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Cluster Computing

, Volume 21, Issue 1, pp 377–391 | Cite as

Optimizing the minimum spanning tree-based extracted clusters using evolution strategy

  • Zahid HalimEmail author
  • Uzma
Article

Abstract

There are many approaches available for extracting clusters. A few are based on the partitioning of the data and others rely on extracting hierarchical structures. Graphs provide a convenient representation of entities having relationships. Clusters can be extracted from a graph-based structure using minimum spanning trees (MSTs). This work focuses on optimizing the MST-based extracted clusters using Evolution Strategy (ES). A graph may have multiple MSTs causing varying cluster formations based on different MST selection. This work uses (1+1)-ES to obtain the optimal MST-based clustering. The Davies–Bouldin Index is utilized as fitness function to evaluate the quality of the clusters formed by the ES population. The proposed approach is evaluated using eleven benchmark datasets. Seven of these are based on microarray and the rest are taken from the UCI machine learning repository. Both, external and internal cluster validation indices are used to evaluate the results. The performance of the proposed approach is compared with two state-of-the-art MST-based clustering algorithms. The results support promising performance of the proposed approach in terms of time and cluster validity indices.

Keywords

Minimum spanning trees Clustering Graphs Evolution strategy 

References

  1. 1.
    Datta, S., Datta, S.: Comparisons and validation of statistical clustering techniques for microarray gene expression data. Bioinformatics 19(4), 459–466 (2003)CrossRefGoogle Scholar
  2. 2.
    Shen, H., Yang, J., Wang, S., Liu, X.: Attribute weighted mercer kernel based fuzzy clustering algorithm for general non-spherical datasets. Soft Comput. 10(11), 1061–1073 (2006)CrossRefGoogle Scholar
  3. 3.
    Srinivasan, G.: A clustering algorithm for machine cell formation in group technology using minimum spanning trees. Int. J. Prod. Res. 32(9), 2149–2158 (1994)CrossRefzbMATHGoogle Scholar
  4. 4.
    Thawonmas, R., Ashida, T.: Evolution strategy for optimizing parameters in Ms Pac-Man controller ICE Pambush 3. In: IEEE Symposium on Computational Intelligence and Games, pp. 235–240 (2010)Google Scholar
  5. 5.
    Eberhart, R.C., Shi, Y.: Tracking and optimizing dynamic systems with particle swarms. In: IEEE Evolutionary Computation, pp. 94–100 (2001)Google Scholar
  6. 6.
    Wu, F., Mueller, L.A., Crouzillat, D., Pétiard, V., Tanksley, S.D.: Combining bioinformatics and phylogenetics to identify large sets of single-copy orthologous genes (COSII) for comparative, evolutionary and systematic studies: a test case in the euasterid plant clade. Genetics 174(3), 1407–1420 (2006)CrossRefGoogle Scholar
  7. 7.
    Huang, A.: Similarity measures for text document clustering. In: Proceedings of the sixth new zealand computer science research student conference (NZCSRSC2008), Christchurch, pp. 49–56 (2008)Google Scholar
  8. 8.
    Zha, H., He, X., Ding, C., Simon, H., Gu, M.: Bipartite graph partitioning and data clustering. In: Proceedings of the tenth international conference on Information and knowledge management, pp. 25–32 (2001)Google Scholar
  9. 9.
    Grygorash, O., Zhou, Y., Jorgensen, Z.: Minimum spanning tree based clustering algorithms. In: Tools with Artificial Intelligence, pp. 73–81 (2006)Google Scholar
  10. 10.
    Halim, Z., Kalsoom, R., Baig, A.R.: Profiling drivers based on driver dependent vehicle driving features. Appl. Intell. 44(3), 645–664 (2016)CrossRefGoogle Scholar
  11. 11.
    Hussain, S.F., Mushtaq, M., Halim, Z.: Multi-view document clustering via ensemble methods. J. Intell. Inf. Syst. 43(1), 81–99 (2014)CrossRefGoogle Scholar
  12. 12.
    Abraham, A., Guo, H., Liu, H.: Swarm intelligence: foundations, perspectives and applications. In: Swarm Intelligent Systems, pp. 3–25 (2006)Google Scholar
  13. 13.
    Pirim, H., Ekşioğlu, B., Perkins, A.D.: Clustering high throughput biological data with B-MST, a minimum spanning tree based heuristic. Comput. Biol. Med. 62, 94–102 (2015)CrossRefGoogle Scholar
  14. 14.
    Müller, A.C., Nowozin, S., Lampert, C.H.: Information theoretic clustering using minimum spanning trees. In: Joint DAGM (German Association for Pattern Recognition) and OAGM Symposium, pp. 205–215 (2012)Google Scholar
