Generalization performance of multiclass discriminant models

Starting from a direct definition of the notion of margin in the multiclass case, we study the generalization performance of multiclass discriminant systems. In the framework of statistical learning theory, we establish on this performance a bound based on covering numbers. An application to a linear ensemble method which estimates the class posterior probabilities provides us with a way to compare this bound and another one based on combinatorial dimensions, with respect to the capacity measure they incorporate. Experimental results highlight their usefulness for a real-world problem