Fuzzy support vector machines for multiclass problems

Since support vector machines for pattern classification are based on two-class classification problems, unclassifiable regions exist when extended to n (> 2)-class problems. In our previous work, to solve this problem, we developed fuzzy support vector machines for oneto-(n−1) classification. In this paper, we extend our method to pairwise classification. Namely, using the decision functions obtained by training the support vector machines for classes i and j (j = i, j = 1, . . . , n), for class i we define a truncated polyhedral pyramidal membership function. The membership functions are defined so that, for the data in the classifiable regions, the classification results are the same for the two methods. Thus, the generalization ability of the fuzzy support vector machine is the same with or better than that of the support vector machine for pairwise classification. We evaluate our method for four benchmark data sets and demonstrate the superiority of our method.