Possibilistic classification by support vector networks.

Abstract

In many real-world classification problems, the available information is often uncertain. In order to effectively describe the inherent vagueness and improve the classification performance, this paper proposes a novel possibilistic classification algorithm using support vector machines (SVMs). Based on possibility theory, the proposed algorithm aims at finding a maximal-margin fuzzy hyperplane by solving a fuzzy mathematical optimization problem Moreover, the decision function of the proposed approach is generalized such that the values assigned to the data vectors fall within a specified range and indicate the membership grade of these data vectors in the positive class. The proposed algorithm retains the advantages of fuzzy set theory and SVM theory. The proposed approach is more robust for handling data corrupted by outliers. Moreover, the structural risk minimization principle of SVMs enables the proposed approach to effectively classify the unseen data. Furthermore, the proposed algorithm has additional advantage of using vagueness parameter v for controlling the bounds on fractions of support vectors and errors. The extensive experiments performed on benchmark datasets and real applications demonstrate that the proposed algorithm has satisfactory generalization accuracy and better describes the inherent vagueness in the given dataset.