Alternating direction method of multipliers for regularized multiclass support vector machines

Yangyang Xu; Ioannis Akrotirianakis; Amit Chakraborty

doi:10.1007/978-3-319-27926-8_10

Alternating direction method of multipliers for regularized multiclass support vector machines

Yangyang Xu
, Ioannis Akrotirianakis
, Amit Chakraborty

Institute for Mathematics and its Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Machine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers
Editors	Mario Pavone, Giovanni Maria Farinella, Vincenzo Cutello, Panos Pardalos
Publisher	Springer Verlag
Pages	105-117
Number of pages	13
ISBN (Print)	9783319279251
DOIs	https://doi.org/10.1007/978-3-319-27926-8_10
State	Published - 2015
Event	1st International Workshop on Machine Learning, Optimization, and Big Data, MOD 2015 - Taormina, Sicily, Italy Duration: Jul 21 2015 → Jul 23 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9432
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	1st International Workshop on Machine Learning, Optimization, and Big Data, MOD 2015
Country/Territory	Italy
City	Taormina, Sicily
Period	7/21/15 → 7/23/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Keywords

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

Publisher link

10.1007/978-3-319-27926-8_10

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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

Alternating direction method of multipliers for regularized multiclass support vector machines. / Xu, Yangyang; Akrotirianakis, Ioannis; Chakraborty, Amit.
Machine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers. ed. / Mario Pavone; Giovanni Maria Farinella; Vincenzo Cutello; Panos Pardalos. Springer Verlag, 2015. p. 105-117 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9432).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Xu, Y, Akrotirianakis, I & Chakraborty, A 2015, Alternating direction method of multipliers for regularized multiclass support vector machines. in M Pavone, GM Farinella, V Cutello & P Pardalos (eds), Machine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9432, Springer Verlag, pp. 105-117, 1st International Workshop on Machine Learning, Optimization, and Big Data, MOD 2015, Taormina, Sicily, Italy, 7/21/15. https://doi.org/10.1007/978-3-319-27926-8_10

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

Xu, Yangyang ; Akrotirianakis, Ioannis ; Chakraborty, Amit. / Alternating direction method of multipliers for regularized multiclass support vector machines. Machine Learning, Optimization, and Big Data - 1st International Workshop, MOD 2015 Taormina, Revised Selected Papers. editor / Mario Pavone ; Giovanni Maria Farinella ; Vincenzo Cutello ; Panos Pardalos. Springer Verlag, 2015. pp. 105-117 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Alternating direction method of multipliers for regularized multiclass support vector machines

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