The Support Vector Machine (SVM) has been an important classification technique in both machine learning and statistics communities. The robust SVM is an improved version of the SVM so that the resulting classifier can be less sensitive to outliers. In many practical problems, it may be advantageous to use different weights for different types of misclassification. However, the existing RSVM treats different kinds of misclassification equally. In this paper, we propose the weighted RSVM, as an extension of the standard SVM. We show that surprisingly, the cost-based weights do not work well for weighted extensions of the RSVM. To solve this problem, we propose a novel utility-based weighting scheme for the weighted RSVM. Both theoretical and numerical studies are presented to investigate the performance of the proposed weighted multicategory RSVM.
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