Contributions on Symbolic Data Analysis:A Model Data Approach.

Abstract

This work aims at analysing complex phenomena through the construction of appropriate models, followed by an analysis of the characteristic parameters of the models. It all derives from the need to work, not only with empirical values but with functions that are able to smooth the histogram and give us the possiblity to omit values that could be outlier. According to the classical theory of measure, the data generated by a “correct” model are more “real” then the empirical one, because they are purified from error sampling and from error of measurement. We should never forget that there are no “real” models, but rather models that approximate the reality in a more ore less accuracy. Models compatible with empirical data can be manifold. The idea proposed in this thesis is to trasform the histogram data by means of an approximation function in order to control the error deriving from empirical data. What we look for is the right compromise between model and error. Our target is to be able to work with models that are comparable in order to be able to apply the techniques of a Multidimensional Data Analysis. For that reason, all the histograms will be transformed into models through the approximation by means of functions of the same family. In that case we would work with data that have been synthesized through a model, and from there we would obtain N models for each variable, all corresponding to the i-th observation. Models constructed that way can be synthesized through parameters and through an appropriate quality index of adaptation. Successively we will pass on to the analysis of the data achieved through adequate techniquesof Multidimensional Analysis.