A novel kernel-free nonlinear SVM for semi-supervised classification in disease diagnosis

  • Xin Yan
  • Hongmiao Zhu
  • Jian LuoEmail author


Semi-supervised classification methods are widely-used and attractive for dealing with both labeled and unlabeled data in real-world problems. In this paper, a novel kernel-free Laplacian twin support vector machine method is proposed for semi-supervised classification. Its main idea is to classify data points into two classes by constructing two nonparallel quadratic surfaces so that each surface is close to one class of points and far away from the other class of points. The proposed method not only saves much computational time by avoiding choosing a kernel function and its related parameters in the classical support vector machine, but also addresses the issue of computational complexity by adopting manifold regularization technique. Moreover, two small-sized convex quadratic programming problems need to be solved to implement the proposed method, which is much easier than solving the non-convex problem of mixed integer programming to implement the well-known semi-supervised support vector machine. Finally, the numerical results on some artificial and benchmark data sets validate the competitive performance of proposed method in terms of efficiency, classification accuracy and generalization ability, by comparing to well-known semi-supervised methods. In particular, the proposed method handles five benchmarking disease diagnosis problems well and efficiently, which indicates the potential of proposed method in diagnosing and forecasting the diseases.


Support vector machine Kernel-free Quadratic surface Semi-supervised classification Disease diagnosis 



This research has been supported by MOE (Ministry of Education in China) Youth Foundation of Humanities and Social Sciences (No. 18YJC630220), the National Natural Science Foundation of China (Nos. 71901140, 71701035 and 71831003), Project of Philosophy and Social Science Planning in Shanghai (No. 2018EGL016).


  1. Astorino A, Fuduli A (2007) Nonsmooth optimization techniques for semisupervised classification. IEEE Trans Pattern Anal 29(12):2135–2142CrossRefGoogle Scholar
  2. Astorino A, Fuduli A (2015a) Semisupervised spherical separation. Appl Math Model 39(20):6351–6358MathSciNetCrossRefGoogle Scholar
  3. Astorino A, Fuduli A (2015b) Support vector machine polyhedral separability in semisupervised learning. J Optim Theory Appl 164(3):1039–1050MathSciNetCrossRefGoogle Scholar
  4. Bai Y, Yan X (2016) Conic relaxation for semi-supervised support vector machines. J Optim Theory Appl 169(1):299–313MathSciNetCrossRefGoogle Scholar
  5. Bai Y, Han X, Chen T, Yu H (2015) Quadratic kernel-free least squares support vector machine for target diseases classification. J Comb Optim 30(4):850–870MathSciNetCrossRefGoogle Scholar
  6. Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434MathSciNetzbMATHGoogle Scholar
  7. Chapelle O, Sindhwani V, Keerthi SS (2008) Optimization techniques for semi-supervised support vector machines. J Mach Learn Res 9:203–233zbMATHGoogle Scholar
  8. Chen WJ, Shao YH, Hong N (2014) Laplacian smooth twin support vector machine for semi-supervised classification. Int J Mach Learn Cybern 5(3):459–468CrossRefGoogle Scholar
  9. Chen X, Fan Z, Li Z, Han X, Zhang X, Jia H (2015) A two-stage method for member selection of emergency medical service. J Comb Optim 30(4):871–891MathSciNetCrossRefGoogle Scholar
  10. Collobert R, Sinz F, Weston J, Bottou L (2006) Large scale transductive SVMs. J Mach Learn Res 7:1687–1712MathSciNetzbMATHGoogle Scholar
  11. Dagher I (2008) Quadratic kernel-free non-linear support vector machine. J Global Optim 41(1):15–30MathSciNetCrossRefGoogle Scholar
  12. Deng N, Tian Y, Zhang C (2012) Support vector machines-optimization based theory, algorithms and extensions. CRC Press, Boca RatonCrossRefGoogle Scholar
  13. Gao W, Bao W, Zhou X (2019) Analysis of cough detection index based on decision tree and support vector machine. J Comb Optim 37(1):375–384MathSciNetCrossRefGoogle Scholar
  14. Gao Z, Yang L (2019) Energy-saving operation approaches for urban railtransit systems. Front Eng 6(2):139–151CrossRefGoogle Scholar
  15. Jayadeva Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRefGoogle Scholar
  16. Joachims T (1999) Transductive inference for text classification using support vector machines. In: Proceedings of the 16th international conference on machine learning, pp 200–209Google Scholar
  17. Luo J, Fang SC, Deng Z, Guo X (2016) Soft quadratic surface support vector machine for binary classification. Asia Pac J Oper Res 33(6):1650046MathSciNetCrossRefGoogle Scholar
  18. Luo J, Hong T, Fang SC (2018) Benchmarking robustness of load forecasting models under data integrity attacks. Int J Forecast 34(1):89–104CrossRefGoogle Scholar
  19. Melacci S, Belkin M (2011) Laplacian support vector machines trained in the primal. J Mach Learn Res 12:1149–1184MathSciNetzbMATHGoogle Scholar
  20. Niu D, Ma T, Liu B (2017) Power load forecasting by wavelet least squares support vector machine with improved fruit fly optimization algorithm. J Comb Optim 33(3):1122–1143MathSciNetCrossRefGoogle Scholar
  21. Qi Z, Tian Y, Shi Y (2012) Laplacian twin support vector machine for semi-supervised classification. Neural Netw 35:46–53CrossRefGoogle Scholar
  22. Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968CrossRefGoogle Scholar
  23. Tian Y, Qi Z, Ju X, Shi Y, Liu X (2014) Nonparallel support vector machines for pattern classification. IEEE Trans Cyber 44(7):1067–1079CrossRefGoogle Scholar
  24. Tian Y, Sun M, Deng Z, Luo J, Li Y (2017) A new fuzzy set and non-kernel svm approach for mislabeled binary classification with applications. IEEE Trans Fuzzy Syst 25(6):1536–1545CrossRefGoogle Scholar
  25. Yan X, Bai Y, Fang SC, Luo J (2018) A proximal quadratic surface support vector machine for semi-supervised binary classification. Soft Comput 22(20):6905–6919CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Statistics and InformationShanghai University of International Business and EconomicsShanghaiChina
  2. 2.School of ManagementShanghai University of International Business and EconomicsShanghaiChina
  3. 3.School of Management Science and EngineeringDongbei University of Finance and EconomicsDalianChina

Personalised recommendations