Integration of Linear SVM Classifiers in Geometric Space Using the Median

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 892)


An ensemble of classifiers can improve the performance of a pattern recognition system. The task of constructing multiple classifier systems can be generally divided into three steps: generation, selection and integration. In this paper, we propose an integration process which takes place in the geometric space. It means that the fusion of base classifiers is done using decision boundaries. In our approach, we use the linear SVM model as a base classifier, the selection process is based on the accuracy and the final decision boundary is calculated by using the median of the decision boundary. The aim of the experiments was to compare the proposed algorithm and the majority voting method.


Ensemble of classifiers Multiple classifier system Decision boundary Linear SVM 



This work was supported in part by the National Science Centre, Poland under the grant no. 2017/25/B/ST6/01750.


  1. 1.
    Britto, A.S., Sabourin, R., Oliveira, L.E.: Dynamic selection of classifiers-a comprehensive review. Pattern Recogn. 47(11), 3665–3680 (2014)CrossRefGoogle Scholar
  2. 2.
    Burduk, R.: Integration base classifiers based on their decision boundary. In: Artificial Intelligence and Soft Computing–ICAISC 2017, vol. 10246. LNCS, pp. 13–20. Springer, Heidelberg (2017)CrossRefGoogle Scholar
  3. 3.
    Burduk, R.: Integration base classifiers in geometry space by harmonic mean. In: Artificial Intelligence and Soft Computing–ICAISC 2018, vol. 10841. LNCS, pp. 585–592. Springer, Heidelberg (2018)CrossRefGoogle Scholar
  4. 4.
    Cavalin, P.R., Sabourin, R., Suen, C.Y.: Dynamic selection approaches for multiple classifier systems. Neural Comput. Appl. 22(3–4), 673–688 (2013)CrossRefGoogle Scholar
  5. 5.
    Cyganek, B.: One-class support vector ensembles for image segmentation and classification. J. Math. Imaging Vis. 42(2–3), 103–117 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Didaci, L., Giacinto, G., Roli, F., Marcialis, G.L.: A study on the performances of dynamic classifier selection based on local accuracy estimation. Pattern Recogn. 38, 2188–2191 (2005)CrossRefGoogle Scholar
  7. 7.
    Drucker, H., Cortes, C., Jackel, L.D., LeCun, Y., Vapnik, V.: Boosting and other ensemble methods. Neural Comput. 6(6), 1289–1301 (1994)CrossRefGoogle Scholar
  8. 8.
    Giacinto, G., Roli, F.: An approach to the automatic design of multiple classifier systems. Pattern Recogn. Lett. 22, 25–33 (2001)CrossRefGoogle Scholar
  9. 9.
    Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)zbMATHGoogle Scholar
  10. 10.
    Korytkowski, M., Rutkowski, L., Scherer, R.: From ensemble of fuzzy classifiers to single fuzzy rule base classifier. In: Artificial Intelligence and Soft Computing–ICAISC 2008, vol. 5097. LNCS, pp. 265–272. Springer, Heidelberg (2008)Google Scholar
  11. 11.
    Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. Wiley, New York (2004)Google Scholar
  12. 12.
    Li, Y., Meng, D., Gui, Z.: Random optimized geometric ensembles. Neurocomputing 94, 159–163 (2012)CrossRefGoogle Scholar
  13. 13.
    Ponti Jr., M.P.: Combining classifiers: from the creation of ensembles to the decision fusion. In: 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images Tutorials (SIBGRAPI-T), pp. 1–10. IEEE (2011)Google Scholar
  14. 14.
    Pujol, O., Masip, D.: Geometry-based ensembles: toward a structural characterization of the classification boundary. IEEE Trans. Pattern Anal. Mach. Intell. 31(6), 1140–1146 (2009)CrossRefGoogle Scholar
  15. 15.
    Rejer, I.: Genetic algorithms for feature selection for brain computer interface. Int. J. Pattern Recognit. Artif. Intell. 29(5), 1559008 (2015)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tulyakov, S., Jaeger, S., Govindaraju, V., Doermann, D.: Review of classifier combination methods. In: Machine Learning in Document Analysis and Recognition, pp. 361–386. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Woźniak, M., Graña, M., Corchado, E.: A survey of multiple classifier systems as hybrid systems. Inf. Fusion 16, 3–17 (2014)CrossRefGoogle Scholar
  18. 18.
    Xu, L., Krzyzak, A., Suen, C.Y.: Methods of combining multiple classifiers and their applications to handwriting recognition. IEEE Trans. Syst. Man Cybern. 22(3), 418–435 (1992)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Systems and Computer NetworksWroclaw University of Science and TechnologyWroclawPoland

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