Feature selection combining linear support vector machines and concave optimization

In this work we consider feature selection for two-class linear models, a challenging task arising in several real-world applications. Given an unknown functional dependency that assigns a given input to the class to which it belongs, and that can be modelled by a linear machine, we aim to find the relevant features of the input space, namely we aim to detect the smallest number of input variables while granting no loss in classification accuracy. Our main motivation lies in the fact that the detection of the relevant features provides a better understanding of the underlying phenomenon, and this can be of great interest in important fields such as medicine and biology. Feature selection involves two competing objectives: the prediction capability (to be maximized) of the linear classifier and the number of features (to be minimized) employed by the classifier. In order to take into account both the objectives, we propose a feature selection strategy based on the combination of support vector machines (for obtaining good classifiers) with a concave optimization approach (for finding sparse solutions). We report results of an extensive computational experience showing the efficiency of the proposed methodology.