L<sub>1</sub>-Norm Least Squares Support Vector Regression via the Alternating Direction Method of Multipliers

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  • Ye Ya-Fen
    College of Economics, Zhejiang University Zhijiang College, Zhejiang University of Technology
  • Ying Chao
    Rainbow City Primary School
  • Jiang Yue-Xiang
    College of Economics, Zhejiang University
  • Li Chun-Na
    Zhijiang College, Zhejiang University of Technology

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  • L₁-Norm Least Squares Support Vector Regression via the Alternating Direction Method of Multipliers

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<p>In this study, we focus on the feature selection problem in regression, and propose a new version of L1 support vector regression (L1-SVR), known as L1-norm least squares support vector regression (L1-LSSVR). The alternating direction method of multipliers (ADMM), a method from the augmented Lagrangian family, is used to solve L1-LSSVR. The sparse solution of L1-LSSVR can realize feature selection effectively. Furthermore, L1-LSSVR is decomposed into a sequence of simpler problems by the ADMM algorithm, resulting in faster training speed. The experimental results demonstrate that L1-LSSVR is not only as effective as L1-SVR, LSSVR, and SVR in both feature selection and regression, but also much faster than L1-SVR and SVR.</p>

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