> >> Tsjerk<br>> >><br>> >> On Thu, Mar 18, 2010 at 7:01 PM, vijaya subramanian<br>> >> <vijaya65@hotmail.com> wrote:<br>> >> > PCA refers to covariance analysis (though SVD gives the same results).<br>> >> > Principal components are obtained by projecting the trajectory onto<br>> >> > the eigenvectors of the covariance matrix.<br>> >> > I just wanted to know why the option -ref was offered and if it had any<br>> >> > significance.<br>> >> > Thanks<br>> >> > Vijaya<br>> >> ><br>> >> >> Date: Thu, 18 Mar 2010 17:51:04 +0100<br>> >> >> Subject: Re: [gmx-users] g_covar -ref<br>> >> >> From: tsjerkw@gmail.com<br>> >> >> To: gmx-users@gromacs.org<br>> >> >><br>> >> >> Hi Vijaya,<br>> >> >><br>> >> >> Well, to start with that will be something as calculating the<br>> >> >> 'fluctuation' as sum((xi-ri)^2)/N, with xi and ri denoting the ith<br>> >> >> atom of the conformation x and the reference structure r and the sum<br>> >> >> is over time/observations. In the case of no variation in xi, the<br>> >> >> value you get will still be finite, in stead of zero, as would<br>> >> >> probably be most meaningful.<br>> >> >> Now for the covariances, there's a bit more to it. The covariance is<br>> >> >> the product moment of the deviations: sum((xi-ri)(xj-rj))/N. When<br>> >> >> there is no correlation, the deviations about the mean are random and<br>> >> >> average out to zero. But with the deviations against a reference, that<br>> >> >> is not the case. So the results should be regarded meaningless, unless<br>> >> >> you have a good reason for doing so, and come with a solid<br>> >> >> justification. Okay, there may be a purpose, but I'll leave that to<br>> >> >> your imagination :)<br>> >> >><br>> >> >> Hope it helps,<br>> >> >><br>> >> >> Tsjerk<br>> >> >><br>> >> >> On Thu, Mar 18, 2010 at 5:33 PM, vijaya subramanian<br>> >> >> <vijaya65@hotmail.com> wrote:<br>> >> >> > Hi<br>> >> >> > Has anyone studied the effect of using different reference<br>> >> >> > structures,<br>> >> >> > not the average structure, when carrying out PCA. Does it make sense<br>> >> >> > to<br>> >> >> > use<br>> >> >> > a structure besides the average to calculate the covariance matrix?<br>> >> >> > Thanks<br>> >> >> > Vijaya<br>> >> >> ><br>> >> >> ><br>> >> >> ><br>> >> >> > ________________________________<br>> >> >> > Hotmail: Trusted email with powerful SPAM protection. Sign up now.<br>> >> >> > --<br>> >> >> > gmx-users mailing list gmx-users@gromacs.org<br>> >> >> > http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> >> >> > Please search the archive at http://www.gromacs.org/search before<br>> >> >> > posting!<br>> >> >> > Please don't post (un)subscribe requests to the list. Use the<br>> >> >> > www interface or send it to gmx-users-request@gromacs.org.<br>> >> >> > Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br>> >> >> ><br>> >> >><br>> >> >><br>> >> >><br>> >> >> --<br>> >> >> Tsjerk A. Wassenaar, Ph.D.<br>> >> >><br>> >> >> post-doctoral researcher<br>> >> >> Molecular Dynamics Group<br>> >> >> Groningen Institute for Biomolecular Research and Biotechnology<br>> >> >> University of Groningen<br>> >> >> The Netherlands<br>> >> >> --<br>> >> >> gmx-users mailing list gmx-users@gromacs.org<br>> >> >> http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> >> >> Please search the archive at http://www.gromacs.org/search before<br>> >> >> posting!<br>> >> >> Please don't post (un)subscribe requests to the list. Use the<br>> >> >> www interface or send it to gmx-users-request@gromacs.org.<br>> >> >> Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br>> >> ><br>> >> > ________________________________<br>> >> > Hotmail: Trusted email with Microsoft’s powerful SPAM protection. Sign<br>> >> > up<br>> >> > now.<br>> >> > --<br>> >> > gmx-users mailing list gmx-users@gromacs.org<br>> >> > http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> >> > Please search the archive at http://www.gromacs.org/search before<br>> >> > posting!<br>> >> > Please don't post (un)subscribe requests to the list. Use the<br>> >> > www interface or send it to gmx-users-request@gromacs.org.<br>> >> > Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br>> >> ><br>> >><br>> >><br>> >><br>> >> --<br>> >> Tsjerk A. Wassenaar, Ph.D.<br>> >><br>> >> post-doctoral researcher<br>> >> Molecular Dynamics Group<br>> >> Groningen Institute for Biomolecular Research and Biotechnology<br>> >> University of Groningen<br>> >> The Netherlands<br>> >> --<br>> >> gmx-users mailing list gmx-users@gromacs.org<br>> >> http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> >> Please search the archive at http://www.gromacs.org/search before posting!<br>> >> Please don't post (un)subscribe requests to the list. Use the<br>> >> www interface or send it to gmx-users-request@gromacs.org.<br>> >> Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br>> ><br>> > ________________________________<br>> > Hotmail is redefining busy with tools for the New Busy. Get more from your<br>> > inbox. Sign up now.<br>> > --<br>> > gmx-users mailing list gmx-users@gromacs.org<br>> > http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> > Please search the archive at http://www.gromacs.org/search before posting!<br>> > Please don't post (un)subscribe requests to the list. Use the<br>> > www interface or send it to gmx-users-request@gromacs.org.<br>> > Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br>> ><br>> <br>> <br>> <br>> -- <br>> Tsjerk A. Wassenaar, Ph.D.<br>> <br>> post-doctoral researcher<br>> Molecular Dynamics Group<br>> Groningen Institute for Biomolecular Research and Biotechnology<br>> University of Groningen<br>> The Netherlands<br>> -- <br>> gmx-users mailing list gmx-users@gromacs.org<br>> http://lists.gromacs.org/mailman/listinfo/gmx-users<br>> Please search the archive at http://www.gromacs.org/search before posting!<br>> Please don't post (un)subscribe requests to the list. Use the <br>> www interface or send it to gmx-users-request@gromacs.org.<br>> Can't post? Read http://www.gromacs.org/mailing_lists/users.php<br> <br /><hr />Hotmail: Trusted email with Microsoft’s powerful SPAM protection. <a href='http://clk.atdmt.com/GBL/go/210850552/direct/01/' target='_new'>Sign up now.</a></body>
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