A robust support vector regression with a linear-log concave loss function

Dohyun Kim, Chungmok Lee, Sangheum Hwang, Myong K. Jeong

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)735-742
Number of pages8
JournalJournal of the Operational Research Society
Issue number5
StatePublished - May 1 2016

All Science Journal Classification (ASJC) codes

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing


  • linear-log concave loss function
  • outlier
  • ramp loss function
  • robust regression
  • robust support vector regression
  • virtual metrology


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