Abstract
This paper aims to improve hard margin support vector machines (SVMs) by considering the membership of every training sample in constraints. The membership is computed by employing the technique of fuzzy rough sets so that hard margin SVMs can be combined with fuzzy rough sets and the inconsistence between conditional features and decision labels can be taken into account at the same time. In this paper, we first propose fuzzy transitive kernel based fuzzy rough sets. For binary classification, we use a lower approximation operator in fuzzy transitive kernel based fuzzy rough sets to compute the membership for every training input. And then we reformulate hard margin support vector machines into fuzzy rough set based SVMs (FRSVMs) with new constraints in which the membership is taken into account. Finally, comparisons with soft margin SVMs and fuzzy SVMs are made. The experimental results show that the proposed approach is feasible and valid. It significantly improved the performance of the hard margin SVMs.
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