Recently, the so-called $\psi$-learning approach, the Support Vector Machine (SVM) classifier obtained with the ramp loss, has attracted attention from the computational point of view. A Mixed Integer Nonlinear Programming (MINLP) formulation has been proposed for $\psi$-learning, but solving this MINLP formulation to optimality is only possible for datasets of small size. For datasets of more realistic size, the state-of-the-art is a recent matheuristic, which attempts to solve the MINLP formulation with an optimization engine imposing a time limit. In this technical note, we propose two new matheuristics, the first one based on solving the continuous relaxation of the MINLP formulation, and the second one based on the training of an SVM classifier on a reduced dataset identified by an Integer Linear Problem. Our computational results illustrate the ability of our matheuristics to handle datasets of much larger size than those previously addressed in the literature.
Citation
2012