The Framework as a Mathematical Object. The final goal of this thesis is to define a general framework in an abstract sense, in addition to the practical and implementation one. We aim to design a general form of operator that applies to classically presented data, i.e., in tabular form, by taking into account their components: instances, attributes, and dimensional characteristics. We are interested in problems with final solutions that will be the result of feature selections, outlier detections, and feature extraction and transformation. Inspired by the wrapper-based approach to feature selection, we defined all such processes as wrappers and, in the end, as particular cases of the same mathematical operator acts on the data. Such an operator is parameterized by the specific preprocessing that the data require, and the parameterization determines the shape and the interpretation of an individual (in terms of multi-objective optimization solved via a genetic algorithm). By abstracting all such processes, our purpose is to study the properties of this operator and, in due course, to lay down the bases for their integrated treatment. In this sense, we shall define very practical objects such as water fingerprints or geochemical characterization as, depending on the case, specific applications of the same, general operator, therefore offering a clean, mathematically well-founded characterization of processes that in the literature are, in many cases, simply applied (that is, without any formal treatment or interpretation).
