Set-valued samples based support vector regression and its applications

• Initial representative points of set-valued data are selected via weighted distance.
• An algorithm determining the best representative points of set-valued data is designed.
• Set-valued samples based support vector regression (SSVR) is constructed.
• Efficiency of SSVR is demonstrated via experiments about real-world examples.

In this study, we address the regression problem on set-valued samples that appear in applications. To solve this problem, we propose a support vector regression approach for set-valued samples that generalizes the classical ε-support vector regression. First, an initial representative point (or an element) for every set-valued sample is selected, and a weighted distance between the initial representative point and other points is determined. Second, based on the classification consistency principle, a search algorithm to determine the best representative point for every set-valued datum is designed. Thus, the set-valued samples are converted into numeric samples. Finally, a support vector regression that is based on set-valued data is constructed, and the regression results of the set-valued samples can be approximated using the method used for the numeric samples. Furthermore, the feasibility and efficiency of the proposed method is demonstrated using experiments with real-world examples concerning wind speed prediction and the prediction of peak particle velocity.