An uncertain support vector machine based on soft margin method.

Abstract

Traditional support vector machines (SVMs) play an important role in the classification of precise data. However, due to various reasons, available data are sometimes imprecise. In this paper, uncertain variables are adopted to describe the imprecise data, and an uncertain support vector machine (USVM) is built for linearly alpha-nonseparable sets based on soft margin method, where a penalty coefficient is utilized as the trade-off between the maximum margin and the sum of slack variables. Then the equivalent crisp model is derived based on the inverse uncertainty distributions. Numerical experiments are designed to illustrate the application of the soft margin USVM. Finally, metrics, such as accuracy, precision, and recall are used to evaluate the robustness of the proposed model.