Fuzzy SVM with a New Fuzzy Membership Function Based on Gray Relational Grade
In dealing with the two-class classification problems, the traditional support vector machine (SVM) often cannot achieve good classification accuracy when outliers exist in the training data set. The fuzzy support vector machine (FSVM) can resolve this problem with an appropriate fuzzy membership for each data point. The effect of the outliers can be effectively reduced when the classification problem is solved. In this paper, gray relational analysis (GRA) is employed to search for gray relational grade (GRG) which can be used to describe the relationships between the data attributes and to determine the important samples that significantly influence some defined objectives. A new fuzzy membership function for the FSVM is calculated based on the GRG. This method can distinguish the support vectors and the outliers effectively. Experimental results show that this approach contributes greatly to the reduction of the effect of the outliers and significantly improves the classification accuracy and generalization.
KeywordsSupport vector machine Fuzzy support vector machine Fuzzy membership function Two-class problems Gray relational analysis Gray relational grade
This work is partially supported by the National Natural Science Foundation of China (Grant No. 10771228), the Natural Science Foundation Project of CQ CSTC (Grant No. CSTC, 2010BB2090), Education Commission project Research Foundation of Chongqing (No. KJ110617, No. 50, No. KJ120628), PR China, and the Program for Innovative Research Team in Higher Educational Institutions of Chongqing, P. R China.
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