Novel algorithm to select basis functions in spline regression: applications in quantitative structure–activity relationship studies

Abstract

Selection of the most significant basis functions to perform spline regressions is an extremely challenging problem in quantitative structure-activity relationship studies. Normally, spline-based regression models are derived either incrementally or using genetic algorithms, and they may not provide optimal solutions. To address this issue in a systematic way, we described herein a novel variable selection method, namely, random replacement method (RRM) combining the principles of replacement methods (RMs) and genetic algorithms. We applied RRM for the selection of variables in multiple linear regression on two model data sets and showed that the method outperforms other approaches, namely, variable selection and model building using prediction and ant colony optimization. We extended the application of RRM for the selection of basis functions in spline regression, and this approach is named as random function approximation (RFA). We compared the performance of RFA with that of multivariate adaptive regression splines and genetic function approximation and demonstrated the improved performances of the proposed method and the quality of the generated models based on coefficient of determination, R 2 and Q 2 loo

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