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DCA for Sparse Quadratic Kernel-Free Least Squares Semi-Supervised Support Vector Machine

Author

Listed:
  • Jun Sun

    (School of Mathematics and Statistics, Linyi University, Linyi 276000, China)

  • Wentao Qu

    (Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

With the development of science and technology, more and more data have been produced. For many of these datasets, only some of the data have labels. In order to make full use of the information in these data, it is necessary to classify them. In this paper, we propose a strong sparse quadratic kernel-free least squares semi-supervised support vector machine ( S S Q L S S 3 V M ), in which we add a ℓ 0 norm regularization term to make it sparse. An NP-hard problem arises since the proposed model contains the ℓ 0 norm and another nonconvex term. One important method for solving the nonconvex problem is the DC (difference of convex function) programming. Therefore, we first approximate the ℓ 0 norm by a polyhedral DC function. Moreover, due to the existence of the nonsmooth terms, we use the sGS-ADMM to solve the subproblem. Finally, empirical numerical experiments show the efficiency of the proposed algorithm.

Suggested Citation

  • Jun Sun & Wentao Qu, 2022. "DCA for Sparse Quadratic Kernel-Free Least Squares Semi-Supervised Support Vector Machine," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2714-:d:877626
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    References listed on IDEAS

    as
    1. Hoai Le Thi & Hoai Le & Van Nguyen & Tao Pham Dinh, 2008. "A DC programming approach for feature selection in support vector machines learning," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 2(3), pages 259-278, December.
    2. Xin Yan & Yanqin Bai & Shu-Cherng Fang & Jian Luo, 2016. "A kernel-free quadratic surface support vector machine for semi-supervised learning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(7), pages 1001-1011, July.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    5. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    6. Hoai An, Le Thi & Minh, Le Hoai & Tao, Pham Dinh, 2007. "Optimization based DC programming and DCA for hierarchical clustering," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1067-1085, December.
    Full references (including those not matched with items on IDEAS)

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