Métodos de projeção multidimensional

• Ano de defesa: 2013
• Autor(a) principal: Dal Col Júnior, Alcebíades
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Mestrado em Matemática; Centro de Ciências Exatas; UFES; Programa de Pós-Graduação em Matemática
• Palavras-chave em Português: Projection; Matemática aplicada; Visualização de dados; Métodos de projeção multidimensional; Matemática; 51
• Link de acesso: http://repositorio.ufes.br/handle/10/7500

The problem we are interested in solving comes from a area of knowledge called data visualization. In our studies, groups of objects are analyzed to produce the input data of our problem, each object is represented by attributes, have so a list of attributes for each object. The idea is to represent, through these lists of attributes, objects through points in R 2 so that we can conduct a group of objects. As we said each object is represented by a list of attributes, this may be interpreted as a point of a multidimensional space. For example, if they are considered m valued attributes for all objects can interpret them as points in a space of dimension m, or m-dimensional. But we want to produce a visualization of the data on the computer screen through points in R 2 , it was then performs a process known as multidimensional projection, that is obtaining points in a low dimensional space representing points in a high dimensional space preserving neighborhood relations as much as possible. Various methods of multidimensional projection are found in the literature. In this work, study and implement methods NNP, Force, LSP, PLP and LAMP. These methods deal with the problem in different ways: geometrically; linear systems, in particular, laplacian systems; and mappings related orthogonal. The lists of attributes associated with the groups of objects are called dataset. Two sets of data in this paper present trends grouping known a priori, therefore were used to give credibility to our implementations of the methods. Two other data set are studied and these were not provided with such feature, the methods of multidimensional projection are then used to define trends grouping for these two data sets.