title: Algorithmic dimensionality reduction for molecular structure analysis.
abstract: 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.
authors: Discrete Mathematics and Complex Systems, Sandia National Laboratories, Albuquerque, New Mexico 87185-1316, USA. wmbrown@sandia.gov
authors: W Michael
authors: WM
authors: Brown
authors: Shawn
authors: S
authors: Martin
authors: Sara N
authors: SN
authors: Pollock
authors: Evangelos A
authors: EA
authors: Coutsias
authors: Jean-Paul
authors: JP
authors: Watson
mesh_terms: D000465:Algorithms; D019985:Benchmarking; D034242:Cyclooctanes / Q000737:chemistry*; D008968:Molecular Conformation; D012680:Sensitivity and Specificity
chemical_list: D034242:Cyclooctanes; C474479:cyclooctane