Fuzzy least squares support vector machines for multiclass problems

Authors:
Daisuke Tsujinishi;Shigeo Abe
Affiliations:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe, Japan;Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe, Japan
Venue:
Neural Networks - 2003 Special issue: Advances in neural networks research — IJCNN'03
Year:
2003

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Abstract

In least squares support vector machines (LS-SVMs), the optimal separating hyperplane is obtained by solving a set of linear equations instead of solving a quadratic programming problem. But since SVMs and LS-SVMs are formulated for two-class problems, unclassifiable regions exist when they are extended to multiclass problems.In this paper, we discuss fuzzy LS-SVMs that resolve unclassifiable regions for multiclass problems. We define a membership function in the direction perpendicular to the optimal separating hyperplane that separates a pair of classes. Using the minimum or average operation for these membership functions, we define a membership function for each class. Using some benchmark data sets, we show that recognition performance of fuzzy LS-SVMs with the minimum operator is comparable to that of fuzzy SVMs, but fuzzy LS-SVMs with the average operator showed inferior performance.