A survey of Clustering Algorithms

  • Lior RokachEmail author


This chapter presents a tutorial overview of the main clustering methods used in Data Mining. The goal is to provide a self-contained review of the concepts and the mathematics underlying clustering techniques. The chapter begins by providing measures and criteria that are used for determining whether two objects are similar or dissimilar. Then the clustering methods are presented, divided into: hierarchical, partitioning, density-based, model-based, grid-based, and soft-computing methods. Following the methods, the challenges of performing clustering in large data sets are discussed. Finally, the chapter presents how to determine the number of clusters.

Key words

Clustering K-means Intra-cluster homogeneity Inter-cluster separability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Al-Sultan K. S., A tabu search approach to the clustering problem, Pattern Recognition, 28:1443-1451,1995.CrossRefGoogle Scholar
  2. Al-Sultan K. S. , Khan M. M. : Computational experience on four algorithms for the hard clustering problem. Pattern Recognition Letters 17(3): 295-308, 1996.CrossRefGoogle Scholar
  3. Arbel, R. and Rokach, L., Classifier evaluation under limited resources, Pattern Recognition Letters, 27(14): 1619–1631, 2006, Elsevier.CrossRefGoogle Scholar
  4. Averbuch, M. and Karson, T. and Ben-Ami, B. and Maimon, O. and Rokach, L., Contextsensitive medical information retrieval, The 11th World Congress on Medical Informatics (MEDINFO 2004), San Francisco, CA, September 2004, IOS Press, pp. 282–286.Google Scholar
  5. Banfield J. D. and Raftery A. E. Model-based Gaussian and non-Gaussian clustering. Biometrics, 49:803-821, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  6. Bentley J. L. and Friedman J. H., Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27(2):97-105, February 1978. 275CrossRefGoogle Scholar
  7. Bonner, R., On Some Clustering Techniques. IBM journal of research and development, 8:22-32, 1964.zbMATHCrossRefGoogle Scholar
  8. Can F. , Incremental clustering for dynamic information processing, in ACM Transactions on Information Systems, no. 11, pp 143-164, 1993.CrossRefGoogle Scholar
  9. Cheeseman P., Stutz J.: Bayesian Classification (AutoClass): Theory and Results. Advances in Knowledge Discovery and Data Mining 1996: 153-180Google Scholar
  10. Cohen S., Rokach L., Maimon O., Decision Tree Instance Space Decomposition with Grouped Gain-Ratio, Information Science, Volume 177, Issue 17, pp. 3592-3612, 2007.CrossRefGoogle Scholar
  11. Dhillon I. and Modha D., Concept Decomposition for Large Sparse Text Data Using Clustering. Machine Learning. 42, pp.143-175. (2001).zbMATHCrossRefGoogle Scholar
  12. Dempster A.P., Laird N.M., and Rubin D.B., Maximum likelihood from incomplete data using the EM algorithm. Journal of the Royal Statistical Society, 39(B), 1977.Google Scholar
  13. Duda, P. E. Hart and D. G. Stork, Pattern Classification, Wiley, New York, 2001.zbMATHGoogle Scholar
  14. Ester M., Kriegel H.P., Sander S., and Xu X., A density-based algorithm for discovering clusters in large spatial databases with noise. In E. Simoudis, J. Han, and U. Fayyad, editors, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), pages 226-231, Menlo Park, CA, 1996. AAAI, AAAI Press.Google Scholar
  15. Estivill-Castro, V. and Yang, J. A Fast and robust general purpose clustering algorithm. Pacific Rim International Conference on Artificial Intelligence, pp. 208-218, 2000.Google Scholar
  16. Fraley C. and Raftery A.E., “How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis”, Technical Report No. 329. Department of Statistics University of Washington, 1998.Google Scholar
  17. Fisher, D., 1987, Knowledge acquisition via incremental conceptual clustering, in machine learning 2, pp. 139-172.Google Scholar
  18. Fortier, J.J. and Solomon, H. 1996. Clustering procedures. In proceedings of the Multivariate Analysis, ’66, P.R. Krishnaiah (Ed.), pp. 493-506.Google Scholar
