A non-smooth dual formulation of ε-Insensitive Weighted Least Square Support Vector Regression

Kocaoğlu A.

4th International Conference on Data Science and Applications (ICONDATA’21, Muğla, Turkey, 4 - 06 June 2021, vol.2, pp.66

  • Publication Type: Conference Paper / Summary Text
  • Volume: 2
  • City: Muğla
  • Country: Turkey
  • Page Numbers: pp.66
  • Dokuz Eylül University Affiliated: Yes


Least Square Support Vector Machine (LSSVM) is a well-known and powerful tool for both classification and regression tasks. It employs a regularized 𝑙2 error loss function with equality constraints and forms a Quadratic Programming (QP) problem in dual. However, it is lack of sparseness, as all data points are used to determine the output function. It is also lack of outlier robustness since it employs 𝑙2 error loss function. In this paper, an ε-insensitive Weighted Least Square Support Vector Regression (ε-WLSSVR) with equality constraints is introduced to improve outlier robustness by weighting error terms as well as sparseness using the ε-insensitive 𝑙2 error loss function and its dual problem is formulated as a nonsmooth, indeed piecewise quadratic, optimization problem. This non-smooth problem with L optimization parameters, same as the number of the training samples, is solved by the Sequential Minimal Optimization (SMO) algorithm based on the second-order like information. The effectiveness of the proposed ε-WLSSVR model is validated by a number of real-world benchmark datasets.