Regular Article

Advances in Data Analysis and Classification

, Volume 2, Issue 1, pp 17-43

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

SVM-Maj: a majorization approach to linear support vector machines with different hinge errors

  • P. J. F. GroenenAffiliated withEconometric Institute, Erasmus University Rotterdam Email author 
  • , G. NalbantovAffiliated withERIM and Econometric Institute, Erasmus University Rotterdam
  • , J. C. BiochAffiliated withEconometric Institute, Erasmus University Rotterdam


Support vector machines (SVM) are becoming increasingly popular for the prediction of a binary dependent variable. SVMs perform very well with respect to competing techniques. Often, the solution of an SVM is obtained by switching to the dual. In this paper, we stick to the primal support vector machine problem, study its effective aspects, and propose varieties of convex loss functions such as the standard for SVM with the absolute hinge error as well as the quadratic hinge and the Huber hinge errors. We present an iterative majorization algorithm that minimizes each of the adaptations. In addition, we show that many of the features of an SVM are also obtained by an optimal scaling approach to regression. We illustrate this with an example from the literature and do a comparison of different methods on several empirical data sets.


Support vector machines Iterative majorization Absolute hinge error Quadratic hinge error Huber hinge error Optimal scaling

Mathematics Subject Classification (2000)

90C30 62H30 68T05