A1 Refereed original research article in a scientific journal
Nonsmooth DC optimization support vector machines method for piecewise linear regression
Authors: Bagirov, A.M.; Taheri, S.; Karmitsa, N.; Joki, K.; Mäkelä, M.M.
Publisher: Institute of Applied Mathematics of Baku State University
Publication year: 2024
Journal: Applied and Computational Mathematics
Journal name in source: Applied and Computational Mathematics
Volume: 23
Issue: 3
First page : 282
Last page: 306
ISSN: 1683-3511
eISSN: 1683-6154
DOI: https://doi.org/10.30546/1683-6154.23.3.2024.282
Web address : https://doi.org/10.30546/1683-6154.23.3.2024.282
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457906850
A new regression method called the adaptive piecewise linear support vector regression (A-PWLSVR) is introduced. We use the L1-risk function to define regression errors and apply the support vector machine approach in combination with the piecewise linear regression to develop a model for regression problems. We formulate the model as an unconstrained nonconvex nonsmooth optimization problem, where the objective function is represented as a difference of two convex (DC) functions. To address the nonconvexity of the problem a novel incremental approach is proposed. This approach builds the piecewise linear estimates by applying an adaptive selection procedure for the model parameters. The approach enables us to select starting points being rough approximations of the solution. The double bundle method for nonsmooth DC optimization is applied to solve the optimization problems. The proposed A-PWLSVR method is evaluated on several synthetic and real-world data sets for regression and compared with some mainstream regression methods.
Downloadable publication This is an electronic reprint of the original article. |  |
Funding information in the publication:
The research was supported by the Australian Government through the Australian Research Council\u2019s Discovery Projects funding scheme (Project No. DP190100580) and by the Research Council of Finland (Project No. 289500, 319274, 345804, and 345805).
