On support vector machines under a multiple-cost scenario
Sandra Benítez-Peña Rafael Blanquero Emilio Carrizosa Pepa Ramírez-Cobo
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.