Multidimensional calibration: application to spectral data

Spectrometric methods are used in many laboratory and industrial assays. These methods are often well suited to routine analysis: they can be specific, precise and easy to apply under industrial conditions. Some of them, such as those based on vibrational spectroscopy (in the visible or near- to mid-infrared spectral ranges) lend themselves well to automation and measurement on the production line. They are fast and can often be applied to complex products, without tedious sample preparation. These methods are at the origin of a large number of analysis instruments, often dedicated to a very specific range of products, used in virtually every industrial sector.

Despite their appeal, spectrometric analysis methods can present certain difficulties, particularly when it comes to calibration. Indeed, these methods are almost always used indirectly, replacing more or less standardized, so-called "reference" analytical methods. During the development of a spectrometric analysis, it is implicitly assumed that the data from the physical measuring instrument (the spectrometer) contains information that can be used to estimate the analytical value that would have been obtained had the reference method been used. A first step in the development process is to establish a predictive model, the aim of which is to provide an estimate of the reference value from the measured data (spectrum) on the sample to be analyzed. Once validated, the model is then applied in routine analyses to samples for which the analytical reference value is unknown.

Based on spectroscopic knowledge alone, it is generally impossible to model a spectrometer's response very precisely. There is usually insufficient information available on the composition of the sample being analyzed, or on its physical characteristics, which play an important role in the spectral measurement. For this reason, predictive models are generally established by applying an experimental approach, based on the study of products representative of the population and analyzed by the reference method. Numerous mathematical and statistical methods can, in principle, be used to perform this calibration. The development of these methods is one of the themes of chemometrics, the aim of which is to use mathematical, computer and statistical sciences to extract relevant information from sensor measurements in the field of chemistry.

The calibration of spectrometric methods can be based on two main categories of methods: multidimensional (linear) methods and connectionist methods, based on the concept of neural networks. In connectionist methods, the predictive model takes the form of a set of small interconnected units, called "neurons", each of which performs a very simple mathematical transformation and passes...