Applying norm concepts for solving interval support vector machine

Abstract

Abstract In this paper, a new variation of Support Vector Machine (SVM) is proposed which is named Interval Support Vector Machine (ISVM). The uncertainty of input data is one of the main problems to handle the real-world problems. Uncertainty factors could be a result of random variables existence, incorrect or imperfect data, and approximations instead of measurements or incomparability of data that is very dependent on different measurement or observation conditions. Interval numbers generally can be used for the representation of real data. In this version, SVM with interval samples is presented and reformulation of SVM performs real sample classification. Here, ISVM could be interchanged with an interval quadratic programming problem which itself can be converted to a pair of the so-called two-level mathematical programs based on norm concepts. The two-level mathematical programs are formed to find the upper and the lower bounds corresponding to the objective values of the interval quadratic program. Numerical experiments are examined for variant datasets such as normal, noisy, and interval-valued dataset to illustrate the performance of our approach.