Many margin-based binary classification techniques such as support vector machine (SVM) and Ψ-learning deliver high performance. An earlier article proposed a new multicategory Ψ-learning methodology that shows great promise in generalization ability. However, Ψ-learning is computationally difficult because it requires handling a nonconvex minimization problem. In this article, we propose two computational tools for multicategory Ψ-learning. The first one is based on d.c. algorithms and solved by sequential quadratic programming, while the second one uses the outer approximation method, which yields the global minimizer via sequential concave minimization. Numerical examples show the proposed algorithms perform well.
Bibliographical noteFunding Information:
The authors thank the editor, the AE, and the referees for their helpful comments. The research is supported in part by NSF Grant IIS-0328802, DMS-0072635, and NSA grant MDA904-03-1-0021.
- Concave minimization
- D.c. algorithms
- Nonconvex minimization
- Outer approximation
- Quadratic programming