Multiphase support vector regression for function approximation with break-points

Abstract

In this paper, we propose a novel multiphase support vector regression (mp-SVR) technique to approximate a true relationship for the case where the effect of input on output changes abruptly at some break-points. A new formulation for mp-SVR is presented to allow such structural changes in regression function. And then, we present a new hybrid-encoding scheme in genetic algorithms to select the best combination of the kernel functions and to determine both break-points and hyperparameters of mp-SVR. The proposed method has a major advantage over the conventional ones that different kernel functions can be possibly adapted to different regions of the data domain. Computational results in two examples including a real-life data demonstrate its capability in capturing the local characteristics of the data more effectively. Consequently, the mp-SVR has a high potential value in a wide range of applications for function approximations.

Keywords:

• function approximation
• break-points
• multiphase support vector regression
• kernel selection
• hyperparameter optimization
• genetic algorithms