M. Mohammadi - Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran
M. Sarmad - Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

The fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers.  To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance.  Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.

Support vector machine, Outliers, noise, Fuzzification, gaussian mixture model, distance-based membership function, bayes-based membership function