New Classical Least-Squares/Partial Least-Squares Hybrid Algorithm for Spectral Analyses

Abstract

A new classical least-squares/partial least-squares (CLS/PLS) hybrid algorithm has been developed that demonstrates the best features of both the CLS and PLS algorithms during the analysis of spectroscopic data. By adding our recently reported prediction-augmented classical least-squares (PACLS) to the hybrid algorithm, we have the additional benefit that known or empirically derived spectral shape information can be incorporated into the hybrid algorithm to correct for the presence of unmodeled sources of spectral variation. A detailed step-by-step description of the new hybrid algorithm in calibration and prediction is presented. The powerful capabilities of the new PACLS/PLS hybrid are demonstrated for near-infrared spectra of dilute aqueous solutions containing the analytes urea, creatinine, and NaCl. The PACLS/PLS method is demonstrated to correct the detrimental effects of unmodeled solution temperature changes and spectrometer drift in the multivariate spectral calibration models. Initially, PLS and PACLS/PLS predictions of analytes from variable-temperature solution spectra were made with models based upon spectra previously taken of the samples at constant temperature. The presence of unmodeled temperature variations and system drift caused the prediction errors from these models to be inflated by more than an order of magnitude relative to the cross-validated errors from the calibrations. PLS achieved improved predictions of the variable-temperature spectra by adding spectra of a few variable-temperature samples into the original calibration data followed by recalibration. PACLS/PLS predictions were corrected for temperature variations and system drift by adding spectral differences of the same subset of samples collected under constant- and variable-temperature conditions to the PACLS prediction portion of the hybrid algorithm during either calibration or prediction. Comparisons of the prediction ability of the hybrid algorithm relative to the PLS method using the same calibration and subset information demonstrated hybrid prediction improvements that were significant at least at the 0.01 level for all three analytes. The new hybrid algorithm has widespread uses, some of which are also discussed in the paper.