"Alternative second-order cone programming formulations for support vector classification"

Research areas:
  • Uncategorized
Year:
2014
Type of Publication:
Article
Keywords:
Support Vector Machine, Second order cone programming, Linear programming SVM
Authors:
  • S. Maldonado
  • J. Lopez
Journal:
IInformation Sciences
Volume:
268
Pages:
328-341
Month:
June
ISSN:
0020-0255
Abstract:
This paper presents two novel second-order cone programming (SOCP) formulations that determine a linear predictor using Support Vector Machines (SVMs). Inspired by the soft-margin SVM formulation, our first approach (ξ-SOCP-SVM) proposes a relaxation of the conic constraints via a slack variable, penalizing it in the objective function. The second formulation (r -SOCP-SVM) is based on the LP-SVM formulation principle: the bound of the VC dimension is loosened properly using the l∞-norm, and the margin is directly maximized. The proposed methods have several advantages: The first approach constructs a flexible classifier, extending the benefits of the soft-margin SVM formulation to second-order cones. The second method obtains comparable results to the SOCP-SVM formulation with less computational effort, since one conic restriction is eliminated. Experiments on well-known benchmark datasets from the UCI Repository demonstrate that our approach accomplishes the best classification performance compared to the traditional SOCP-SVM formulation, LP-SVM, and to standard linear SVM.