Métodos espectrais de agrupamento

• Autor(a) principal: Almeida, Deise Mara Barbosa de
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13751
• topic: Laplacian; Fiedler Vector; Clustering; Graph; Similarity; Laplaciano; Vetor de Fiedler; Agrupamento; Grafo; Similaridade; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

Spectral methods are useful tools in data analysis, being able to provide information on the organizational structure of data. The grouping of data using spectral methods is commonly based on similarity relations between the data set. The aim of this study is to test the capabilities of spectral methods to cluster data in limiting situations, we consider a set of points in the plane and use the similarity between nodes as the inverse of the standard Euclidean distance. We investigate the minimum critical distance between two central points in which the method is able to reassemble the data in two distinct groups. We further studied the ability of regrouping as a function of the dispersion of the data as the dispersion is increased. Initially we did experiments considering a fixed distance between two points, from which the data are generated and shorten the distance between these points until the methods was not able to separate the data in two distinct groups. Then we kept the initial distance, generated data by add a normal perturbation, and we let the variance increase. We determined the largest value of the variance that allowed the methods to separate the data in two distinct group correctly. From a set of points obtained with the implementation of Differential Evolution algorithm, to solve an issue multi-modal assue. It's tests the capability of the method in separate the individuals in different groups.