Assessment of Pareto Calibration, Stability, and Wavelength Selection

Abstract

Recent work has shown that ridge regression (RR) is Pareto to partial least squares (PLS) and principal component regression (PCR) when the variance indicator Euclidian norm of the regression coefficients, ‖p̂‖, is plotted against the bias indicator root mean square error of calibration (RMSEC). Simplex optimization demonstrates that RR is Pareto for several other spectral data sets when ‖p̂‖ is used with RMSEC and the root mean square error of evaluation (RMSEE) as optimization criteria. From this investigation, it was observed that while RR is Pareto optimal, PLS and PCR harmonious models are near equivalent to harmonious RR models. Additionally, it was found that RR is Pareto robust, i.e., models formed at one temperature were then used to predict samples at another temperature. Wavelength selection is commonly performed to improve analysis results such that bias indicators RMSEC, RMSEE, root mean square error of validation, or root mean square error of cross-validation decrease using a subset of wavelengths. Just as critical to an analysis of selected wavelengths is an assessment of variance. Using wavelengths deemed optimal in a previous study, this paper reports on the variance/bias tradeoff. An approach that forms the Pareto model with a Pareto wavelength subset is suggested.