training fuzzy support vector machines by using boundary of rough set
Support Vector Machines (SVMs) are statistical learning methods based on two-class problems and exist unclassifiable regions when they are extended to multi-class problems. In order to reduce unclassifiable regions, S. Abe and T. Inoue proposed the improved multi-class SVMs called Fuzzy Support Vector Machines (FSVMs) by which the unclassifiable regions are reduced. In this paper, we train FSVMs by using the training data lying in the boundary of rough set. Firstly, the whole training set is divided into some equivalence classes by transforming all attribute values into discrete ones. Secondly, the lower approximation sets of the training data with the same categories are obtained by the formed equivalence classes. Thirdly, the boundary induced by the whole training set and the lower approximation sets is selected to form FSVMs. The experimental results on classic benchmark data sets show that the proposed learning machines can downsize the number of training data and achieve the higher predictions.
fuzzy support vector machines support vector machines boundary rough set equivalence class