Fuzzy least squares support vector machines for multiclass problems

doi:10.1016/S0893-6080(03)00110-2

2003-06-01

200

D. Tsujinishi

Shigeo Abe

DOI：10.1016/S0893-6080(03)00110-2

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摘要

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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. (C) 2003 Elsevier Science Ltd. All rights reserved.

Keyword:

least squares support vector machines

multiclass problems

membership functions