Chemometryczne metody modelowania danych : studium porównawcze

The chemometric methods of data analysis allow to resolve complex multi-component systems by decomposing a measured signal into the contributions of pure substances. Mathematical procedure of such decomposition is called empirical data modelling. The main aim and subject of this article is to provide some basic information on the chemometric analysis. The chemometric techniques are divided into three categories, resulting from the assumed premises. A base of hard type of modelling is an assumption, that the measured dataset can be a priori described by generally accepted physical or chemical laws, expressed by analytical forms of mathematical functions, however with unknown values of parameters [1]. Numerical values of those constants are optimised by using procedures such as the least squares curve fitting [1, 2]. When explicit form of equations are found, the whole system of data can be resolved. Therefore, the white types of data modelling are often used for kinetic measurements [3–8] and analysis of fluorescence quenching [9–13]. Completely different approach to data modelling is offered by so called soft chemometric methods [14–20]. Those techniques do not require any presumptions; solutions obtained for the considered system are thus far much more unconstrained. The black types of analysis make use not only of the least squares fitting procedures [18, 19], but also some other geometrical optimisation algorithms [16, 17]. The results of that approach suffer however from one main drawback: the final outcome is not unique – system is described by a set of feasible solutions. As a consequence, soft data modelling is generally applied to resolve empirical data, which cannot be easily expressed by an explicit form of a function. Such measurement techniques are for example chromatography or volumetry. However, if some conjecture could be made about the measurement system and the obtained data, it is possible to stiffen the black methods by applying white constraints [20]. These types of the chemometric analysis are called grey or hard-soft, and are a practical combination of model-free optimisation with the limitations of feasible solutions, resulting from conformity with physical or chemical laws. Due to the fact, that data modelling provides an opportunity for simultaneous identification of several components of the analysed mixture, the chemometric procedures, although not so popular yet, are extremely powerful research tools.