A game theory approach to pairwise classification with support vector machines

Support Vector Machines (SVM) for pattern recognition are discriminant binary classifiers. One of the approaches to extend them to multi-class case is pairwise classification. Pairwise comparisons for each pair of classes are combined together to predict the class or to estimate class probabilities. This paper presents a novel approach, which considers the pairwise SVM classification as a decision-making problem and involves game theory methods to solve it. We prove that in such formulation the solution in pure minimax strategies is equivalent to the solution given by standard fuzzy pairwise SVM method. On the other hand, if we use mixed strategies it,e formulate new linear programming based pairwise SVM method for estimating class probabilities. We evaluate the performance of the proposed method in experiments with several benchmark datasets, including datasets for optical character recognition and multi-class text categorization problems.