  15. 15.
    Zahn, C.T.: Graph theoretical methods for detecting and describing gestalt clusters. IEEE Trans. Comput. C–20(1), 68–86 (1971)CrossRefzbMATHGoogle Scholar
  16. 16.
    Xu, Y., Olman, V., Xu, D.: Clustering gene expression data using a graph-theriotic approach: an application of minimum spanning trees. Bioinformatics 18, 536–545 (2002)CrossRefGoogle Scholar
  17. 17.
    Gonzalez, R.C., Wintz, P.: Digital Image Processing. Addison-Wesley, Reading, MA (1987)zbMATHGoogle Scholar
  18. 18.
    Xu, Y., Olman, V., Uberbacher, E.C.: A segmentation algorithm for noisy images: design and evaluation. Pattern Recognit. Lett. 19, 1213–1224 (1998)CrossRefzbMATHGoogle Scholar
  19. 19.
    Zhong, C., Malinen, M., Miao, D., Fränti, P.: A fast minimum spanning tree algorithm based on K-means. Inf. Sci. 295, 1–17 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Zhou, R., Shu, L., Su, Y.: An adaptive minimum spanning tree test for detecting irregularly-shaped spatial clusters. Comput. Stat. Data Anal. 89, 134–146 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhou, Y., Grygorash, O., Hain, T.F.: Clustering with minimum spanning trees. Int. J. Artif. Intell. Tools 20(01), 139–177 (2011)CrossRefGoogle Scholar
  22. 22.
    Wang, X., Wang, X.L., Chen, C., Wilkes, D.M.: Enhancing minimum spanning tree-based clustering by removing density-based outliers. Digit. Signal Process. 23(5), 1523–1538 (2013)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Jothi, R., Mohanty, S.K., Ojha, A.: Fast minimum spanning tree based clustering algorithms on local neighborhood graph. In: International Workshop on Graph-Based Representations in Pattern Recognition, pp. 292–301 (2015)Google Scholar
  24. 24.
    Tzortzis, G., Likas, A.: The MinMax k-Means clustering algorithm. Pattern Recognit. 47(7), 2505–2516 (2014)CrossRefGoogle Scholar
  25. 25.
    Yu, M., Hillebrand, A., Tewarie, P., Meier, J., van Dijk, B., Van Mieghem, P., Stam, C.J.: Hierarchical clustering in minimum spanning trees. Chaos: an interdisciplinary. J. Nonlinear Sci. 25(2), 023107 (2015)Google Scholar
  26. 26.
    Huang, G., Dong, S., Ren, J.: A minimum spanning tree clustering algorithm based on density. Adv. Inf. Sci. Serv. Sci. 5(2), 44 (2013)Google Scholar
  27. 27.
    Zhong, C., Miao, D., Fränti, P.: Minimum spanning tree based split-and-merge: a hierarchical clustering method. Inf. Sci. 181(16), 3397–3410 (2011)CrossRefGoogle Scholar
  28. 28.
    Abraham, A., Nedjah, N., Mourelle, L.: Evolutionary computation: from genetic algorithms to genetic programming. In: Genetic Systems Programming, pp. 1–20 (2006)Google Scholar
  29. 29.
    Halim, Z., Waqas, M., Hussain, S.F.: Clustering large probabilistic graphs using multi-population evolutionary algorithm. Inf. Sci. 317, 78–95 (2015)CrossRefGoogle Scholar
  30. 30.
    Csardi, G., Nepusz, T.: The igraph software package for complex network research. InterJournal Complex Syst. 1695(5), 1–9 (2006)Google Scholar
  31. 31.
    Bandyopadhyay, S., Mukhopadhyay, A., Maulik, U.: An improved algorithm for clustering gene expression data. Bioinformatics 23(21), 2859–2865 (2007)CrossRefGoogle Scholar
  32. 32.
    Rendón, E., Abundez, I., Arizmendi, A., Quiroz, E.: Internal versus external cluster validation indexes. Int. J. Comput. Commun. 5(1), 27–34 (2011)Google Scholar
  33. 33.
    Iwata, T., Lloyd, J.R., Ghahramani, Z.: Unsupervised many-to-many object matching for relational data. IEEE Trans. Pattern Anal. Mach. Intell. 38(3), 607–617 (2016)CrossRefGoogle Scholar
  34. 34.
    Halim, Z., Muhammad, T.: Quantifying and optimizing visualization: an evolutionary computing-based approach. Inf. Sci. 385, 284–313 (2017)CrossRefGoogle Scholar
  35. 35.
    Muhammad, T., Halim, Z.: Employing artificial neural networks for constructing metadata-based model to automatically select an appropriate data visualization technique. Appl. Soft Comput. 49, 365–384 (2016)CrossRefGoogle Scholar
  36. 36.
    Leskovec, J., Mcauley, J.J.: Learning to discover social circles in ego networks. Adv. Neural Inf. Process. Syst. 25, 539–547 (2012)Google Scholar
  37. 37.
    Mcauley, J.J., Leskovec, J.: Discovering social circles in ego networks. ACM Trans. Knowl. Discov. Data 8(1), 4 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Faculty of Computer Science and EngineeringGhulam Ishaq Khan Institute of Engineering Sciences and TechnologyTopiPakistan

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