Asymmetrical interval regression using extended ε-SVM with robust algorithm

In an asymmetrical interval data set, the error ranges of the upper and lower interval ends are different. This situation is common in practice because of the usual presence of uncertain influences. In prior “crisp input and interval output” regression analysis, a crude symmetrical estimation is obtained, and the asymmetrical character of training data cannot be depicted exactly. In this paper, an asymmetrical interval data analysis is proposed for the first time. The two interval ends are studied independently, and a set of regression models and ε-insensitive functions are proposed to strengthen the description of the interval ends. The support vector machine (SVM) is imported into this approach (for its model-free character in nonlinear regression) and further extended by ε-insensitive functions to the extended ε-SVM. A robust algorithm is presented to eliminate the effect of outliers. Experiments are then presented to verify the quality of performance of the extended ε-SVM. Advantages over other approaches are considered in the conclusion.