Contribuições a técnicas de agrupamento e visualização de dados multivariados utilizando mapas auto-organizáveis

Self-organizing maps (SOM) are artificial neural networks widely used in the data mining field, mainly because they constitute a dimensionality reduction technique given the fixed grid of neurons associated with the network. In order to properly the partition and visualize the SOM network, the various methods available in the literature must be applied in a post-processing stage, that consists of inferring, through its neurons, relevant characteristics of the data set. In general, such processing applied to the network neurons, instead of the entire database, reduces the computational costs due to vector quantization. This work proposes a post-processing of the SOM neurons in the input and output spaces, combining visualization techniques with algorithms based on gravitational forces and the search for the shortest path with the greatest reward. Such methods take into account the connection strength between neighbouring neurons and characteristics of pattern density and distances among neurons, both associated with the position that the neurons occupy in the data space after training the network. Thus, the goal consists of defining more clearly the arrangement of the clusters present in the data. Experiments were carried out so as to evaluate the proposed methods using various artificially generated data sets, as well as real world data sets. The results obtained were compared with those from a number of well-known methods existent in the literature

Não-extensividade no contexto da atividade magnética solar: o problema da assimetria hemisférica

Solar activity indicators, each as sunspot numbers, sunspot area and flares, over the Sun’s photosphere are not considered to be symmetric between the northern and southern hemispheres of the Sun. This behavior is also known as the North-South Asymmetry of the different solar indices. Among the different conclusions obtained by several authors, we can point that the N-S asymmetry is a real and systematic phenomenon and is not due to random variability. In the present work, the probability distributions from the Marshall Space Flight Centre (MSFC) database are investigated using a statistical tool arises from well-known Non-Extensive Statistical Mechanics proposed by C. Tsallis in 1988. We present our results and discuss their physical implications with the help of theoretical model and observations. We obtained that there is a strong dependence between the nonextensive entropic parameter q and long-term solar variability presents in the sunspot area data. Among the most important results, we highlight that the asymmetry index q reveals the dominance of the North against the South. This behavior has been discussed and confirmed by several authors, but in no time they have given such behavior to a statistical model property. Thus, we conclude that this parameter can be considered as an effective measure for diagnosing long-term variations of solar dynamo. Finally, our dissertation opens a new approach for investigating time series in astrophysics from the perspective of non-extensivity.