Abordagem contextual paramétrica na análise de componentes principais

Abstract

In unsupervised analysis, the quality of a dispersion can be measured by the relation between the proximity of the samples of one class, and the inter-classes separation. One relevant task in this context is characterized by the mapping of a dispersion X into a new X' of higher quality, which preserves the neighborhood relationships. The PCA is a mapping method that possesses as property the maintenance of the samples global maximum scatter. Such property can generate both higher inter-class separation and higher intra-class spreads. The intra-class spread can be diminished by the smoothing of the influence fo samples that are distant from their cluster. Such smoothing can be obtained by the substitution of the proximity calculation between individual samples by a similarity measure between contexts. From this idea, a PCA modification is proposed where the contextual information is extracted from the neighborhood graph, and a feature values set is mapped to a parametric statistical distribution, allowing that a distribution divergence can be used as similarity measure. Previous experiments with a limited set of divergences indicate that the approach is able to produce superior results than several existing mapping methods. The first investigation line of this work employ a larger set of divergences in order to verify the approach robustness. The obtained results show that, for a large set of divergences, the proposal shows a superior performance than all other compared algorithms in the majority of the tested sample set. The second investigation line of the work is defined by the verification of existence of relationship between the performance of a divergence and the properties of a sample set. From the study is possible to infer that higher value divergences tend to generate better dispersions for higher class quantities.