Skip to main content
SpringerLink
Log in

Mixed-norm linear support vector machine

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper presents a new version of support vector machine (SVM) named l 2 − l p SVM (0 < p < 1) which introduces the l p -norm (0 < p < 1) of the normal vector of the decision plane in the standard linear SVM. To solve the nonconvex optimization problem in our model, an efficient algorithm is proposed using the constrained concave–convex procedure. Experiments with artificial data and real data demonstrate that our method is more effective than some popular methods in selecting relevant features and improving classification accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  2. Deng NY, Tian YJ, Zhang CH (2012) Suppport vector machines: optimization based theory, algorithms and applications. CRC press, Boca Raton (in press)

  3. Guyon I, Weston J, Barnhill S, Vapnik VN (2002) Gene selection for cancer classification using support vector machines. Mach Learn 46:389–422

    Article  MATH  Google Scholar 

  4. Mangasarian OL (1997) Minimum-support solutions of polyhedral concave programs, Technical Report Tr-1997-05, Mathematical Programming, University of Wisconsin

  5. Zhu J, Rosset S, Hastie T, Tibshirani R (2003) 1-norm support vector machines. Adv Neural Inf Process Syst 16:49-56

    Google Scholar 

  6. Bradley PS, Mangasarian OL (1998) Feature selection via concave minimization and support vector machines. In: Proceedings of the 13th ICML, pp 82–90

  7. Mangasarian OL, Wild EW (2007) Feature selection for nonlinear kernel support vector machines. In: IEEE seventh international conference on data mining, pp 231–236

  8. Chen XJ, Xu FM, Ye YY (2009) Lower bound theory of nonzero entries in solutions of l 2-l p minimization. http://www.standardford.edu/yyye/

  9. Bruckstein AM, Donoho DL, Elad M (2009) From sparse sulutions of systems of equations to sparse modeling of signals and images. SIAM Rev 51:34–81

    Article  MathSciNet  MATH  Google Scholar 

  10. Fan J, Li R (2001) Varible selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu Z, Zhang H, Wang Y, Chang X (2009) L1/2 regularizer. Sci Chin Ser F-Inf Sci 52:1–9

    Article  Google Scholar 

  12. Tan JY, Zhang CH, etc. (2010) Cancer Related Gene Identification via p-norm support vector machine. In: The international conference on computational systems biology, pp 101–108

  13. Zhang CH, Tan JY et al (2010) Feature Selection in multi-instance learning. In: The international symposium on operations research and its Applications: 462-469

  14. Tan JY, Zhang ZQ, Zhen L, Zhang CH, Deng NY (2012) Adaptive feature selection via a new version of support vector machine. Neural Comput Appl. doi:10.1007/s00521-012-1018-y

  15. Chen WJ, Tian YJ (2010) l p -norm proximal support vector machine and its application. Proc Comput Sci ICCS 1(1):2411-2417

    Google Scholar 

  16. Yuille AL, Rangarijan (2003) The concave-convex procedure. Neural Comput 15:915–936

  17. Smola AJ, Vishwanathan SVN, Hofman T (2005) Kernel methods for missing variables. In: Proceedings of the tenth international workshop on artificial intelligence and statistics, Barbodos

  18. Singh D, Febbo P, Ross K, Jackson D, Manola J, Ladd C, Tamayo P, Renshaw A, D’Amico A, Richie J, Lander E, Loda M, Kantoff P, Golub T, Sellers W (2002) Gene expression correlates of clinical prostate cancer behavior. Cancer Cell 1:203–209

    Article  Google Scholar 

  19. Golub TR, Slonim DK, Tamayo P, Huard C, Gaasenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, Bloomfield CD, Lander ES (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286:531–537

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by Chinese Universities Scientific Fund (No. 2011JS039), the Zhejiang Provincial Natural Science Foundation of China (No. LQ12A01020) and the National Natural Science Foundation of China (Nos. 10971223, 11201480, 11201426).

Author information

Authors and Affiliations

  1. Department of Mathematics, Information School, Renmin University of China, Beijing, 100872, China

    Chunhua Zhang

  2. Zhijiang College, Zhejiang University of Technology, Hangzhou, 310024, China

    Yuanhai Shao

  3. College of Science, China Agricultural University, Beijing, 100083, China

    Junyan Tan & Naiyang Deng

Authors
  1. Chunhua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanhai Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junyan Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Naiyang Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junyan Tan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, C., Shao, Y., Tan, J. et al. Mixed-norm linear support vector machine. Neural Comput & Applic 23, 2159–2166 (2013). https://doi.org/10.1007/s00521-012-1166-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-1166-0

Keywords

Search

Navigation