Interval Regression Analysis with Soft-Margin Reduced Support Vector Machine

Abstract

The support vector machine (SVM) has shown to be an efficient approach for a variety of classification problems. It has also been widely used in pattern recognition, regression and distribution estimation for crisp data. However, there are three main problems while using SVM model: (1) Large-scale: when dealing with large-scale data sets, the solution by using SVM with nonlinear kernels may be difficult to find; (2) Unbalance: the number of samples from one class is much larger than the number of samples from other classes. It causes the excursion of separation margin; (3) Noises and Interaction: the distribution of data becomes hard to be described and the separation margin between classes becomes a “gray” zone. Under this circumstance, to develop an efficient method is necessary. Recently the reduced support vector machine (RSVM) was proposed as an alternative of the standard SVM. It has been proved more efficient than the traditional SVM in processing large-scaled data. In this paper we introduce the principle of RSVM to evaluate interval regression analysis. In addition the soft margin method is proposed to modify the excursion of separation margin and to be effective in the gray zone.