A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization
Year: 2018
Author: Zheng Li, Guohui Song, Yuesheng Xu
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 154–169
Abstract
We introduce an optimization model of the support vector regression with the group lasso regularization and develop a class of efficient two-step fixed-point proximity algorithms to solve it numerically. To overcome the difficulty brought by the non-differentiability of the group lasso regularization term and the loss function in the proposed model, we characterize its solutions as fixed-points of a nonlinear map defined in terms of the proximity operators of the functions appearing in the objective function of the model. We then propose a class of two-step fixed-point algorithms to solve numerically the optimization problem based on the fixed-point equation. We establish convergence results of the proposed algorithms. Numerical experiments with both synthetic data and real-world benchmark data are presented to demonstrate the advantages of the proposed model and algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-10561
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 154–169
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Two-step fixed-point algorithm proximity operator group lasso support vector machine ADMM.