Mathematical Programming

, Volume 95, Issue 1, pp 161–185 | Cite as

Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases

  • Dexuan Xie
  • Suresh B. Singh
  • Eugene M. Fluder
  • Tamar Schlick

Abstract.

 The similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases. As a first step to their solution, we propose an efficient projection/ refinement protocol based on the principal component analysis (PCA) and the truncated-Newton minimization method implemented by our package TNPACK (PCA/TNPACK). We show that PCA can provide the same initial guess as the singular value decomposition (SVD) for the optimization task of solving the distance-geometry optimization problem if each column of a database matrix has a mean of zero. Hence, our PCA/TNPACK approach is analogous to the SVD/TNPACK projection/refinement protocol that we developed recently for visualizing large chemical databases. Using PCA/TNPACK and the Merck MDDR database (MDL Drug Data Report), we further investigate the projection/refinement procedure with regards to the preservation of the original clusters of chemical compounds, the accuracy of similarity and diversity sampling of chemical compounds, and the potential application in the study of structure activity relationships. We also explore by simple experiments accuracy and efficiency aspects of the PCA/TNPACK procedure compared to those of a global optimization algorithm (simulated annealing, as implemented by the program package SIMANN) in terms of producing the projection mapping of a database. Numerical results show that the 2D PCA/TNPACK mapping can preserve the distance relationships of the original database and is thus valuable as a first step in similarity and diversity applications. Of course, the generation of a global rather than local minimizer and its interpretation in terms of pharameceutical applications remains a challenge. Since all numerical tests are performed on the Merck MDDR database, results are representative of realistic cases encountered in the field of drug design, and may help analyze properties of medicinal compounds.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dexuan Xie
    • 1
  • Suresh B. Singh
    • 2
  • Eugene M. Fluder
    • 2
  • Tamar Schlick
    • 3
  1. 1.Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, e-mail: dxie@uwm.eduUS
  2. 2.Merck Research Laboratories, Mail Stop RY50-SW100, Rahway, NJ 07065, e-mail: suresh_singh@merck.com, fluder@merck.comUS
  3. 3.Departments of Chemistry and Mathematics, Courant Institute of Mathematical Sciences, New York University and the Howard Hughes Medical Institute, 251 Mercer Street, New York, NY 10012, e-mail: schlick@nyu.eduUS

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