A projection method for multiobjective multiclass SVM

Support Vector Machines (SVMs) have become a very popular technique in the machine learning field for classification problems. It was originally proposed for classification of two classes. Various multiclass models with a single objective have been proposed mostly based on two 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 misclassification nor the user's preferences. To overcome these drawbacks, multiobjective models have been proposed.In this paper we rewrite the different approaches that deal with the multiclass SVM using multiobjective techniques. These multiobjective techniques can give us weakly Pareto-optimal solutions. 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 multiobjective techniques we get approximate sets of the Pareto-optimal solutions. For these sets, we use hypervolume and epsilon indicators to evaluate different multiobjective techniques. From the experimental 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 technique