  19. Gluck, M. and Corter, J., 1985. Information, uncertainty, and the utility of categories. Proceedings of the Seventh Annual Conference of the Cognitive Science Society (pp. 283- 287). Irvine, California: Lawrence Erlbaum Associates.Google Scholar
  20. Guha, S., Rastogi, R. and Shim, K. CURE: An efficient clustering algorithm for large databases. In Proceedings of ACM SIGMOD International Conference on Management of Data, pages 73-84, New York, 1998.Google Scholar
  21. Han, J. and Kamber, M. Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, 2001.Google Scholar
  22. Hartigan, J. A. Clustering algorithms. John Wiley and Sons., 1975.Google Scholar
  23. Huang, Z., Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Mining and Knowledge Discovery, 2(3), 1998.Google Scholar
  24. Hoppner F. , Klawonn F., Kruse R., Runkler T., Fuzzy Cluster Analysis, Wiley, 2000.Google Scholar
  25. Hubert, L. and Arabie, P., 1985 Comparing partitions. Journal of Classification, 5. 193-218.CrossRefGoogle Scholar
  26. Jain, A.K. Murty, M.N. and Flynn, P.J. Data Clustering: A Survey. ACM Computing Surveys, Vol. 31, No. 3, September 1999.Google Scholar
  27. Kaufman, L. and Rousseeuw, P.J., 1987, Clustering by Means of Medoids, In Y. Dodge, editor, Statistical Data Analysis, based on the L1 Norm, pp. 405-416, Elsevier/North Holland, Amsterdam.Google Scholar
  28. Kim, D.J., Park, Y.W. and Park,. A novel validity index for determination of the optimal number of clusters. IEICE Trans. Inf., Vol. E84-D, no.2, 2001, 281-285.Google Scholar
  29. King, B. Step-wise Clustering Procedures, J. Am. Stat. Assoc. 69, pp. 86-101, 1967.CrossRefGoogle Scholar
  30. Larsen, B. and Aone, C. 1999. Fast and effective text mining using linear-time document clustering. In Proceedings of the 5th ACM SIGKDD, 16-22, San Diego, CA.Google Scholar
  31. Maimon O., and Rokach, L. Data Mining by Attribute Decomposition with semiconductors manufacturing case study, in Data Mining for Design and Manufacturing: Methods and Applications, D. Braha (ed.), Kluwer Academic Publishers, pp. 311–336, 2001.Google Scholar
  32. Maimon O. and Rokach L., “Improving supervised learning by feature decomposition”, Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems, Lecture Notes in Computer Science, Springer, pp. 178-196, 2002.Google Scholar
  33. Maimon, O. and Rokach, L., Decomposition Methodology for Knowledge Discovery and Data Mining: Theory and Applications, Series in Machine Perception and Artificial Intelligence - Vol. 61, World Scientific Publishing, ISBN:981-256-079-3, 2005.Google Scholar
  34. Marcotorchino, J.F. and Michaud, P. Optimisation en Analyse Ordinale des Donns. Masson, Paris.Google Scholar
  35. Mishra, S. K. and Raghavan, V. V., An empirical study of the performance of heuristic methods for clustering. In Pattern Recognition in Practice, E. S. Gelsema and L. N. Kanal, Eds. 425436, 1994.Google Scholar
  36. Moskovitch R, Elovici Y, Rokach L, Detection of unknown computer worms based on behavioral classification of the host, Computational Statistics and Data Analysis, 52(9):4544– 4566, 2008.zbMATHCrossRefMathSciNetGoogle Scholar
  37. Murtagh, F. A survey of recent advances in hierarchical clustering algorithms which use cluster centers. Comput. J. 26 354-359, 1984.Google Scholar
  38. Ng, R. and Han, J. 1994. Very large data bases. In Proceedings of the 20th International Conference on Very Large Data Bases (VLDB94, Santiago, Chile, Sept.), VLDB Endowment, Berkeley, CA, 144155.Google Scholar
  39. Rand,W. M., Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66: 846–850, 1971.CrossRefGoogle Scholar
  40. Ray, S., and Turi, R.H. Determination of Number of Clusters in K-Means Clustering and Application in Color Image Segmentation. Monash university, 1999.Google Scholar
  41. Rokach, L., Decomposition methodology for classification tasks: a meta decomposer framework, Pattern Analysis and Applications, 9(2006):257–271.CrossRefMathSciNetGoogle Scholar
  42. Rokach L., Genetic algorithm-based feature set partitioning for classification problems, Pattern Recognition, 41(5):1676–1700, 2008.zbMATHCrossRefGoogle Scholar
