Partial least squares–slice transform hybrid model for nonlinear calibration

•The PLS-SLT hybrid model is equivalent to the PLS-based piecewise linear model in the y-space.•In PLS-SLT, firstly a single PLS model is established to provide predicted value; then the SLT is utilized to extract the piecewise linear mapping functions between predicted values of PLS and reference values.•Using the SLT technique, the PLS-SLT model could flexibly and effectively implement nonlinear calibration in a linear manner.•The modeling error tested by the Wilcoxon signed rank test demonstrated that compared with PLS, QPLS, KPLS, LW-PLS, SLT-PLS and PLS-Poly, PLS-SLT is at least statistically not worse than these models.

A hybrid model (herein referred to as PLS-SLT) founded on partial least squares (PLS) and slice transform (SLT) is proposed to model nonlinear chemical systems with a wide range of response variable. In the modeling process, PLS predicted values of calibration set were taken as inputs for the subsequent SLT to further approximate to observed values by a least square criterion. The estimated optimal piecewise linear mapping function was then applied to test set to give the final prediction result. Theoretically, PLS-SLT can be proven to be equivalent to the PLS-based piecewise linear model in the y-space. PLS-SLT is compared with PLS and other calibration models on two spectral datasets. The Wilcoxon signed rank test is used to statistically compare predictive performance of two competing calibration models. Experimental results show that the performance of PLS-SLT is at least statistically not worse than PLS and other models.