Multicategory ψ-Learning

In binary classification, margin-based techniques usually deliver high performance. As a result, a multicategory problem is often treated as a sequence of binary classifications. In the absence of a dominating class, this treatment may be suboptimal and may yield poor performance, such as for support vector machines (SVMs). We propose a novel multicategory generalization of ψ-learning that treats all classes simultaneously. The new generalization eliminates this potential problem while at the same time retaining the desirable properties of its binary counterpart. We develop a statistical learning theory for the proposed methodology and obtain fast convergence rates for both linear and nonlinear learning examples. We demonstrate the operational characteristics of this method through a simulation. Our results indicate that the proposed methodology can deliver accurate class prediction and is more robust against extreme observations than its SVM counterpart.