Using Particle Swarm Optimisation and the Silhouette Metric to Estimate the Number of Clusters, Select Features, and Perform Clustering

  • Andrew Lensen
  • Bing Xue
  • Mengjie Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10199)


One of the most difficult problems in clustering, the task of grouping similar instances in a dataset, is automatically determining the number of clusters that should be created. When a dataset has a large number of attributes (features), this task becomes even more difficult due to the relationship between the number of features and the number of clusters produced. One method of addressing this is feature selection, the process of selecting a subset of features to be used. Evolutionary computation techniques have been used very effectively for solving clustering problems, but have seen little use for simultaneously performing the three tasks of clustering, feature selection, and determining the number of clusters. Furthermore, only a small number of existing methods exist, but they have a number of limitations that affect their performance and scalability. In this work, we introduce a number of novel techniques for improving the performance of these three tasks using particle swarm optimisation and statistical techniques. We conduct a series of experiments across a range of datasets with clustering problems of varying difficulty. The results show our proposed methods achieve significantly better clustering performance than existing methods, while only using a small number of features and automatically determining the number of clusters more accurately.


Particle swarm optimisation Clustering Feature selection Automatic clustering Silhouette 


  1. 1.
    Xue, B., Zhang, M., Browne, W.N., Yao, X.: A survey on evolutionary computation approaches to feature selection. IEEE Trans. Evol. Comput. 20(4), 606–626 (2016)CrossRefGoogle Scholar
  2. 2.
    García, A.J., Gómez-Flores, W.: Automatic clustering using nature-inspired metaheuristics: a survey. Appl. Soft Comput. 41, 192–213 (2016)CrossRefGoogle Scholar
  3. 3.
    Sheng, W., Liu, X., Fairhurst, M.C.: A niching memetic algorithm for simultaneous clustering and feature selection. IEEE Trans. Knowl. Data Eng. 20(7), 868–879 (2008)CrossRefGoogle Scholar
  4. 4.
    Javani, M., Faez, K., Aghlmandi, D.: Clustering and feature selection via PSO algorithm. In: International Symposium on Artificial Intelligence and Signal Processing (AISP), pp. 71–76. IEEE (2011)Google Scholar
  5. 5.
    Lensen, A., Xue, B., Zhang, M.: Particle swarm optimisation representations for simultaneous clustering and feature selection. In: Proceedings of the Symposium Series on Computational Intelligence. IEEE (2016, to appear)Google Scholar
  6. 6.
    Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3(3), 370–379 (1995)CrossRefGoogle Scholar
  7. 7.
    Alelyani, S., Tang, J., Liu, H.: Feature selection for clustering: a review. In: Data Clustering: Algorithms and Applications, pp. 29–60 (2013)Google Scholar
  8. 8.
    Aggarwal, C.C., Reddy, C.K. (eds.): Data Clustering: Algorithms and Applications. CRC Press (2014)Google Scholar
  9. 9.
    Chiang, M.M., Mirkin, B.G.: Intelligent choice of the number of clusters in K-means clustering: an experimental study with different cluster spreads. J. Classif. 27(1), 3–40 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Muni, D.P., Pal, N.R., Das, J.: Genetic programming for simultaneous feature selection and classifier design. IEEE Trans. Syst. Man Cybern. Part B 36(1), 106–117 (2006)CrossRefGoogle Scholar
  11. 11.
    Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)zbMATHGoogle Scholar
  12. 12.
    Liu, H., Motoda, H., Setiono, R., Zhao, Z.: Feature selection: an ever evolving frontier in data mining. In: Proceedings of the Fourth International Workshop on Feature Selection in Data Mining, pp. 4–13 (2010)Google Scholar
  13. 13.
    Van Den Bergh, F.: An analysis of particle swarm optimizers. PhD thesis, University of Pretoria (2006)Google Scholar
  14. 14.
    Lichman, M.: UCI machine learning repository (2013)Google Scholar
  15. 15.
    Handl, J., Knowles, J.D.: An evolutionary approach to multiobjective clustering. IEEE Trans. Evol. Comput. 11(1), 56–76 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Engineering and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand

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