Summary
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Al-Sultan K. S., A tabu search approach to the clustering problem, Pattern Recognition, 28:1443-1451,1995.
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.
Arbel, R. and Rokach, L., Classifier evaluation under limited resources, Pattern Recognition Letters, 27(14): 1619–1631, 2006, Elsevier.
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.
Banfield J. D. and Raftery A. E. Model-based Gaussian and non-Gaussian clustering. Biometrics, 49:803-821, 1993.
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. 275
Bonner, R., On Some Clustering Techniques. IBM journal of research and development, 8:22-32, 1964.
Can F. , Incremental clustering for dynamic information processing, in ACM Transactions on Information Systems, no. 11, pp 143-164, 1993.
Cheeseman P., Stutz J.: Bayesian Classification (AutoClass): Theory and Results. Advances in Knowledge Discovery and Data Mining 1996: 153-180
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.
Dhillon I. and Modha D., Concept Decomposition for Large Sparse Text Data Using Clustering. Machine Learning. 42, pp.143-175. (2001).
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.
Duda, P. E. Hart and D. G. Stork, Pattern Classification, Wiley, New York, 2001.
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.
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.
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.
Fisher, D., 1987, Knowledge acquisition via incremental conceptual clustering, in machine learning 2, pp. 139-172.
Fortier, J.J. and Solomon, H. 1996. Clustering procedures. In proceedings of the Multivariate Analysis, ’66, P.R. Krishnaiah (Ed.), pp. 493-506.
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.
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.
Han, J. and Kamber, M. Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, 2001.
Hartigan, J. A. Clustering algorithms. John Wiley and Sons., 1975.
Huang, Z., Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Mining and Knowledge Discovery, 2(3), 1998.
Hoppner F. , Klawonn F., Kruse R., Runkler T., Fuzzy Cluster Analysis, Wiley, 2000.
Hubert, L. and Arabie, P., 1985 Comparing partitions. Journal of Classification, 5. 193-218.
Jain, A.K. Murty, M.N. and Flynn, P.J. Data Clustering: A Survey. ACM Computing Surveys, Vol. 31, No. 3, September 1999.
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.
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.
King, B. Step-wise Clustering Procedures, J. Am. Stat. Assoc. 69, pp. 86-101, 1967.
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.
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.
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.
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.
Marcotorchino, J.F. and Michaud, P. Optimisation en Analyse Ordinale des Donns. Masson, Paris.
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.
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.
Murtagh, F. A survey of recent advances in hierarchical clustering algorithms which use cluster centers. Comput. J. 26 354-359, 1984.
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.
Rand,W. M., Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66: 846–850, 1971.
Ray, S., and Turi, R.H. Determination of Number of Clusters in K-Means Clustering and Application in Color Image Segmentation. Monash university, 1999.
Rokach, L., Decomposition methodology for classification tasks: a meta decomposer framework, Pattern Analysis and Applications, 9(2006):257–271.
Rokach L., Genetic algorithm-based feature set partitioning for classification problems, Pattern Recognition, 41(5):1676–1700, 2008.
Rokach L., Mining manufacturing data using genetic algorithm-based feature set decomposition, Int. J. Intelligent Systems Technologies and Applications, 4(1):57-78, 2008.
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.
Rokach L. and Maimon O., Feature Set Decomposition for Decision Trees, Journal of Intelligent Data Analysis, Volume 9, Number 2, 2005b, pp 131–158.
Rokach, L. and Maimon, O., Clustering methods, Data Mining and Knowledge Discovery Handbook, pp. 321–352, 2005, Springer.
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.
Rokach, L., Maimon, O., Data Mining with Decision Trees: Theory and Applications,World Scientific Publishing, 2008.
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.
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.
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.
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.
Selim, S. Z. AND Al-Sultan, K. 1991. A simulated annealing algorithm for the clustering problem. Pattern Recogn. 24, 10 (1991), 10031008.
Sneath, P., and Sokal, R. Numerical Taxonomy.W.H. Freeman Co., San Francisco, CA, 1973.
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.
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.
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.
Tyron R. C. and Bailey D.E. Cluster Analysis. McGraw-Hill, 1970.
Urquhart, R. Graph-theoretical clustering, based on limited neighborhood sets. Pattern recognition, vol. 15, pp. 173-187, 1982.
Veyssieres, M.P. and Plant, R.E. Identification of vegetation state and transition domains in California’s hardwood rangelands. University of California, 1998.
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.
Wang, X. and Yu, Q. Estimate the number of clusters in web documents via gap statistic. May 2001.
Ward, J. H. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58:236-244, 1963.
Zahn, C. T., Graph-theoretical methods for detecting and describing gestalt clusters. IEEE trans. Comput. C-20 (Apr.), 68-86, 1971.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Rokach, L. (2009). A survey of Clustering Algorithms. In: Maimon, O., Rokach, L. (eds) Data Mining and Knowledge Discovery Handbook. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09823-4_14
Download citation
DOI: https://doi.org/10.1007/978-0-387-09823-4_14
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-09822-7
Online ISBN: 978-0-387-09823-4
eBook Packages: Computer ScienceComputer Science (R0)