Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more effective by reducing noise and data overfit. The relevance of features in a classification procedure is linked to the fact that misclassifications costs are frequently asymmetric, since false positive and false negative cases may have very different consequences. However, off-the-shelf Feature Selection procedures seldom take into account such cost-sensitivity of errors. In this paper we propose a mathematical-optimization-based Feature Selection procedure embedded in one of the most popular classification procedures, namely, Support Vector Machines, accommodating asymmetric misclassification costs. The key idea is to replace the traditional margin maximization by minimizing the number of features selected, but imposing upper bounds on the false positive and negative rates. The problem is written as an integer linear problem plus a quadratic convex problem for Support Vector Machines with both linear and radial kernels. The reported numerical experience demonstrates the usefulness of the proposed Feature Selection procedure. Indeed, our results on benchmark data sets show that a substantial decrease of the number of features is obtained, whilst the desired trade-off between false positive and false negative rates is achieved.

Feature selection aims to select a small subset from the high-dimensional features which can lead to better learning performance, lower computational complexity, and better model readability. The class imbalance problem has been neglected by traditional feature selection methods, therefore the selected features will be biased towards the majority classes. Because of the superiority of F-measure to accuracy for imbalanced data, we propose to use F-measure as the performance measure for feature selection algorithms. As a pseudo-linear function, the optimization of F-measure can be achieved by minimizing the total costs. In this paper, we present a novel cost-sensitive feature selection (CSFS) method which optimizes F-measure instead of accuracy to take class imbalance issue into account. The features will be selected according to optimal F-measure classifier after solving a series of cost-sensitive feature selection sub-problems. The features selected by our method will fully represent the characteristics of not only majority classes, but also minority classes. Extensive experimental results conducted on synthetic, multi-class and multi-label datasets validate the efficiency and significance of our feature selection method.