Support Vector Machine for data with tolerance based on Hard-margin and Soft-Margin

This paper presents two new types of support vector machine (SVM) algorithms, one is based on Hard-margin SVM and the other is based on Soft-margin SVM. These algorithms can handle data with tolerance of which the concept includes some errors, ranges or missing values in data. First, the concept of tolerance is introduced into optimization problems of Support Vector Machine. Second, the optimization problems with the tolerance are solved by using the Karush-Kuhn-Tucker conditions. Next, new algorithms are constructed based on the unique and explicit optimal solutions of the optimization problem. Finally, the effectiveness of the proposed algorithms is verified through some numerical examples for the artificial data.