A review of orthogonal projections for calibration

In recent decades, analytical chemistry labs have been populated with machines with less poetic profiles than traditional craft glass appliances. The use of these new machines, such as near‐infrared spectrometers, requires chemometrics, in particular for their calibration. Since the 1980s, many studies have focused on extracting the net analyte signal, that is to say, the signal perfectly and linearly related to the concentration of interest. This task is very difficult in NIR spectrometry because the spectra are the result of an intimate mixture of many influences, including that of the compound of interest. Instead of focusing on this useful signal, the orthogonal projection methods propose to eliminate the detrimental signals. In this, these methods are similar to spectral pretreatment methods, widely used in chemometrics, which aim to eliminate noise (smoothing), baselines (derivatives) or disturbed areas (selection of spectral zones). Orthogonal projections can do all of this in one go because, rather than correcting the spectra one by one, they suppress the subspaces that carry the deleterious effects. For example, instead of deleting the baseline of each spectrum, they delete the subspace containing all possible baselines of the spectral space in which the calibration is calculated. Orthogonal projection pre‐treatments allow us to effectively use all knowledge and data related to adverse effects. These spectral cleaning methods must be used in addition to conventional tools. Unlike regression methods, they can be used without risk of over‐fitting; the only risk is over‐cleaning and therefore loose the model.