Fuzzy least squares support vector machines for multiclass problems.
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.
Tsujinishi
Daisuke
D
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe, Japan. tujinisi@frenchblue.scitec.kobe-u.ac.jp
Abe
Shigeo
S
D017143:Fuzzy Logic; D016018:Least-Squares Analysis; D011340:Problem Solving / Q000502:physiology