An efficient algorithm for computing the HHSVM and its generalizations

Yi Yang, Hui Zou

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The hybrid Huberized support vector machine (HHSVM) has proved its advantages over the ℓ1 support vector machine (SVM) in terms of classification and variable selection. Similar to the ℓ1 SVM, the HHSVM enjoys a piecewise linear path property and can be computed by a least-angle regression (LARS)-type piecewise linear solution path algorithm. In this article, we propose a generalized coordinate descent (GCD) algorithm for computing the solution path of the HHSVM. The GCD algorithm takes advantage of a majorization-minimization trick to make each coordinatewise update simple and efficient. Extensive numerical experiments show that the GCD algorithm is much faster than the LARS-type path algorithm. We further extend the GCD algorithm to solve a class of elastic net penalized large margin classifiers, demonstrating the generality of the GCD algorithm. We have implemented the GCD algorithm in a publicly available R package gcdnet.

Original languageEnglish (US)
Pages (from-to)396-415
Number of pages20
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - 2013

Bibliographical note

Funding Information:
The authors thank the editor, an associate editor, and two referees for their helpful comments and suggestions. This work is supported in part by NSF grant DMS-08-46068.


  • Coordinate descent
  • Elastic net
  • Hubernet
  • Large margin classifiers
  • Majorization-minimization
  • SVM


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