Multiclass Learning with Simplex Coding

In this paper we dicuss a novel framework for multiclass learning, defined by a suitable coding/decoding strategy, namely the simplex coding, that allows to generalize to multiple classes a relaxation approach commonly used in binary classification. In this framework a relaxation error analysis can be developed avoiding constraints on the considered hypotheses class. Moreover, we show that in this setting it is possible to derive the first provably consistent regularized methods with training/tuning complexity which is {\em independent} to the number of classes. Tools from convex analysis are introduced that can be used beyond the scope of this paper.