Fuzzy wavelet network based on extended Kalman filter training algorithm combined with least square weight estimation: Efficient and improved chromatographic QSRR/QSPR models

Abstract

Inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts, a fuzzy wavelet network (FWN) is proposed for predicting the gas chromatographic retention time of phenol derivatives on fused-silica, wide-bore, and open-tubular columns with different polarities in terms of quantitative structure-retention relationship (QSRR) studies. The FWN consists of a set of fuzzy rules. Each rule corresponding to a sub-wavelet neural network (WNN) consists of single-scaling wavelets. The proposed FWN follows a two-stage efficient learning algorithm scheme, which undertakes the extended Kalman filter (EKF) training algorithm for adjusting all translation parameters, dilation parameters, and weight coefficients of the WNNs and then least square estimation for updating all the weights. 4-3-1 FWNs were developed using the descriptors selected by the multiple linear regression (MLR) models as inputs. By learning the translation parameters of the wavelets and adjusting the shape of membership functions, the model accuracy was remarkably improved. The accuracy and robustness of the generated models were illustrated using leave-one-out and leave-multiple-out cross-validations and also by Y-randomization. Sensitivity analysis by sequential zeroing of weights revealed that the molecular geometry and electronic interactions play a major role in the retention behavior of these compounds on non-polar and semi-polar columns, respectively.