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Pareto Optimal Multivariate Calibration for Spectroscopic Data

Multivariate calibration of spectral data is considered with an emphasis on prediction. An abundance of methods are available to develop such calibration models. Using a harmonious approach with target vector optimization, the best calibration models are identified relative to the criteria used. Criteria utilized to determine the adequacy of models are minimization of the root mean square error of calibration (RMSEC) and the norm of the regression vector. Because of the simplicity of the optimization response surfaces, the method of simplex was found to function much faster than generalized simulated annealing. Using a near infrared spectral example to demonstrate concepts, a family of models are established to be good, i.e., Pareto optimal models. For the data set investigated, it is found that the Pareto optimal models are essentially the same as models obtained by ridge regression and generalized ridge regression and are more harmonious than models obtained by principal component regression (PCR), partial least-squares (PLS), continuum regression, and cyclic subspace regression as the Pareto optimal models have smaller regression vector norms, RMSEC, and root mean square error of validation (RMSEV) values. The PLS models are found to be Pareto optimal relative to the PCR models. The paper presents an explanation of when the RR model will not be acceptable.