Sample-distance partial least squares: PLS optimized for many variables, with application to CoMFA

J Comput Aided Mol Des. 1993 Oct;7(5):587-619. doi: 10.1007/BF00124364.


Three-dimensional molecular modeling can provide an unlimited number m of structural properties. Comparative Molecular Field Analysis (CoMFA), for example, may calculate thousands of field values for each model structure. When m is large, partial least squares (PLS) is the statistical method of choice for fitting and predicting biological responses. Yet PLS is usually implemented in a property-based fashion which is optimal only for small m. We describe here a sample-based formulation of PLS which can be used to fit any single response (bioactivity). SAMPLS reduces all explanatory data to the pairwise 'distances' among n samples (molecules), or equivalently to an n-by-n covariance matrix C. This matrix, unmodified, can be used to fit all PLS components. Furthermore, SAMPLS will validate the model by modern resampling techniques, at a cost independent of m. We have implemented SAMPLS as a Fortran program and have reproduced conventional and cross-validated PLS analyses of data from two published studies. Full (leave-each-out) cross-validation of a typical CoMFA takes 0.2 CPU s. SAMPLS is thus ideally suited to structure-activity analysis based on CoMFA fields or bonded topology. The sample-distance formulation also relates PLS to methods like cluster analysis and nonlinear mapping, and shows how drastically PLS simplifies the information in CoMFA fields.

MeSH terms

  • Computer Simulation*
  • Histamine Antagonists / chemistry
  • Humans
  • In Vitro Techniques
  • Least-Squares Analysis*
  • Models, Molecular*
  • Molecular Structure
  • Software
  • Steroids / chemistry
  • Steroids / metabolism
  • Transcortin / metabolism


  • Histamine Antagonists
  • Steroids
  • Transcortin