An uncertain support vector machine with imprecise observations

Support vector machines have been widely applied in binary classification, which are constructed based on crisp data. However, the data obtained in practice are sometimes imprecise, in which classical support vector machines fail in these situations. In order to handle such cases, this paper employs uncertain variables to describe imprecise observations and further proposes a hard margin uncertain support vector machine for the problem with imprecise observations. Specifically, we first define the distance from an uncertain vector to a hyperplane and give the concept of a linearly alpha-separable data set. Then, based on maximum margin criterion, we propose an uncertain support vector machine for the linearly alpha-separable data set, and derive the corresponding crisp equivalent forms. New observations can be classified through the optimal hyperplane derived from the model. Finally, a numerical example is given to illustrate the uncertain support vector machine.

Automated summary

Support vector machines have been widely used in binary classification, but they struggle with handling imprecise observations in practical applications. This paper proposes a hard margin uncertain support vector machine that uses uncertain variables to describe imprecise observations. The model defines the distance between an uncertain vector and a hyperplane and introduces the concept of a linearly alpha-separable data set. Through maximum margin criterion, the model can classify new observations using the optimal hyperplane derived from the model. A numerical example is provided to illustrate the uncertain support vector machine.