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Sparse Support Vector Machines in Reproducing Kernel Banach Spaces

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Zheng Li

    (Sun Yat-sen University, Guangdong Province Key Lab of Computational Science, School of Mathematics)

  • Yuesheng Xu

    (Sun Yat-Sen University, School of Data and Computer Science, Guangdong Province Key Laboratory of Computational Science
    Old Dominion University, Department of Mathematics and Statistics)

  • Qi Ye

    (South China Normal University, School of Mathematical Sciences)

Abstract

We present a novel approach for support vector machines in reproducing kernel Banach spaces induced by a finite basis. In particular, we show that the support vector classification in the 1-norm reproducing kernel Banach space is mathematically equivalent to the sparse support vector machine. Finally, we develop fixed-point proximity algorithms for finding the solution of the non-smooth minimization problem that describes the sparse support vector machine. Numerical results are presented to demonstrate that the sparse support vector machine outperforms the classical support vector machine for the binary classification of simulation data.

Suggested Citation

  • Zheng Li & Yuesheng Xu & Qi Ye, 2018. "Sparse Support Vector Machines in Reproducing Kernel Banach Spaces," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 869-887, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_38
    DOI: 10.1007/978-3-319-72456-0_38
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