Interrelationships between generalized Tikhonov regularization, generalized net analyte signal, and generalized least squares for desensitizing amultivariate calibration to interferences

摘要

Orthogonal pre-processing (orthogonal projection) of spectral data is a common approach to generate analytespecific information for use in multivariate calibration. The goal of this pre-processing is to remove from each spectrum the respective sample interferent contributions (spectral interferences from overlap, scatter, noise, etc.). Two approaches to accomplish orthogonal pre-processing are net analyte signal (NAS) and generalized least squares (GLS). Developed in this paper is the mathematical relationship between NAS and GLS. It is also realized that orthogonal NAS pre-processing can remove too much analyte signal and that the degree of interferent correction can be regulated. Similar to GLS, the degree of correction is accomplished by using a regularization (tuning) parameter to form generalized NAS (GNAS). Also developed in this paper is an alternative to GNAS and GLS based on generalized Tikhonov regularization (GTR). The mathematical relationships between GTR, GNAS, and GLS are derived. A result is the ability to express the model vector as the sum of two contributions: the orthogonal NAS contribution and a non-NAS contribution from the interferent components. Thus, rather than the usual situation of sequentially pre-processing data by either GNAS or GLS followed by model building with the pre-processed data, the methods of GTR, GNAS, and GLS are expressed as direct computations of model vectors allowing concurrent pre-processing and model building to occur. Simultaneous pre-processing and model forming are shown to be natural to the GTR process. Two near-infrared spectroscopic data sets are studied to compare the theoretical relationships between GTR, GNAS, and GLS. One data set covers basic calibration, and the other data set is for calibration maintenance. Filter factor representation is key to developing the interprocess relationships.