A rough nu-twin support vector regression machine

摘要

After combining the nu-Twin Support Vector Regression (nu-TWSVR) with the rough set theory, we propose an efficient Rough nu-Twin Support Vector Regression, called Rough nu-TWSVR for short. We construct a pair of optimization problems which are motivated by and mathematically derived from a related nu-TWSVR Rastogi et al. (Appl Intell 46(3):670-683 2017) and Rough nu-SVR Zhao et al. (Expert Syst Appl 36(6):9793-9798 2009). Rough nu-TWSVR not only utilizes more data information rather than the extreme data points in the nu-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 epsilon s are utilized to construct the rough tube for upper(lower)-bound Rough nu-TWSVR instead of a single epsilon in the upper(lower)-bound nu-TWSVR. Moreover, This rough tube consisting of positive region, boundary region, and negative region yields the feasible set of the Rough nu-TWSVR larger than that of the nu-TWSVR, which makes the objective function of the Rough nu-TWSVR no more than that of nu-TWSVR. The Rough nu-TWSVR improves the generalization performance of the nu-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 nu-TWSVR.