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The Support Vector Machines (SVMs) have been widely used for classification due to its ability to give low generalization error. In many practical applications of classification, however, the wrong prediction of a certain class is much severer than that of the other classes, making the original SVM unsatisfactory. In this paper, we propose the notion of Asymmetric Support Vector Machine (ASVM), an asymmetric extension of the SVM, for these applications. Different from the existing SVM extensions such as thresholding and parameter tuning, ASVM employs a new objective that models the imbalance between the costs of false predictions from different classes in a novel way such that user tolerance on false-positive rate can be explicitly specified. Such a new objective formulation allows us of obtaining a lower false-positive rate without much degradation of the prediction accuracy or increase in training time. Furthermore, we show that the generalization ability is preserved with the new objective. We also study the effects of the parameters in ASVM objective and address some implementation issues related to the Sequential Minimal Optimization (SMO) to cope with large-scale data. An extensive simulation is conducted and shows that ASVM is able to yield either noticeable improvement in performance or reduction in training time as compared to the previous arts.