NDLI: Principle Component Analysis and Model Reduction for Dynamical Systems with Symmetry Constraints

Content Provider	IEEE Xplore Digital Library
Author	Shah, M. Sorensen, D.C.
Copyright Year	2005
Description	Author affiliation: graduate student in the Department of Computational and Applied Mathematics, Rice University, 6100 Main St., Houston, TX 77005-1892, USA, mili@caam.rice.edu (Shah, M.)
Abstract	Dimension reduction in molecular dynamics simulation is often realized through a principle component analysis based upon a singular value decomposition (SVD) of the trajectory. The left singular vectors of a truncated SVD provide the reduced basis. In many biological molecules, such as HIV1 protease, reflective or rotational symmetry should be present in the molecular configuration. Determining this symmetry allows one to provide SVD major modes of motion that best describe the symmetric movements of the protein. We present a method to compute the plane of reflective symmetry or the axis of rotational symmetry of a large set of points. Moreover, we develop an SVD that best approximates the given set while respecting the symmetry. Interesting subproblems arise in the presence of noisy data or in situations where most, but not all of the structure is symmetric. An important part of the determination of the axis of rotational symmetry or the plane of reflection symmetry is an iterative re-weighting scheme. This scheme is rapidly convergent in practice and seems to be very effective in ignoring outliers (points that do not respect the symmetry).
Starting Page	2260
Ending Page	2264
File Size	148124
Page Count	5
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1582498
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Reduced order systems Biological system modeling Singular value decomposition Biology computing Reflection Computational fluid dynamics Matrix decomposition Mathematics Analytical models Proteins
Content Type	Text
Resource Type	Article

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