On-line Robust Fuzzy Clustering for Anomalies Detection

  • Yevgeniy Bodyanskiy
  • Oleksii Didyk
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)


Widly-used fuzzy c-means algorithm (FCM) has been utilized, with much success, in a variety of applications. The algorithm is known as an objective function based fuzzy clustering technique that extends the use of classical k-means method to fuzzy partitions. However, one of the most important drawbacks of this method is its sensitivity to noise and outliers in data since the objective function is the sum of squared distance. New robust fuzzy clustering algorithm (RFC) for exploring of signals of different nature taking into account the presence of noise with unknown density distributions and anomalous outliers in the data being analyzed is presented in this paper. By rejection of the Euclidean distance in the objective function the insensibility to the noise and outliers in the data was archived. Our approach introduces a robust probabilistic clustering procedure and is based on a modified objective function.


Robust fuzzy clustering Fuzzy c-means Anomalies detection 


  1. 1.
    Delen, D.: Real-World Data Mining: Applied Business Analytics and Decision Making. Pearson FT Press, New Jersey (2015)Google Scholar
  2. 2.
    Aggarwal, C.C.: A Data Mining: The Textbook. Springer, New York (2015)CrossRefGoogle Scholar
  3. 3.
    Larose, D.T.: Discovering Knowledge in Data: An Introduction to Data Mining. Wiley, Hoboken (2014)CrossRefGoogle Scholar
  4. 4.
    Yang, M.-S., Chang-Chien, S.-J., Hung, W.-L.: An unsupervised clustering algorithm for data on the unit hypersphere. Appl. Soft Comput. 42, 290–313 (2016)CrossRefGoogle Scholar
  5. 5.
    Dunn, J.C.: A fuzzy relative of the ISODATA process and its Use in detecting compact well-separated clusters. J. Cybern. 3(3), 32–57 (1973)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithm. Plenum Press, New York (1981)CrossRefGoogle Scholar
  7. 7.
    Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Springer, Boston (1999)CrossRefGoogle Scholar
  8. 8.
    Xu, R., Wunsch II, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005)CrossRefGoogle Scholar
  9. 9.
    Davé, R.N.: Characterization and detection of noise in clustering. Patt. Recogn. Lett. 12(11), 657–664 (1991)CrossRefGoogle Scholar
  10. 10.
    Krishnapuram, R., Joshi, A., Nasraoui, O., Yi, L.: Low-complexity fuzzy relational clustering algorithms for Web mining. IEEE Trans. Fuzzy Syst. 9(4), 595–607 (2001)CrossRefGoogle Scholar
  11. 11.
    Bodyanskiy, Y.: Computational intelligence techniques for data analysis. In: Proceedings of the LIT 2005, vol. P-72, pp. 15–36. Gesellschaft für Informatik, Bonn (2005)Google Scholar
  12. 12.
    Bodyanskiy, Y., Gorshkov, Y., Kokshenov, I., Kolodyazhniy, V.: Robust recursive fuzzy clustering algorithms. In: Proceedings of the East West Fuzzy Colloqium 2005, pp. 301–308. HS Zittau/Görlitz (2005)Google Scholar
  13. 13.
    Tsuda, K., Senda, S., Minoh, M., Ikeda, K.: Sequential fuzzy cluster extraction and its robustness against noise. Syst. Comp. Jpn. 28(6), 10–17 (1997)CrossRefGoogle Scholar
  14. 14.
    Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. Wiley, Chichester (1999)zbMATHGoogle Scholar
  15. 15.
    Georgieva, O., Klawonn, F.: A clustering algorithm for identification of single clusters in large data sets. In: Proceedings of the East West Fuzzy Colloquium 2004, pp. 118–125. HS Zittau/Görlitz (2004)Google Scholar
  16. 16.
    Butkiewicz, B.S.: Robust fuzzy clustering with fuzzy data. In: Szczepaniak, P.S., Kacprzyk, J., Niewiadomski, A. (eds.) Advances in Web Intelligence, vol. 3528, pp. 76–82. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Bodyanskiy, Y., Kokshenev, I., Gorshkov, Y., Kolodyazhniy, V.: Outlier resistant recursive fuzzy clustering algorithms. In: International Conference 9th Fuzzy Days in Dortmund: Computational Intelligence, Theory and Applications, pp. 647–652. Dortmund (2006)Google Scholar
  18. 18.
    Gorshkov, Y., Kokshenev, I., Bodyanskiy, Y., Kolodyazhniy, V., Shylo, O.: Robust recursive fuzzy clustering-based segmentation of biological time series. In: Proceedings of the 2006 International Symposium on Evolving Fuzzy Systems (EFS 2006), pp. 101–105 (2006)Google Scholar
  19. 19.
    Tsypkin, Y.Z.: Foundations of the Information Theory of Identification. Science, Moscow (1984). (in Russian)zbMATHGoogle Scholar
  20. 20.
    Hu, Z., Bodyanskiy, Y.V., Tyshchenko, O.K., Samitova, V.O.: Fuzzy clustering data given on the ordinal scale based on membership and likelihood functions sharing. Int. J. Intell. Syst. Appl. (IJISA) 9(2), 1–9 (2017). Scholar
  21. 21.
    Hu, Z., Bodyanskiy, Y.V., Tyshchenko, O.K., Samitova, V.O.: Fuzzy clustering data given in the ordinal scale. Int. J. Intell. Syst. Appl. (IJISA) 9(1), 67–74 (2017). Scholar
  22. 22.
    Hu, Z., Bodyanskiy, Y.V., Tyshchenko, O.K., Samitova, V.O.: Possibilistic fuzzy clustering for categorical data arrays based on frequency prototypes and dissimilarity measures. Int. J. Intell. Syst. Appl. (IJISA) 9(5), 55–61 (2017). Scholar
  23. 23.
    Hu, Z., Bodyanskiy, Y.V., Tyshchenko, O.K., Tkachov, V.M.: Fuzzy clustering data arrays with omitted observations. Int. J. Intell. Syst. Appl. (IJISA) 9(6), 24–32 (2017). Scholar
  24. 24.
    Zhang, Z.: Parameter estimation techniques: a tutorial with application to conic fitting. Image Vis. Comput. 15(1), 59–76 (1997)CrossRefGoogle Scholar
  25. 25.
    Galvin, F., Shore, S.D.: Distance functions and topologies. Am. Math. Mon. 98(7), 620 (1991)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Bodyanskiy, Y., Vynokurova, O., Savvo, V., Tverdokhlib, T., Mulesa, P.: Hybrid clustering-classification neural network in the medical diagnostics of the reactive arthritis. Int. J. Intell. Syst. Appl. (IJISA) 8(8), 1–9 (2016). Scholar
  27. 27.
    Coppola, C., Pacelli, T.: Approximate distances, pointless geometry and incomplete information. Fuzzy Sets Syst. 157(17), 2371–2383 (2006)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Perova, I., Pliss, I.: Deep hybrid system of computational intelligence with architecture adaptation for medical fuzzy diagnostics. Int. J. Intell. Syst. Appl. (IJISA) 9(7), 12–21 (2017). Scholar
  29. 29.
    Li, S.Z.: Markov Random Field Modeling in Computer Vision. Springer, Tokyo (1995)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Kharkiv National University of Radio ElectronicsKharkivUkraine
  2. 2.Kherson National Technical UniversityKhersonUkraine

Personalised recommendations