A rough ν-twin support vector regression machine

摘要

After combining the ν-Twin Support Vector Regression (ν-TWSVR) with the rough set theory, we propose an efficient Rough ν-Twin Support Vector Regression, called Rough ν-TWSVR for short. We construct a pair of optimization problems which are motivated by and mathematically derived from a related ν-TWSVR Rastogi et al. (Appl Intell 46(3):670–683 2017) and Rough ν-SVR Zhao et al. (Expert Syst Appl 36(6):9793–9798 2009). Rough ν-TWSVR not only utilizes more data information rather than the extreme data points in the ν-TWSVR, but also makes different points having different effects on the regressor depending on their positions. This method can implement the structural risk minimization and automatically control accuracies according to the structure of the data sets. In addition, the double ε s are utilized to construct the rough tube for upper(lower)-bound Rough ν-TWSVR instead of a single ε in the upper(lower)-bound ν-TWSVR. Moreover, This rough tube consisting of positive region, boundary region, and negative region yields the feasible set of the Rough ν-TWSVR larger than that of the ν-TWSVR, which makes the objective function of the Rough ν-TWSVR no more than that of ν-TWSVR. The Rough ν-TWSVR improves the generalization performance of the ν-TWSVR, especially for the data sets with outliers. Experimental results on toy examples and benchmark data sets confirm the validation and applicability of our proposed Rough ν-TWSVR.