Dual‐domain regression analysis for spectral calibration models

Abstract

Taking advantage of the local nature of spectral data in both the time and frequency domains, two novel chemometric algorithms using the wavelet transform, namely dual-domain partial least squares (DDPLS) and dual-domain principal component regression (DDPCR), are reported here. The proposed algorithms establish parallel, regular models to describe spectral variation in the time (wavelength) domain. They incorporate these parallel models as a way of emphasizing local features in the frequency domain. Compared with regular PLS or PCR regression models applied to a single domain, these algorithms generate more parsimonious regression models that are also more robust against unexpected variations in the prediction set. Simulation data have been used in this paper to demonstrate this improvement. The new methods have also been successfully applied to NIR spectral data sets to predict moisture, oil, protein and starch content in Cargill corn samples, as well as a set of properties in a series of Amoco hydrocarbon samples. Through their special emphasis on the local nature of spectral signals in the frequency domain, spectral variance can be separately explained over the frequency and time domains with fewer latent variables and with better predictive performance.

Stacked partial least squares regression analysis for spectral calibration and prediction

“…In a stacked regression, a series of separate regression models built on subsets of the full data set are combined by determining a set of weights for each subset or sub-model, and these weights are used to produce a fused prediction from the set of predictions generated from the set of sub-models. These weights can be obtained from cross-validation [9,10] of each model or subset, or from use of a Bayesian criterion [12]. Stacking does not involve a conventional variable selection, and so a stacked model reduces the information loss associated with wavelength selection while gaining many of the benefits demonstrated from focusing on relevant portions of the data [9].…”

“…Fusion methods rely on the idea of combining predictors instead of selecting only the single best predictor or best set of predictors to improve model robustness [9][10][11]. In a stacked regression, a series of separate regression models built on subsets of the full data set are combined by determining a set of weights for each subset or sub-model, and these weights are used to produce a fused prediction from the set of predictions generated from the set of sub-models.…”

Selecting wavelet transform scales for multivariate classification

“…The most recent chemical applications of the DWT have included applications such as variable selection of the coefficients [9], removal of selected scales [5], and fusion of all scales [1,20]. The DWT is particularly attractive as a preprocessing method for classification problems because the transform process itself makes no use of class label information in the wavelet decomposition of the data.…”

“…Individual models are then built for each scale matrix and the predictions from each scale are combined using a weighted average scheme for the final prediction. This multi-scale approach changes the focus away from improving modeling by either scale or variable selection to finding ways for combining models made from multiple scales [1].…”

“…The tools used to achieve this goal range from manual correction of baseline effects to those based on derivatives and orthogonalization techniques. In recent years, the discrete wavelet transform (DWT) has received significant attention in a variety of fields dependent on signal processing and particularly in chemistry, where it has been applied to multivariate regression [1,2], calibration transfer [3,4], signal compression [5,6], signal denoising [7] and baseline removal [8], variable selection [9], image classification [10], and regression [11]. The DWT has been the subject of much attention for chemical data because of its ability to simultaneously look at structures local to the time and frequency domains.…”