A study on output normalization in multiclass SVMs

► This normalization overcomes the scaling problem in multi-classification with SVMs. ► It does not require additional steps of re-training. ► The keypoint is the use of the convex hulls that contain the classes to be separated. ► In some cases, the accuracy rate can be improved with respect to non-normalization. The use of binary support vector machines (SVMs) in multi-classification is addressed in this paper. Margins associated to the bi-classifiers, since they depend on the geometrical disposition of the classes being separated, are, in general, of various magnitudes. In order to overcome this scaling problem, a normalization process should be applied on the SVMs’ outputs. Thus, a new normalization approach is presented based on the convex hulls that contain the classes to be separated. Furthermore, a theoretical study is developed which justifies the proposed approach, and an interpretation is provided. An empirical study is also carried out to compare this normalization with others found in the literature.