A new perspective on convex relaxations of sparse SVM

Noam Goldberg; Sven Leyffer; Todd Munsonz

doi:10.1137/1.9781611972832.50

A new perspective on convex relaxations of sparse SVM

Noam Goldberg
, Sven Leyffer
, Todd Munsonz

Argonne National Laboratory

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

2 Scopus citations

Abstract

This paper proposes a convex relaxation of a sparse support vector machine (SVM) based on the perspective relaxation of mixed-integer nonlinear programs. We seek to minimize the zero-norm of the hyperplane normal vector with a standard SVM hinge-loss penalty and extend our approach to a zero-one loss penalty. The relaxation that we propose is a second-order cone formulation that can be efficiently solved by standard conic optimization solvers. We compare the optimization properties and classification performance of the second-order cone formulation with previous sparse SVM formulations suggested in the literature.

Original language	English
Title of host publication	Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013
Editors	Joydeep Ghosh, Zoran Obradovic, Jennifer Dy, Zhi-Hua Zhou, Chandrika Kamath, Srinivasan Parthasarathy
Publisher	Siam Society
Pages	450-457
Number of pages	8
ISBN (Electronic)	9781611972627
DOIs	https://doi.org/10.1137/1.9781611972832.50
State	Published - 2013
Externally published	Yes
Event	SIAM International Conference on Data Mining, SDM 2013 - Austin, United States Duration: 2 May 2013 → 4 May 2013

Publication series

Name	Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013

Conference

Conference	SIAM International Conference on Data Mining, SDM 2013
Country/Territory	United States
City	Austin
Period	2/05/13 → 4/05/13

Bibliographical note

Publisher Copyright:
Copyright © SIAM.

Access to Document

10.1137/1.9781611972832.50

Cite this

Goldberg, N., Leyffer, S., & Munsonz, T. (2013). A new perspective on convex relaxations of sparse SVM. In J. Ghosh, Z. Obradovic, J. Dy, Z.-H. Zhou, C. Kamath, & S. Parthasarathy (Eds.), Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013 (pp. 450-457). (Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013). Siam Society. https://doi.org/10.1137/1.9781611972832.50

Goldberg, Noam ; Leyffer, Sven ; Munsonz, Todd. / A new perspective on convex relaxations of sparse SVM. Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013. editor / Joydeep Ghosh ; Zoran Obradovic ; Jennifer Dy ; Zhi-Hua Zhou ; Chandrika Kamath ; Srinivasan Parthasarathy. Siam Society, 2013. pp. 450-457 (Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013).

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abstract = "This paper proposes a convex relaxation of a sparse support vector machine (SVM) based on the perspective relaxation of mixed-integer nonlinear programs. We seek to minimize the zero-norm of the hyperplane normal vector with a standard SVM hinge-loss penalty and extend our approach to a zero-one loss penalty. The relaxation that we propose is a second-order cone formulation that can be efficiently solved by standard conic optimization solvers. We compare the optimization properties and classification performance of the second-order cone formulation with previous sparse SVM formulations suggested in the literature.",

author = "Noam Goldberg and Sven Leyffer and Todd Munsonz",

note = "Publisher Copyright: Copyright {\textcopyright} SIAM.; SIAM International Conference on Data Mining, SDM 2013 ; Conference date: 02-05-2013 Through 04-05-2013",

year = "2013",

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Goldberg, N, Leyffer, S & Munsonz, T 2013, A new perspective on convex relaxations of sparse SVM. in J Ghosh, Z Obradovic, J Dy, Z-H Zhou, C Kamath & S Parthasarathy (eds), Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013. Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013, Siam Society, pp. 450-457, SIAM International Conference on Data Mining, SDM 2013, Austin, United States, 2/05/13. https://doi.org/10.1137/1.9781611972832.50

A new perspective on convex relaxations of sparse SVM. / Goldberg, Noam; Leyffer, Sven; Munsonz, Todd.
Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013. ed. / Joydeep Ghosh; Zoran Obradovic; Jennifer Dy; Zhi-Hua Zhou; Chandrika Kamath; Srinivasan Parthasarathy. Siam Society, 2013. p. 450-457 (Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013).

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

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Goldberg N, Leyffer S, Munsonz T. A new perspective on convex relaxations of sparse SVM. In Ghosh J, Obradovic Z, Dy J, Zhou ZH, Kamath C, Parthasarathy S, editors, Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013. Siam Society. 2013. p. 450-457. (Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013). doi: 10.1137/1.9781611972832.50

A new perspective on convex relaxations of sparse SVM

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