  43. Rokach L., Mining manufacturing data using genetic algorithm-based feature set decomposition, Int. J. Intelligent Systems Technologies and Applications, 4(1):57-78, 2008.CrossRefGoogle Scholar
  44. Rokach, L. and Maimon, O., Theory and applications of attribute decomposition, IEEE International Conference on Data Mining, IEEE Computer Society Press, pp. 473–480, 2001.Google Scholar
  45. Rokach L. and Maimon O., Feature Set Decomposition for Decision Trees, Journal of Intelligent Data Analysis, Volume 9, Number 2, 2005b, pp 131–158.Google Scholar
  46. Rokach, L. and Maimon, O., Clustering methods, Data Mining and Knowledge Discovery Handbook, pp. 321–352, 2005, Springer.Google Scholar
  47. Rokach, L. and Maimon, O., Data mining for improving the quality of manufacturing: a feature set decomposition approach, Journal of Intelligent Manufacturing, 17(3):285– 299, 2006, Springer.CrossRefGoogle Scholar
  48. Rokach, L., Maimon, O., Data Mining with Decision Trees: Theory and Applications,World Scientific Publishing, 2008.Google Scholar
  49. Rokach L., Maimon O. and Lavi I., Space Decomposition In Data Mining: A Clustering Approach, Proceedings of the 14th International Symposium On Methodologies For Intelligent Systems, Maebashi, Japan, Lecture Notes in Computer Science, Springer-Verlag, 2003, pp. 24–31.Google Scholar
  50. Rokach, L. and Maimon, O. and Averbuch, M., Information Retrieval System for Medical Narrative Reports, Lecture Notes in Artificial intelligence 3055, page 217-228 Springer- Verlag, 2004.Google Scholar
  51. Rokach, L. and Maimon, O. and Arbel, R., Selective voting-getting more for less in sensor fusion, International Journal of Pattern Recognition and Artificial Intelligence 20 (3) (2006), pp. 329–350.CrossRefGoogle Scholar
  52. Selim, S.Z., and Ismail, M.A. K-means-type algorithms: a generalized convergence theorem and characterization of local optimality. In IEEE transactions on pattern analysis and machine learning, vol. PAMI-6, no. 1, January, 1984.Google Scholar
  53. Selim, S. Z. AND Al-Sultan, K. 1991. A simulated annealing algorithm for the clustering problem. Pattern Recogn. 24, 10 (1991), 10031008.CrossRefMathSciNetGoogle Scholar
  54. Sneath, P., and Sokal, R. Numerical Taxonomy.W.H. Freeman Co., San Francisco, CA, 1973.Google Scholar
  55. Strehl A. and Ghosh J., Clustering Guidance and Quality Evaluation Using Relationship-based Visualization, Proceedings of Intelligent Engineering Systems Through Artificial Neural Networks, 2000, St. Louis, Missouri, USA, pp 483-488.Google Scholar
  56. Strehl, A., Ghosh, J., Mooney, R.: Impact of similarity measures on web-page clustering. In Proc. AAAI Workshop on AI for Web Search, pp 58–64, 2000.Google Scholar
  57. Tibshirani, R.,Walther, G. and Hastie, T., 2000. Estimating the number of clusters in a dataset via the gap statistic. Tech. Rep. 208, Dept. of Statistics, Stanford University.Google Scholar
  58. Tyron R. C. and Bailey D.E. Cluster Analysis. McGraw-Hill, 1970.Google Scholar
  59. Urquhart, R. Graph-theoretical clustering, based on limited neighborhood sets. Pattern recognition, vol. 15, pp. 173-187, 1982.zbMATHCrossRefGoogle Scholar
  60. Veyssieres, M.P. and Plant, R.E. Identification of vegetation state and transition domains in California’s hardwood rangelands. University of California, 1998.Google Scholar
  61. Wallace C. S. and Dowe D. L., Intrinsic classification by mml – the snob program. In Proceedings of the 7th Australian Joint Conference on Artificial Intelligence, pages 37-44, 1994.Google Scholar
  62. Wang, X. and Yu, Q. Estimate the number of clusters in web documents via gap statistic. May 2001.Google Scholar
  63. Ward, J. H. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58:236-244, 1963.CrossRefMathSciNetGoogle Scholar
  64. Zahn, C. T., Graph-theoretical methods for detecting and describing gestalt clusters. IEEE trans. Comput. C-20 (Apr.), 68-86, 1971.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Information Systems EngineeringBen-Gurion University of the NegevBeer-ShebaIsrael

Personalised recommendations