Support Vector Machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud prediction, involve misclassification costs which may be different in the different classes. However, it may be hard for the user to provide precise values for such misclassification costs, whereas it may be much easier to identify acceptable misclassification rates values. In this paper we propose a novel SVM model in which misclassification costs are considered by incorporating performance constraints in the problem formulation. Specifically, our aim is to seek the hyperplane with maximal margin yielding misclassification rates below given threshold values. Such maximal margin hyperplane is obtained by solving a quadratic convex problem with linear constraints and integer variables. The reported numerical experience shows that our model gives the user control on the misclassification rates in one class (possibly at the expense of an increase in misclassification rates for the other class) and is feasible in terms of running times.

翻译：支持向量机（SVM）是二分类问题中的强大工具，以其优异的误分类率表现著称。然而，许多实际分类问题（如医学诊断、客户流失预测或欺诈检测）中，不同类别的误分类成本可能不同。但用户往往难以提供准确的误分类成本数值，而更容易确定可接受的误分类率阈值。本文提出一种新型SVM模型，通过将性能约束纳入问题公式来考虑误分类成本。具体而言，我们的目标是寻找能保证误分类率低于给定阈值且具有最大间隔的超平面。该最大间隔超平面可通过求解一个带线性约束和整数变量的凸二次规划问题获得。数值实验表明，该模型使用户能够控制某一类别的误分类率（可能以另一类别误分类率上升为代价），且在运行时间上具有可行性。