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Support vector regression with the weighted absolute deviation error loss function
Journal of the Korean Data & Information Science Society 2018;29:1707-19
Published online November 30, 2018
© 2018 Korean Data and Information Science Society.

Kang-Mo Jung1

1Department of Statistics and Computer Science, Kunsan National University
Correspondence to: Professor, Department of Statistics and Computer Science, Kunsan National University, Kunsan 54150, Korea. E-mail: kmjung@kunsan.ac.kr
Received October 29, 2018; Revised November 16, 2018; Accepted November 18, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper we propose robust support vector regression algorithms to deal with noisy data sets. We adopt the absolute deviation error function for a loss function of regression model, and the proposed algorithms preserves the structure of the least squares support vector regression. The proposed algorithms are very fast and the procedures are much simpler than other support vector machine algorithms. They are robust to regression outliers, because the loss functions are less increasing than the squares error function for large errors and it uses a weight function for each observation. By comparing the proposed algorithms with other methods for the simulated datasets and benchmark datasets, the proposed methods are more robust than the least squares support vector regression when outliers exist.
Keywords : Absolute deviation, least squares, outliers, robust methods, support vector regression, weights.