Nature Inspired Clustering – Use Cases of Krill Herd Algorithm and Flower Pollination Algorithm

  • Piotr A. KowalskiEmail author
  • Szymon Łukasik
  • Małgorzata Charytanowicz
  • Piotr Kulczycki
Part of the Studies in Computational Intelligence book series (SCI, volume 794)


Nature inspired metaheuristics were found to be applicable in deriving best solutions for several optimization tasks, and clustering represents a typical problem which can be successfully tackled with these methods. This paper investigates certain techniques of cluster analysis based on two recent heuristic algorithms mimicking natural processes: the Krill Herd Algorithm (KHA) and the Flower Pollination Algorithm (FPA). Beyond presenting both procedures and their implementation for clustering, a comparison with regard to quality of result was performed for fifteen data sets mainly drawn from the UCI Machine Learning Repository. As a validation of the clustering solution, the Calinski-Harabasz Index was also applied. Moreover, the performance of the investigated algorithms was assessed via Rand index value, with classic k-means procedure being employed as a point of reference. In conclusion it was established, KHA and FPA can be considered as being effective clustering tools.


Clustering Krill herd algorithm Flower pollination algorithm Nature-Inspired algorithms Optimization Metaheuristic 


  1. 1.
    Achtert, E., Goldhofer, S., Kriegel, H.P., Schubert, E., Zimek, A.: Evaluation of clusterings – metrics and visual support. In: 2012 IEEE 28th International Conference on Data Engineering, pp. 1285–1288 (2012)Google Scholar
  2. 2.
    Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Pérez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recognit. 46(1), 243–256 (2013)CrossRefGoogle Scholar
  3. 3.
    Bezdek, J.C., Ehrlich, R., Full, W.: Fcm: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2), 191–203 (1984)CrossRefGoogle Scholar
  4. 4.
    Calinski, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat.-Theory Methods 3(1), 1–27 (1974)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P.A., Łukasik, S., Żak, S.: Complete gradient clustering algorithm for features analysis of x-ray images. In: Pietka, E., Kawa, J. (eds.) Information Technologies in Biomedicine. Advances in intelligent and soft computing, vol. 69, pp. 15–24. Springer, Berlin Heidelberg (2010)Google Scholar
  6. 6.
    Chun-Wei, T., Wei-Cheng, H., Ming-Chao, C.: Recent development of metaheuristics for clustering. In: (Jong Hyuk) Park, J.J., Adeli, H., Park, N., Woungang, I. (eds.) Mobile, Ubiquitous, and Intelligent Computing Volume 274 of Lecture Notes in Electrical Engineering, pp. 629–636. Springer, Heidelberg (2014)Google Scholar
  7. 7.
    Collan, M., Fedrizzi, M., Kacprzyk, J.: Fuzzy Technology Present Applications and Future Challenges. Springer International Publishing (2016)Google Scholar
  8. 8.
    Davidson, I., Ravi, S.: Agglomerative hierarchical clustering with constraints: theoretical and empirical results. In: Knowledge Discovery in Databases: PKDD 2005, pp. 59–70. Springer (2005)Google Scholar
  9. 9.
    Fränti, Pasi, Virmajoki, Olli: Iterative shrinking method for clustering problems. Pattern Recognit. 39(5), 761–775 (2006)CrossRefGoogle Scholar
  10. 10.
    Gagolewski, M., Bartoszuk, M., Cena, A.: Genie: a new, fast, and outlier-resistant hierarchical clustering algorithm. Inf. Sci. 363, 8–23 (2016)CrossRefGoogle Scholar
  11. 11.
    Gandomi, A.H., Alavi, A.H.: Krill herd: a new bio-inspired optimization algorithm. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4831–4845 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kacprzyk, J., Krawczak, M., Szkatua, G.: On bilateral matching between fuzzy sets. Inf. Sci. 402, 244–266 (2017)CrossRefGoogle Scholar
  13. 13.
    Kowalski, P.A., Kusy, M.: Sensitivity analysis for probabilistic neural network structure reduction. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1919–1932 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kowalski, P.A., Łukasik, S.: Experimental study of selected parameters of the krill herd algorithm. In: Intelligent Systems’2014, pp. 473–485. Springer Science Business Media, Berlin (2015)Google Scholar
  15. 15.
    Kowalski, P.A., Łukasik, S., Charytanowicz, M., Kulczycki, P.: Clustering based on the krill herd algorithm with selected validity measures. In: Ganzha M., Maciaszek L., Paprzycki M., (eds.) Proceedings of the 2016 Federated Conference on Computer Science and Information Systems of Annals of Computer Science and Information Systems, vol. 8, pp. 79–87. IEEE (2016)Google Scholar
