  In recent years, feature selection has become a challenging problem in
several machine learning fields, such as classification problems. Support
Vector Machine (SVM) is a well-known technique applied in classification tasks.
Various methodologies have been proposed in the literature to select the most
relevant features in SVM. Unfortunately, all of them either deal with the
feature selection problem in the linear classification setting or propose
ad-hoc approaches that are difficult to implement in practice. In contrast, we
propose an embedded feature selection method based on a min-max optimization
problem, where a trade-off between model complexity and classification accuracy
is sought. By leveraging duality theory, we equivalently reformulate the
min-max problem and solve it without further ado using off-the-shelf software
for nonlinear optimization. The efficiency and usefulness of our approach are
tested on several benchmark data sets in terms of accuracy, number of selected
features and interpretability.
