Critical comparative analysis, validation and interpretation of SVM and PLS regression models in a QSAR study on HIV-1 protease inhibitors

Four Quantitative Structure–Activity Relationship (QSAR) models were constructed for a set of 32 and 16 HIV-1 protease inhibitors in the training and external validation sets, respectively, using the biological activity and molecular descriptors from the literature. Two QSAR models were based on Support Vector Machines methods (SVM): Support Vector Regression (SVR) and Least-Squares Support Vector Machines (LS-SVM) models. The other two models were an ordinary Partial Least Squares (PLS) and Ordered Predictors Selection-based PLS (OPS-PLS). The SVR and LS-SVM models showed to be somewhat better than the PLS model in external validation and leave-N-out crossvalidation. SVR and LS-SVM were better than OPS-PLS in external validation, but showed equal performance in leave-N-out crossvalidation. However, despite of their high predictive ability, the SVM models failed in y-randomization, which did not happen with the PLS and OPS-PLS models. The OPS-PLS model was the only one that undoubtedly showed satisfactory performance both in prediction and all validations. The selection of inhibitors by the SVM-based models and variable selection by the OPS-PLS model were rationalized by means of Hierarchical Cluster Analysis (HCA) and Principal Component Analysis (PCA). Lagrange multipliers from the SVR and LS-SVM models were explained for the first time in terms of molecular structures, descriptors, biological activity and principal components. Some unresolved difficulties in practical usage of SVM in QSAR and QSPR were pointed out. The presented validation and interpretation of SVR and LS-SVM models is a proposal for future investigations about SVM applications in QSAR and QSPR, valid for any modeling and validation condition of the final regression equations.