  16. 16.
    Kowalski, P.A., Łukasik, S., Charytanowicz, M., Kulczycki, P.: Comparison of krill herd algorithm and flower pollination algorithm in clustering task. ESCIM 2016, 31–36 (2016)Google Scholar
  17. 17.
    Kowalski, P.A., Łukasik, S., Kulczycki, P.: Methods of collective intelligence in exploratory data analysis: a research survey. In: Kowalski P.A., Łukasik S., Kulczycki P. (eds) Proceedings of the International Conference on Computer Networks and Communication Technology (CNCT 2016) of Advances in Computer Science Research, vol. 54, pp. 1–7, Atlantis Press, Xiamen (China) (2016)Google Scholar
  18. 18.
    Kulczycki, P., Charytanowicz, M., Kowalski, P.A., Łukasik, S.: The complete gradient clustering algorithm: properties in practical applications. J. Appl. Stat. 39(6), 1211–1224 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Langfelder, P., Zhang, B., Horvath, S.: Defining clusters from a hierarchical cluster tree: the dynamic tree cut package for r. Bioinformatics 24(5), 719–720 (2008)CrossRefGoogle Scholar
  20. 20.
    Lichman, M.: UCI machine learning repository (2013)Google Scholar
  21. 21.
    Łukasik, S., Kowalski, P.A.: Study of flower pollination algorithm for continuous optimization. In: Intelligent Systems’2014, pp. 451–459. Springer Science Business Media, Berlin (2015)Google Scholar
  22. 22.
    Łukasik, S., Kowalski, P.A., Charytanowicz, M., Kulczycki, P.: Fuzzy model identification using kernel-density-based clustering 2, 135–146 (2008). EXIT WarszawaGoogle Scholar
  23. 23.
    Łukasik, s., Kowalski, P.A., Charytanowicz, M., Kulczycki, P.: Fuzzy models synthesis with kernel-density-based clustering algorithm. In: Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008. FSKD ’08, vol. 3, pp. 449–453 (2008)Google Scholar
  24. 24.
    Łukasik, S., Kowalski, P.A., Charytanowicz, M., Kulczycki, P.: Clustering using flower pollination algorithm and calinski-harabasz index. In: IEEE Congress on Evolutionary Computation (CEC 2016), pp. 2724–2728, Vancouver (Canada) (2016). Proceedings: paper E-16413Google Scholar
  25. 25.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297. University of California 1965/66 (1967)Google Scholar
  26. 26.
    Müllner, D.: Modern hierarchical, agglomerative clustering algorithms. ArXiv e-prints (2011)Google Scholar
  27. 27.
    Müllner, D.: fastcluster: Fast hierarchical, agglomerative clustering routines for r and python. J. Stat. Softw. 53(1), 1–18 (2013)Google Scholar
  28. 28.
    Nowak, P., Romaniuk, M.: Catastrophe bond pricing for the two-factor vasicek interest rate model with automatized fuzzy decision making. Soft Comput. 1–23 (2015)Google Scholar
  29. 29.
    Rokach, L., Maimon, O.: Clustering methods. In: Maimon, O., Rokach, L. (eds.) Data Mining and Knowledge Discovery Handbook, pp. 321–352. Springer, US (2005)Google Scholar
  30. 30.
    Taher, N., Babak, A.: An efficient hybrid approach based on pso, ACO and k-means for cluster analysis. Appl. Soft Comput. 10(1), 183–197 (2010)Google Scholar
  31. 31.
    Wang, Gai-Ge: Amir H Gandomi, Amir H Alavi, and Guo-Sheng Hao. Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput. Appl. 25(2), 297–308 (2014)CrossRefGoogle Scholar
  32. 32.
    Welch, William J.: Algorithmic complexity: three np- hard problems in computational statistics. J. Stat. Comput. Simul. 15(1), 17–25 (1982)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Yang, M.-S.: A survey of fuzzy clustering. Math. Comput. Model. 18(11), 1–16 (1993)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Yang, X.-S.: Flower pollination algorithm for global optimization. Lect. Notes Comput. Sci. 7445, 240–249 (2012)Google Scholar
  35. 35.
    Ying, W., Chung, F.L., Wang, S.: Scaling up synchronization-inspired partitioning clustering. IEEE Trans. Knowl. Data Eng. 26(8), 2045–2057 (2014). AugCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Piotr A. Kowalski
    • 1
    • 2
    Email author
  • Szymon Łukasik
    • 1
    • 2
  • Małgorzata Charytanowicz
    • 1
    • 2
    • 3
  • Piotr Kulczycki
    • 1
    • 2
  1. 1.Faculty of Physics and Applied Computer ScienceAGH University of Science and TechnologyKrakówPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  3. 3.Institute of Mathematics and Computer ScienceThe John Paul II Catholic University of LublinLublinPoland

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