Advantages of orthogonal inspection in chemometrics

Abstract

The demand for chemometrics tools and concepts to study complex problems in modern biology and medicine has prompted chemometricians to shift their focus away from a traditional emphasis on model predictive capacity toward optimizing information exchange via model interpretation for biological validation. The interpretation of projection‐based latent variable models is not straightforward because of its confounding of different systematic variations in the model components. Over the last 15 years, this has spurred the development of orthogonal‐based methods that are capable of separating the correlated variation (to Y) from the noncorrelated (orthogonal to Y) variations in a single model. Here, we aim to provide a conceptual explanation of the advantages of orthogonal variation inspection in the context of Partial Least Squares (PLS) in multivariate classification and calibration. We propose that by inspecting the orthogonal variation, both model interpretation and information quality are improved by enhancement of the resulting level of knowledge. Although the predictive capacity of PLS using orthogonal methods may be identical to that of PLS alone, the combined result can be superior when it comes to the model interpretation. By discussing theory and examples, several new advantages revealed by inspection of orthogonal variation are highlighted. Copyright © 2012 John Wiley & Sons, Ltd.

Raman spectroscopy and multivariate analysis for the rapid discrimination between native-like and non-native states in freeze-dried protein formulations

“…PC6 described only 0.03% of the variation in the spectra, which means that there is a lot of other variation in the Raman spectra, not responsible for the discrimination between both classes (e.g. light scattering, physical and environmental effects, instrumental effects...) [23,34]. Yet the loading vector of PC6 or the Author-produced version of the article published in European Journal of Pharmaceutics and Biopharmaceutics, 2013, N°85(2), p. The original publication is available at http://www.sciencedirect.com/science/article/pii/S0939641113001264 Doi: 10.1016/j.ejpb.2013.03.035 discriminant vector can be informative for studying the most important variables responsible for the discrimination.…”

“…As we directly use the unprocessed Raman spectra of a freeze-dried formulation (without the usual blank subtraction), we have to investigate the influence of the excipient signals on the discriminating power of the model. Therefore we applied an orthogonal projection approach [21][22][23][24]. The contributions within the variable space of the calibration matrix X (containing the spectra of the protein formulations) are originating from the pure protein signals (X p ), interferences such as the excipient signals (X b ) and other undefined spectral variance (ε) (eq.…”

Combination of visible and mid-infrared spectra for the prediction of chemical parameters of wines

“…The technique differs from partial least squares (PLS) in the way of handling the variability in X-matrix. OPLS may lead better interpretation and predictions: PLS divides the variance of X-matrix as systematic and residual, whereas OPLS divides the systematic variance into two parts, the part that is correlated to Y (predicted) and the part that is uncorrelated to Y (orthogonal) [19]. The number of components in OPLS regression for a single variable y is given as p p þp o , where p p and p o are the number of components expressing information of X predictive to Y, and information of X orthogonal to Y, respectively.…”

Differentiation of wines with the use of combined data of UV–visible spectra and color characteristics

“…The benefit of predictive and orthogonal variation is the extraction of most of the knowledge, which may lead to better performances than PLS models (Pinto et al, 2012). The number of components in OPLS-DA is given as ''p p + p o ''.…”