A rough margin-based linear ν support vector regression

We propose a rough margin-based linear ν-SVR (rough linear ν-SVR) by introducing the rough set theory into the linear programming-based ν-support vector regression (linear ν-SVR), to deal with the problem of over-fitting. Double ϵs are utilized to construct the rough margin for the rough linear ν-SVR instead of the single ϵ used in the classical linear ν-SVR, and this rough margin is composed of a lower margin and upper margin. Therefore, more data points are adaptively considered in constructing the regressor than in the linear ν-SVR. Moreover, points lying in different positions are given different penalties. Specifically, points within the lower margin are given no penalty, and points in the rough boundary are given small penalties, while the points lying outside the upper margin are given larger penalties. Our proposed algorithm avoids the over-fitting problem to a certain extent. The experimental results on seven datasets demonstrate the feasibility and validity of our proposed algorithm.