## Abstract

The hybrid Huberized support vector machine (HHSVM) has proved its advantages over the ℓ_{1} support vector machine (SVM) in terms of classification and variable selection. Similar to the ℓ_{1} 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 language | English (US) |
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Pages (from-to) | 396-415 |

Number of pages | 20 |

Journal | Journal of Computational and Graphical Statistics |

Volume | 22 |

Issue number | 2 |

DOIs | |

State | Published - 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.

## Keywords

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