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 statis tical 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). SAM PLS reduces all explanatory data to the pairwise 'distances' among n s amples (molecules), or equivalently to an n-by-n covariance matrix C. This matrix, unmodified, can be used to fit all PLS components. Furthe rmore, SAMPLS will validate the model by modern resampling techniques, at a cost independent of m. We have implemented SAMPLS as a Fortran p rogram and have reproduced conventional and cross-validated PLS analys es of data from two published studies. Full (leave-each-out) cross-val idation of a typical CoMFA takes 0.2 CPU s. SAMPLS is thus ideally sui ted to structure-activity analysis based on CoMFA fields or bonded top ology. The sample-distance formulation also relates PLS to methods lik e cluster analysis and nonlinear mapping, and shows how drastically PL S simplifies the information in CoMFA fields.