Sparse rational function methods for developing parsimonious multivariate calibrations

The aim is to demonstrate the flexibility and robustness of two new additions to the rational function methods, namely, rational function least angle regression (LARS), rational function least absolute shrinkage and selection operator (LASSO) and elastic net (ENET) methods. Previous work [1, 2] has been based on the methods that use a L2 regularization to cope with collinearity and measurement noise. In this work, we introduce parsimonious methods for rational function modeling that use rather L1 regularization or the combination of L1 and L2 regularization. These methods provide interesting opportunities for model development and robustification. The key point is to specifically illustrate the flexibility of rational function ENET because it bridges the gap between L1 and L2 methods. The former suffers from spectral noise, which is well known in the context of normal LASSO approaches. The latter has been troublesome in numerous occasions as it involves the use of a broad spectral range that is often prone to suffer from unknown spectral interferences in future samples. These points will also be exemplified using two data sets generated by a multipoint NIR instrument with two 5-channel measurement probes and by a chemical imaging NIR spectrometer. We also briefly demonstrate how to interpret and visualize rational function models efficiently. In summary, this work addresses new and interesting directions in developing calibration models in the field of spectroscopy and multipoint measurements.