Uma proposta de máquina de vetor-suporte nebulosa com opção de rejeição

Abstract

The goal of pattern classification is to assign an element of a data set to one out of many available classes. Due to a precise mathematical foundation and excellent generalization performance, kernel methods based on support vector machines (SVMs) have been successfully applied to pattern classification problems. To build an SVM classifier, we search for the best decision surface that separates the elements of the different classes from each other, keeping the largest margins possible. From this surface, we build a decision function, which is used to classify new elements. Despite being proposed initially to handle linearly separable data sets, to deal with more complex data sets, a regularization parameter and slack variables were introduced into the original SVM formulation. A drawback of this approach is that, in addition to the need for calibrating an additional parameter, there is an increase in the number of support vectors required to build the decision function. The higher the number of support vectors, the higher the computational cost for classifying new incoming patterns. In this thesis, we introduce a novel SVM formulation based on fuzzy logic to handle uncertainties in the data set. Using this approach, drawbacks resulting from the introduction of a regularization parameter are avoided. Additionally, the resulting classifier assigns membership values to the elements of the data set, allowing the introduction of a rejection class into the proposed formulation without further difficulties. The two versions of the proposed model, with and without rejection class, were evaluated on several benchmarking data sets originating from the biomedical research and their performances were compared to those from other SVM formulations. The version without rejection class presented recognition rates comparable to those from soft margin SVM, with the advantage of using considerable less amount of support vectors. The version with rejection class also presented promising results.