A multi-class SVM approach based on the l₁-norm minimization of the distances between the reduced convex hulls.

Multi-class classification is an important pattern recognition task that can be addressed accurately and efficiently by Support Vector Machine (SVM). In this work we present a novel SVM-based multi-class classification approach based on the center of the configuration, a point which is equidistant to all classes. The center of the configuration is obtained from the dual formulation by minimizing the distances between the reduced convex hulls using the l₁-norm, while the decision functions are subsequently constructed from this point. This work also extends the ideas of Zhou et al. (2002) [37] to multi-class classification. The use of l₁-norm provides a single linear programming formulation, which reduces the complexity and confers scalability compared with other multi-class SVM methods based on quadratic programming formulations. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance and running times compared with various other multi-class SVM methods.