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Sparse Support Vector Machines in Reproducing Kernel Banach Spaces

  • Zheng Li
  • Yuesheng XuEmail author
  • Qi Ye
Chapter

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.

Notes

Acknowledgements

The first author is supported in part by the Special Project on High-performance Computing under the National Key R&D Program (No. 2016YFB0200602), and by the Natural Science Foundation of China under grants 11471013 and 91530117. The third author would like to express his gratitude to the grant of the “Thousand Talents Program” for junior scholars of China, the grant of the Natural Science Foundation of China (11601162), and the grant of South China Normal University (671082, S80835, and S81031).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Guangdong Province Key Lab of Computational Science, School of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Data and Computer Science, Guangdong Province Key Laboratory of Computational ScienceSun Yat-Sen UniversityGuangzhouPeople’s Republic of China
  3. 3.Department of Mathematics and StatisticsOld Dominion UniversityNorfolkUSA
  4. 4.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPeople’s Republic of China

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