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Algorithmic dimensionality reduction for molecular structure analysis

J. Chem. Phys. 129, 064118 (2008); doi:10.1063/1.2968610

Published 14 August 2008

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W. Michael Brown,1 Shawn Martin,2 Sara N. Pollock,3,4 Evangelos A. Coutsias,4 and Jean-Paul Watson1
1Discrete Mathematics and Complex Systems, Sandia National Laboratories, Albuquerque, New Mexico 87185-1316, USA
2Computer Science and Informatics, Sandia National Laboratories, Albuquerque, New Mexico 87185-1316, USA
3Department of Biochemistry and Molecular Biology Division of Biocomputing, University of New Mexico, Albuquerque, New Mexico 87131, USA
4Department of Mathematics, University of New Mexico, Albuquerque, New Mexico 87131, USA
Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation—a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation. ©2008 American Institute of Physics
History: Received 28 April 2008; accepted 16 July 2008; published 14 August 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/064118/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.V-
    Electron correlation calculations for atoms, ions and molecules
  • 33.15.Bh
    General molecular conformation and symmetry; stereochemistry
  • YEAR: 2008

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0021-9606 (print)   1089-7690 (online)
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