A robust support vector regression with a linear-log concave loss function
提出一种新的鲁棒支持向量回归方法，使用线性对数凹损失函数，无需平滑或凸凹过程变换，在合成和真实数据集上优于现有方法，适用于含异常值的回归问题，如半导体制造中的虚拟计量预测。
Support vector regression (SVR) is one of the most popular nonlinear regression techniques with the aim to approximate a nonlinear system with a good generalization capability. However, SVR has a major drawback in that it is sensitive to the presence of outliers. The ramp loss function for robust SVR has been introduced to resolve this problem, but SVR with ramp loss function has a non-differentiable and non-convex formulation, which is not easy to solve. Consequently, SVR with the ramp loss function requires smoothing and Concave-Convex Procedure techniques, which transform the non-differentiable and non-convex optimization to a differentiable and convex one. We present a robust SVR with linear-log concave loss function (RSLL), which does not require the transformation technique, where the linear-log concave loss function has a similar effect as the ramp loss function. The zero norm approximation and the difference of convex functions problem are employed for solving the optimization problem. The proposed RSLL approach is used to develop a robust and stable virtual metrology (VM) prediction model, which utilizes the status variables of process equipment to predict the process quality of wafer level in semiconductor manufacturing. We also compare the proposed approach to existing SVR-based methods in terms of the root mean squared error of prediction using both synthetic and real data sets. Our experimental results show that the proposed approach performs better than existing SVR-based methods regardless of the data set and type of outliers (ie, X-space and Y-space outliers), implying that it can be used as a useful alternative when the regression data contain outliers.