Soft Computing

, Volume 21, Issue 18, pp 5235–5243 | Cite as

A robust algorithm of support vector regression with a trimmed Huber loss function in the primal

  • Chuanfa Chen
  • Changqing Yan
  • Na Zhao
  • Bin Guo
  • Guolin Liu


Support vector machine for regression (SVR) is an efficient tool for solving function estimation problem. However, it is sensitive to outliers due to its unbounded loss function. In order to reduce the effect of outliers, we propose a robust SVR with a trimmed Huber loss function (SVRT) in this paper. Synthetic and benchmark datasets were, respectively, employed to comparatively assess the performance of SVRT, and its results were compared with those of SVR, least squares SVR (LS-SVR) and a weighted LS-SVR. The numerical test shows that when training samples are subject to errors with a normal distribution, SVRT is slightly less accurate than SVR and LS-SVR, yet more accurate than the weighted LS-SVR. However, when training samples are contaminated by outliers, SVRT has a better performance than the other methods. Furthermore, SVRT is faster than the weighted LS-SVR. Simulating eight benchmark datasets shows that SVRT is averagely more accurate than the other methods when sample points are contaminated by outliers. In conclusion, SVRT can be considered as an alternative robust method for simulating contaminated sample points.


Support vector regression Robust Outliers Function estimation 



This work is funded by National Natural Science Foundation of China (Grant Nos. 41371367, 41101433), by SDUST Research Fund, by Joint Innovative Center for Safe And Effective Mining Technology and Equipment of Coal Resources, Shandong Province and by Special Project Fund of Taishan Scholars of Shandong Province.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Chuanfa Chen
    • 1
    • 2
  • Changqing Yan
    • 3
  • Na Zhao
    • 4
  • Bin Guo
    • 2
  • Guolin Liu
    • 2
  1. 1.State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and TechnologyShandong University of Science and TechnologyQingdaoChina
  2. 2.College of GeomaticsShandong University of Science and TechnologyQingdaoChina
  3. 3.Department of Information EngineeringShandong University of Science and TechnologyTaianChina
  4. 4.State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijingChina

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