The Margin Vector and Multi-class Margin-based Classifiers

Hui Zou, Ph.D
School of Statistics
University of Minnesota

Wednesday, December 7th
3:30pm
Moos 2-690
Minneapolis Campus

Abstract:
The margin-based classifiers, the support vector machine (SVM) and boosting, have demonstrated their excellent performances in the binary classification problem. However, it is nontrivial to extend the binary margin-based algorithms to multi-class cases, because the current formulation of the margin-based classifier is specifically designed for the binary classification problem. A widely used strategy for solving the multi-class classification problem is to employ the one-versus-all method such that a K-class problem is reduced to K binary classification problems.

In this talk we will present an alternative strategy which treats all classes simultaneously. We define the margin vector which is the multi-class generalization of the margin, then we further generalize the concept of admissible loss in binary classification to the multi-class cases. We show that a multi-class margin-based classifier is produced by minimizing the empirical margin-vector-based admissible loss with proper regularization. We characterize a class of convex losses that are admissible for both binary and multi-class classification problems. To demonstrate the usefulness of the proposed framework, we present some multicategory kernel machines and several new multi-class boosting algorithms.

A social tea will be held at 3:00 P.M. in A434 Mayo. All are Welcome.
For more details contact 612-624-4655 or see http://www.biostat.umn.edu/seminar_academic.html