Agrupamento Fuzzy no espaço de características baseado no Kernel de Mahalanobis com distâncias quadráticas adaptativas

Abstract

In this master’s thesis, fuzzy grouping methods are presented in the space of featuresbasedontheMahalanobiskernelwithadaptivequadraticdistances, labeledrespectively by (KFCM.FS.GD, KFCM.FS.GF, KFCM.FS.LD e KFCM.FS.LF).This study is an extension of the work developed in [26]. The proposed methods were based on the Mahalanobis kernel from adaptive quadratic distances defined by defined positive symmetric covariance matrices. These matrices of covariances are diagonal and complete (not diagonal), common to all groups and different for each group, determined under the clustering approach in the feature space, which performs a mapping of each observation by means of a nonlinear Φ and then obtain the centroids of the groups in the resource space. This technique allows that when we move to a space of higher dimension (space of characteristics), a set of observations in the non-linearly separable input space becomes linearly separable in the space of characteristics. The proposed algorithms were compared with the various traditional clustering methods known in the literature, such as fuzzy k-means and their versions based on the Gaussian kernel, as well as the methods developed by [26]. The evaluation was performed through numerical experiments with simulated and real data.