Contribuições aos Processos de Clustering com Base em Métricas não-Euclidianas

In this work we present a new clustering method that groups up points of a data set in classes. The method is based in a algorithm to link auxiliary clusters that are obtained using traditional vector quantization techniques. It is described some approaches during the development of the work that are based in measures of distances or dissimilarities (divergence) between the auxiliary clusters. This new method uses only two a priori information, the number of auxiliary clusters Na and a threshold distance dt that will be used to decide about the linkage or not of the auxiliary clusters. The number os classes could be automatically found by the method, that do it based in the chosen threshold distance dt, or it is given as additional information to help in the choice of the correct threshold. Some analysis are made and the results are compared with traditional clustering methods. In this work different dissimilarities metrics are analyzed and a new one is proposed based on the concept of negentropy. Besides grouping points of a set in classes, it is proposed a method to statistical modeling the classes aiming to obtain a expression to the probability of a point to belong to one of the classes. Experiments with several values of Na e dt are made in tests sets and the results are analyzed aiming to study the robustness of the method and to consider heuristics to the choice of the correct threshold. During this work it is explored the aspects of information theory applied to the calculation of the divergences. It will be explored specifically the different measures of information and divergence using the Rényi entropy. The results using the different metrics are compared and commented. The work also has appendix where are exposed real applications using the proposed method

Utilização de RNA´s na construção do diagrama de vida constante de probabilidade de materiais compósitos

The static and cyclic assays are common to test materials in structures.. For cycling assays to assess the fatigue behavior of the material and thereby obtain the S-N curves and these are used to construct the diagrams of living constant. However, these diagrams, when constructed with small amounts of S-N curves underestimate or overestimate the actual behavior of the composite, there is increasing need for more testing to obtain more accurate results. Therewith, , a way of reducing costs is the statistical analysis of the fatigue behavior. The aim of this research was evaluate the probabilistic fatigue behavior of composite materials. The research was conducted in three parts. The first part consists of associating the equation of probability Weilbull equations commonly used in modeling of composite materials S-N curve, namely the exponential equation and power law and their generalizations. The second part was used the results obtained by the equation which best represents the S-N curves of probability and trained a network to the modular 5% failure. In the third part, we carried out a comparative study of the results obtained using the nonlinear model by parts (PNL) with the results of a modular network architecture (MN) in the analysis of fatigue behavior. For this we used a database of ten materials obtained from the literature to assess the ability of generalization of the modular network as well as its robustness. From the results it was found that the power law of probability generalized probabilistic behavior better represents the fatigue and composites that although the generalization ability of the MN that was not robust training with 5% failure rate, but for values mean the MN showed more accurate results than the PNL model