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Sparse optimization via vector k-norm and DC programming with an application to feature selection for support vector machines

Author

Listed:
  • Manlio Gaudioso

    (Università della Calabria)

  • Giovanni Giallombardo

    (Università della Calabria)

  • Giovanna Miglionico

    (Università della Calabria)

Abstract

Sparse optimization is about finding minimizers of functions characterized by a number of nonzero components as small as possible, such paradigm being of great practical relevance in Machine Learning, particularly in classification approaches based on support vector machines. By exploiting some properties of the k-norm of a vector, namely, of the sum of its k largest absolute-value components, we formulate a sparse optimization problem as a mixed-integer nonlinear program, whose continuous relaxation is equivalent to the unconstrained minimization of a difference-of-convex function. The approach is applied to Feature Selection in the support vector machine framework, and tested on a set of benchmark instances. Numerical comparisons against both the standard $$\ell _1$$ ℓ 1 -based support vector machine and a simple version of the Slope method are presented, that demonstrate the effectiveness of our approach in achieving high sparsity level of the solutions without impairing test-correctness.

Suggested Citation

  • Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2023. "Sparse optimization via vector k-norm and DC programming with an application to feature selection for support vector machines," Computational Optimization and Applications, Springer, vol. 86(2), pages 745-766, November.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:2:d:10.1007_s10589-023-00506-y
    DOI: 10.1007/s10589-023-00506-y
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    References listed on IDEAS

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    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
    5. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
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