Neural Computing and Applications

, Volume 32, Issue 1, pp 183–193 | Cite as

Parameter selection method for support vector machine based on adaptive fusion of multiple kernel functions and its application in fault diagnosis

  • Hailun WangEmail author
  • Daxing Xu
  • Alexander Martinez
Brain- Inspired computing and Machine learning for Brain Health


A new model parameter selection method for support vector machine based on adaptive fusion of multiple kernel functions is proposed in this paper. Characteristics of local kernels, global kernels, mixtures of kernels and multiple kernels were analyzed. Fusion coefficients of the multiple kernel function, kernel function parameters and regression parameters are combined to form the parameters of the state vector. Thus, the model selection problem is transformed into a nonlinear system state estimation problem. Then, we use a fifth-degree cubature Kalman filter to estimate the parameters. In this way, we realize adaptive selection of the multiple kernel function weighted coefficient, the kernel parameters and the regression parameters. A simulation experiment was performed to interpret the PE process for fault diagnosis.


Support vector regression machine Kernel function characteristics Parameter selection Fifth-degree cubature Kalman filter 



This work was supported by the Natural Science Foundation of China (61403229, 61503213) and Zhejiang Provincial Natural Science Foundation of China (LY13F030011, LQ17F030005).


  1. 1.
    Vapnik VN (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar
  2. 2.
    Wu J (2014) Efficient HIK SVM learning for image classification. IEEE Trans Image Process 21(10):4442–4453MathSciNetzbMATHGoogle Scholar
  3. 3.
    Liu XL, Ding SF, Zhu H (2010) Appropriateness in applying SVMs to text classification. Comput Eng Sci 32(6):106–108Google Scholar
  4. 4.
    Xie SQ, Sheng FM, Qiu XN (2009) Face recognition method based on support vector machine. Comput Eng 35(16):186–188Google Scholar
  5. 5.
    Xiao HJ, Wang XF, Hong F (2016) Attribute selection-based and support vector machine for anomaly detection. J Huazhong Univ Sci Technol (Nat Sci Ed) 36(3):99–102Google Scholar
  6. 6.
    Dileep AD, Sekhar CC (2009) Representation and feature selection using multiple kernel learning. In: Proceedings of international joint conference on neural networks, Atlanta, 14–19 JuneGoogle Scholar
  7. 7.
    Lin YY, Liu TL, Fuh CS (2014) Local ensemble kernel learning for object category recognition. In: Proceedings of IEEE conference on computer vision and pattern recognition, Washington D. C. IEEE, pp 1–8Google Scholar
  8. 8.
    Mak B, Kwok JT, Ho S (2014) A study of various composite kernels for kernel eigenvoice speaker adaptation. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing, Montreal. IEEE, pp 325–328Google Scholar
  9. 9.
    Zhang N, Xia ZQ, Jiang H (2010) Prediction of runoff based on the multiple quantity index of SVM. J Hydraul Eng 40(11):1318–1324Google Scholar
  10. 10.
    Mu T, Nandi AK (2013) Automatic tuning of L2-SVM parameters employing the extended Kalman filter. Expert Syst 26(2):160–175CrossRefGoogle Scholar
  11. 11.
    Rakotomamonjy A, Bach FR, Canu S, Grandvalet Y (2015) Simple MKL. J Mach Learn Res 9(11):2491–2521Google Scholar
  12. 12.
    Bach FR (2008) Consistency of the group Lasso and multiple kernel learning. J Mach Learn Res 9(6):1179–1225MathSciNetzbMATHGoogle Scholar
  13. 13.
    Ong CS, Smola AJ, Williamson RC (2015) Learning the kernel with hyperkernels. J Mach Learn Res 6(7):1043–1071MathSciNetzbMATHGoogle Scholar
  14. 14.
    Jia B, Xin M, Cheng Y (2015) High-degree cubature Kalman filter. Automatica 49(2):510–518MathSciNetCrossRefGoogle Scholar
  15. 15.
    Xu Z, Jin R, Yang H et al (2015) Simple and efficient multiple kernel learning by group lasso. In: Proc. of the 27th international conference on machine learning, Haifa, pp 1175–1182Google Scholar
  16. 16.
    Lee WJ, Verzakov S, Duin RPW (2013) Kernel combination versus classifier combination. In: Proceedings of the multiple classifier systems. Springer, Berlin, pp 22–31Google Scholar
  17. 17.
    Bach FR, Lanckriet GRG, Jordon MI (2004) Multiple kernel learning, conic duality, and the SMO algorithm. In: Proc of the 21st international conference on machine learning, Banff, pp 41–48Google Scholar
  18. 18.
    Sonnenburg S, Ratsch G, Schafer C et al (2006) Large scale multiple kernel learning. J Mach Learn Res 7(1):1531–1565MathSciNetzbMATHGoogle Scholar
  19. 19.
    Rakotomamonjy A, Bach F, Canu S et al (2008) Simple MKL. J Mach Learn Res 9:2491–2521MathSciNetGoogle Scholar
  20. 20.
    Kloft M, Brefeld U, Laskov P et al (2008) Non-sparse multiple kernel learning. In: Proc of the NIPS workshop on kernel learning: automatic selection of optimal kernelsGoogle Scholar
  21. 21.
    Kloft M, Brefeld U, Sonnenburg S et al (2009) Efficient and accurate L p-norm multiple kernel learning. In: Advance in neural information processing systems vol 22, pp 997–1005Google Scholar
  22. 22.
    Nath JS, Dinesh G, Raman S et al (2009) On the algorithmics and applications of a mixed-norm based kernel learning formulation. In: Advances in neural information processing systems vol 22, pp 844–852Google Scholar
  23. 23.
    Cortes C, Mohri M, Rostamizadeh A (2014) Learning non-linear combinations of kernels. In: Advances in neural information processing systems vol 22, pp 396–404Google Scholar
  24. 24.
    Mu S, Tian S, Yin C (2015) Multiple kernel learning based on cooperative clustering. J Beijing Jiaotong Univ 32(2):10–13Google Scholar
  25. 25.
    Wang HQ, Sun FC, Cai YN et al (2016) On multiple kernel learning methods. Acta Automatica Sinica 36(8):1037–1050MathSciNetCrossRefGoogle Scholar
  26. 26.
    Qiu SB, Lane T (2012) Multiple kernel support vector regression for RNA efficacy prediction. In: Proceedings of the 4th international conference on bioinformatics research and applications, Atlanta. Springer, pp 367–378Google Scholar
  27. 27.
    Bosch A, Zisserman A, Munoz X (2014) Representing shape with a spatial pyramid kernel. In: Proceedings of the 6th ACM international conference on image and video retrieval, Amsterdam. ACM, pp 401–408Google Scholar
  28. 28.
    Liu Y (2015) Study on kernel function of support vector machine. Ph.D. dissertation, Xidian University, ChinaGoogle Scholar
  29. 29.
    Chang CC, Lin CJ (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol (TIST) 2(3):27Google Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Logistics Engineering CollegeShanghai Maritime UniversityShanghaiPeople’s Republic of China
  2. 2.College of Electrical and Information EngineeringQuzhou UniversityQuzhouPeople’s Republic of China
  3. 3.School of ComputingNewcastle UniversityNewcastle upon TyneUK

Personalised recommendations