A novel multi-class support vector machine based on fuzzy theories

Support vector machine (SVM), proposed by Vapnik based on statistical learning theory, is a novel machine learning method. However, there are two problems to be solved in this field: one is the multi-class classification problem, and the other is the sensitivity to the noisy data. In order to overcome these difficulties, a novel method of fuzzy compensation multi-class support vector machine, named as FC-SVM, is proposed in this paper. This method imports a fuzzy compensation function to the penalty in the straightly construction multi-class SVM classification problem proposed by Weston and Watkins. Aim at the dual affects to classification results by each input data, this method has punish item be fuzzy, compensates weight to classification, reconstructs the optimization problem and its restrictions, reconstructs Langrage formula, and presents the theories deduction. This method is applied to the benchmark data sets. The experiment presents our method is feasible.