Equivalent and Complementary Variables Screening for the Optimization of Wavelengths in Spectral Multivariate Calibration

Equivalent variables (EVs) were defined on the basis of a finding that replacing a selected variable with its neighbor variable provided a similar model performance. These are a group of variables having nearly equal modeling effects and can be efficient alternative to each other. Complementary variables (CVs) were defined as different variables screened from different variable selection algorithms that can further improve multivariate calibration by combining CVs with the original selected variables. Three variable selection algorithms, stability competitive adaptive reweighted sampling (SCARS), competitive adaptive reweighted sampling (CARS), and Monte Carlo and uninformative variable elimination (MC-UVE), were used for screening EVs and CVs and verifying the replaceability of EVs and model improvability with CVs. The developed strategy of variable selection based on EVs and CVs was investigated using NIR, MIR, and UV-vis spectra datasets. Seventeen basic variables (BVs) and 54 EVs were screened from the corn NIR spectra by SCARS. The selected EVs and BVs were comparable to one another in terms of modeling, and all models built with replaced variables showed close prediction errors with a RMSEP deviation <0.003. Furthermore, 15 CVs of SCARS were screened from EVs of CARS and MC-UVE. The combination of CVs and BVs of SCARS can significantly improve model performance; RMSEC and RMSEP decreased from 0.0207 and 0.0290 to 0.0109 and 0.0136, respectively. Similar results were obtained for other datasets. Results revealed that screening CVs from EVs of other algorithms and combining BVs could effectively optimize variable selection and improve model performance.