Multicategory Ψ-Learning and support vector machine: Computational tools

Yufeng Liu, Xiaotong Shen, Hani Doss

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)219-236
Number of pages18
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - Mar 2005

Bibliographical note

Funding 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.


  • Classification
  • Concave minimization
  • D.c. algorithms
  • Nonconvex minimization
  • Outer approximation
  • Quadratic programming

Fingerprint Dive into the research topics of 'Multicategory Ψ-Learning and support vector machine: Computational tools'. Together they form a unique fingerprint.

Cite this