SVM-Maj: a majorization approach to linear support vector machines with different hinge errors. (English) Zbl 1151.90551

Groenen, P. J. F.; Nalbantov, G.; Bioch, J. C.

Adv. Data Anal. Classif., ADAC 2, No. 1, 17-43 (2008).

Summary: 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.

MSC:

90C30	Nonlinear programming
62H30	Classification and discrimination; cluster analysis (statistical aspects)
68T05	Learning and adaptive systems in artificial intelligence

Keywords:

support vector machines; iterative majorization; absolute hinge error; quadratic hinge error; huber hinge error; optimal scaling

Software:

LIBSVM; UCI-ml; SVMlight

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