Support Vector Machine has shown to have good performance in many practical classification settings. In this paper we propose, for multi-group classification, a biobjective optimization model in which we consider not only the generalization ability (modeled through the margin maximization), but...

The nearest-neighbor classifier has been shown to be a powerful tool for multiclass classification. We explore both theoretical properties and empirical behavior of a variant method, in which the nearest-neighbor rule is applied to a reduced set of prototypes. This set is selected a priori by...

The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this...

The p-principal points of a random variable X with finite second moment are those p points in minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing...

Recently, Support Vector Machines with the ramp loss (RLM) have attracted attention from the computational point of view. In this technical note, we propose two heuristics, the first one based on solving the continuous relaxation of a Mixed Integer Nonlinear formulation of the RLM and the second...

The default approach for tuning the parameters of a Support Vector Machine (SVM) is a grid search in the parameter space. Different metaheuristics have been recently proposed as a more efficient alternative, but they have only shown to be useful in models with a low number of parameters. Complex...

The widely used Support Vector Machine (SVM) method has shown to yield good results in Supervised Classification problems. When the interpretability is an important issue, then classification methods such as Classification and Regression Trees (CART) might be more attractive, since they are...

A number of methods for multiple-objective optimization problems (MOP) give as solution to MOP the set of optimal solutions for some single-objective optimization problems associated with it. Well-known examples of these single-objective optimization problems are the minsum and the minmax. In...

It is known that if that sum of weights in the Weber problem with attraction and repulsion is positive, then the problem attains an optimal solution. In this note we extend this result to the nonlinear extension of the above mentioned problem, which has been only addressed in the literature for...