Sample-distance partial least squares: PLS optimized for many variables, with application to CoMFA.
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.
Bush
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BL
Merck Research Laboratories, Merck & Co., Inc., Rahway, NJ 07065.
Nachbar
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RB
D003198:Computer Simulation; D006633:Histamine Antagonists / Q000737:chemistry; D006801:Humans; D066298:In Vitro Techniques; D016018:Least-Squares Analysis; D008958:Models, Molecular; D015394:Molecular Structure; D012984:Software; D013256:Steroids / Q000737:chemistry / Q000378:metabolism; D014156:Transcortin / Q000378:metabolism
D006633:Histamine Antagonists; D013256:Steroids; D014156:Transcortin