Improvement of Generalization Ability of Multiclass Support Vector Machines by Introducing Fuzzy Logic and Bayes Theory

Abstract

In this paper, to resolve unclassifiable regions in the support vector machines, we propose fuzzy support vector machines (FSVMs). Using the decision function obtained by training the SVM, for each class, we define a truncated polyhedral pyramidal membership function. Since, for the data in the classifiable regions, the classification results are the same, the generalization ability of the FSVM is the same as or better than that of the SVM. To further improve the generalization ability, we introduce the Bayes theory, assuming that the class distributions are normal, to optimize the bias term of the optimal hyperplane. We evaluate our methods for four benchmark data sets and demonstrate the superiority of the FSVM and Bayes FSVM over the SVM.