This matlab code implements classical linear logistic regression, but adds a regularization term that prevents the transition from one class to another to be too sharp, i.e. it penalizes the slope of the transition. As we explain in Appendinx B of the paper cited blow, this approximates support vectors when the classes are well separated. If classes do have many points that overlap, logistic regression assumes a smooth transition between the two classes, wheras support vectors do not make much sense in that case. In a way this code implements the best of both worlds.