Alternating direction method of multipliers for regularized multiclass support vector machines

Yangyang Xu, Ioannis Akrotirianakis, Amit Chakraborty

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to these MSVMs. Using a splitting technique, all considered MSVMs are written as two-block convex programs, for which the ADMM has global convergence guarantees. Numerical experiments on synthetic and real data demonstrate the high efficiency and accuracy of our algorithms.

Original languageEnglish (US)
Title of host publicationMachine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers
EditorsMario Pavone, Giovanni Maria Farinella, Vincenzo Cutello, Panos Pardalos
PublisherSpringer- Verlag
Pages105-117
Number of pages13
ISBN (Print)9783319279251
DOIs
StatePublished - Jan 1 2015
Event1st International Workshop on Machine Learning, Optimization, and Big Data, MOD 2015 - Taormina, Sicily, Italy
Duration: Jul 21 2015Jul 23 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9432
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Workshop on Machine Learning, Optimization, and Big Data, MOD 2015
CountryItaly
CityTaormina, Sicily
Period7/21/157/23/15

Keywords

  • Alternating direction method of multipliers
  • Elastic net
  • Group lasso
  • Multiclass classification
  • Supnorm
  • Support vector machine

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    Xu, Y., Akrotirianakis, I., & Chakraborty, A. (2015). Alternating direction method of multipliers for regularized multiclass support vector machines. In M. Pavone, G. M. Farinella, V. Cutello, & P. Pardalos (Eds.), Machine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers (pp. 105-117). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9432). Springer- Verlag. https://doi.org/10.1007/978-3-319-27926-8_10