A projection method for multiobjective multiclass SVM

Support Vector Machines (SVMs) have become a very popular technique in the machinelearningfield for classification problems. It was originally proposed for classification of twoclasses. Various multiclass models with a single objective have been proposed mostly based ontwo families of methods: an all-together approach and a one-against-all approach. However,most of these single-objective models consider neither the different costs of misclassificationnor the user's preferences. To overcome these drawbacks, multiobjective models have beenproposed.In this paper we rewrite the different approaches that deal with the multiclass SVM usingmultiobjective techniques. These multiobjective techniques can give us weakly Pareto-optimalsolutions. We propose a multiobjective technique called Projected Multiobjective All-Together(PMAT), which works in a higher-dimension space than the object space. With this technique,we can theoretically characterize the Pareto-optimal solution set. For these multiobjectivetechniques we get approximate sets of the Pareto-optimal solutions. For these sets, we usehypervolume and epsilon indicators to evaluate different multiobjective techniques. From theexperimental results, we can see that (PMAT) outperfoms the other multiobjective techniques.When facing classification problems with very large numbers of classes, we suggest combininga tree method and multiobjective techniques.