Abstract
One of the most important steps in the formation of multiple classifier systems is the integration process also called the base classifiers fusion. The fusion process may be applied either to class labels or confidence levels (discriminant functions). These are the two main methods for combining base classifiers. In this paper, we propose an integration process which takes place in the geometry space. It means that the fusion of base classifiers is done using decision boundaries. In our approach, the final decision boundary is calculated by using the geometric mean. The algorithm presented in the paper concerns the case of 3 basic classifiers and two-dimensional features space. The results of the experiment based on several data sets show that the proposed integration algorithm is a promising method for the development of multiple classifiers systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Britto, A.S., Sabourin, R., Oliveira, L.E.: Dynamic selection of classifiersa comprehensive review. Pattern Recognit. 47(11), 3665–3680 (2014)
Burduk, R.: Integration base classifiers based on their decision boundary. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10246, pp. 13–20. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59060-8_2
Burduk, R.: Integration base classifiers in geometry space by harmonic mean. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2018. LNCS (LNAI), vol. 10841, pp. 585–592. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91253-0_54
Cavalin, P.R., Sabourin, R., Suen, C.Y.: Dynamic selection approaches for multiple classifier systems. Neural Comput. Appl. 22(3–4), 673–688 (2013)
Cyganek, B.: One-class support vector ensembles for image segmentation and classification. J. Math. Imaging Vis. 42(2–3), 103–117 (2012)
Didaci, L., Giacinto, G., Roli, F., Marcialis, G.L.: A study on the performances of dynamic classifier selection based on local accuracy estimation. Pattern Recognit. 38, 2188–2191 (2005)
Drucker, H., Cortes, C., Jackel, L.D., LeCun, Y., Vapnik, V.: Boosting and other ensemble methods. Neural Comput. 6(6), 1289–1301 (1994)
Giacinto, G., Roli, F.: An approach to the automatic design of multiple classifier systems. Pattern Recognit. Lett. 22, 25–33 (2001)
Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)
Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. Wiley, New York (2004)
Li, Y., Meng, D., Gui, Z.: Random optimized geometric ensembles. Neurocomputing 94, 159–163 (2012)
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)
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)
Rejer, I.: Genetic algorithms for feature selection for brain computer interface. Int. J. Pattern Recogn. Artif. Intell. 29(5), 1559008 (2015)
Ruta, D., Gabrys, B.: Classifier selection for majority voting. Inf. Fusion 6(1), 63–81 (2005)
Tulyakov, S., Jaeger, S., Govindaraju, V., Doermann, D.: Review of classifier combination methods. In: Marinai, S., Fujisawa, H. (eds.) Machine Learning in Document Analysis and Recognition, vol. 90, pp. 361–386. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-76280-5_14
Woźniak, M., Graña, M., Corchado, E.: A survey of multiple classifier systems as hybrid systems. Inf. Fusion 16, 3–17 (2014)
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)
Acknowledgments.
This work was supported in part by the National Science Centre, Poland under the grant no. 2017/25/B/ST6/01750.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Burduk, R., Kasprzak, A. (2018). The Use of Geometric Mean in the Process of Integration of Three Base Classifiers. In: Saeed, K., Homenda, W. (eds) Computer Information Systems and Industrial Management. CISIM 2018. Lecture Notes in Computer Science(), vol 11127. Springer, Cham. https://doi.org/10.1007/978-3-319-99954-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-99954-8_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99953-1
Online ISBN: 978-3-319-99954-8
eBook Packages: Computer ScienceComputer Science (R0)