Hi,
On Sat, Feb 20, 2016 at 8:57 PM, Joel Lapin <jlapin.ncsu.edu> wrote:
> Just one more question guys. Does the physical interpretation of any row or
> column index still correspond to a specific atom coordinate, as it does in
> the construction of the original covariance matrix?
No. The eigenvectors you obtain from principal component analysis are
a transformed orthonormal set of vectors, in which the individual
components do not correspond to the originals. You can think of it as
a rotation of the data to a new reference frame in which the axes now
correspond to the variance in your data. A specific subset of this
transform that I find easy to comprehend is aligning your coordinates
along the principal axes (the 'principal' command). The first
principal axis of a molecule is the one which if you rotate around it
you get the most motion. The wikipedia article for PCA (e.g.
https://en.wikipedia.org/wiki/Principal_component_analysis) probably
has a much better explanation.
-Dan
>
> On Sat, Feb 20, 2016 at 8:33 PM, Joel Lapin <jlapin.ncsu.edu> wrote:
>
>> Thank you as well Jason.
>>
>> On Sat, Feb 20, 2016 at 8:27 PM, Jason Swails <jason.swails.gmail.com>
>> wrote:
>>
>>> On Sat, Feb 20, 2016 at 7:29 PM, Joel Lapin <jlapin.ncsu.edu> wrote:
>>>
>>> > Thanks a lot Daniel. My only issue is that each coordinate in the
>>> original
>>> > matrix corresponded to an x, y or z component of a specific atom, so
>>> > wouldn't that mean that each eigenvector corresponds to an x, y or z
>>> > component of a specific atom?
>>>
>>>
>>> No. The standard coordinate space for molecules is x1, y1, z1, x2, y2,
>>> z2, ..., xN, yN, zN (a 3-N dimensional space). The diagonalized
>>> covariance
>>> matrix defines a basis set of motions that is some sort of linear
>>> combinations of the original basis set (i.e., the cartesian coordinates
>>> for
>>> each atom individually). The eigenvectors are basically the projection of
>>> each original basis vector along the *new* basis vectors (each of the
>>> eigenvectors).
>>>
>>> It's a change in coordinate system from the arbitrary (but easy to
>>> conceptualize) cartesian space of each atom to a coordinate system that
>>> more fully describes your system.
>>>
>>> HTH,
>>> Jason
>>>
>>> --
>>> Jason M. Swails
>>> BioMaPS,
>>> Rutgers University
>>> Postdoctoral Researcher
>>> _______________________________________________
>>> AMBER mailing list
>>> AMBER.ambermd.org
>>> http://lists.ambermd.org/mailman/listinfo/amber
>>>
>>
>>
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--
-------------------------
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)
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Received on Sun Feb 21 2016 - 07:00:03 PST
