Abstract
The two classes of agglomerative hierarchical clustering algorithms and K-means algorithms are overviewed. Moreover recent topics of kernel functions and semi-supervised clustering in the two classes are discussed. This paper reviews traditional methods as well as new techniques.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akaike, H.: A Bayesian Analysis of the Minimum AIC Procedure. Annals of the Institute of Statistical Mathematics 30(1), 9–14 (1978)
Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, New York (1973)
Basu, S., Bilenko, M., Mooney, R.J.: A Probabilistic Framework for Semi-Supervised Clustering. In: Proc. of the Tenth ACM SIGKDD (KDD 2004), pp. 59–68 (2004)
Basu, S., Banerjee, A., Mooney, R.J.: Active Semi-Supervision for Pairwise Constrained Clustering. In: Proc. of the SIAM International Conference on Data Mining (SDM 2004), pp. 333–344 (2004)
Basu, S., Davidson, I., Wagstaff, K.L. (eds.): Constrained Clustering: Advances in Algorithms, Theory, and Applications. Chapman & Hall/CRC, Boca Raton (2009)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press (1981)
Bezdek, J.C., Keller, J., Krishnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer, Boston (1999)
Bouchachia, A., Pedrycz, W.: A Semi-supervised Clustering Algorithm for Data Exploration. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS (LNAI), vol. 2715, pp. 328–337. Springer, Heidelberg (2003)
Chapelle, O., Schölkopf, B., Zien, A. (eds.): Semi-Supervised Learning. MIT Press, Cambridge (2006)
Davé, R.N., Krishnapuram, R.: Robust Clustering Methods: A Unified View. IEEE Trans. on Fuzzy Systems 5(2), 270–293 (1997)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. J. R. Stat. Soc. B39, 1–38 (1977)
Dumitrescu, D., Lazzerini, B., Jain, L.C.: Fuzzy Sets and Their Application to Clustering and Training. CRC Press, Boca Raton (2000)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley & Sons (1973)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley, New York (2001)
Dunn, J.C.: A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-separated Clusters. J. of Cybernetics 3, 32–57 (1974)
Dunn, J.C.: Well-separated Clusters and Optimal Fuzzy Partitions. J. of Cybernetics 4, 95–104 (1974)
Endo, Y., Haruyama, H., Okubo, T.: On Some Hierarchical Clustering Algorithms Using Kernel Functions. In: Proc. of FUZZ-IEEE 2004, CD-ROM Proc., Budapest, Hungary, July 25-29, pp. 1–6 (2004)
Everitt, B.S.: Cluster Analysis, 3rd edn. Arnold, London (1993)
Girolami, M.: Mercer Kernel Based Clustering in Feature Space. IEEE Trans. on Neural Networks 13(3), 780–784 (2002)
Hashimoto, W., Nakamura, T., Miyamoto, S.: Comparison and Evaluation of Different Cluster Validity Measures Including Their Kernelization. Journal of Advanced Computational Intelligence and Intelligent Informatics 13(3), 204–209 (2009)
Hathaway, R.J., Bezdek, J.C.: Switching Regression Models and Fuzzy Clustering. IEEE Trans. on Fuzzy Systems 1, 195–204 (1993)
Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. Wiley, Chichester (1999)
Hwang, J., Miyamoto, S.: Kernel Functions Derived from Fuzzy Clustering and Their Application to Kernel Fuzzy c-Means. Journal of Advanced Computational Intelligence and Intelligent Informatics 15(1), 90–94 (2011)
Ichihashi, H., Honda, K., Tani, N.: Gaussian Mixture PDF Approximation and Fuzzy c-Means Clustering with Entropy Regularization. In: Proc. of Fourth Asian Fuzzy Systems Symposium, vol. 1, pp. 217–221 (2000)
Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)
Klein, D., Kamvar, S.D., Manning, C.: From Instance-level Constraints to Space-level Constraints: Making the Most of Prior Knowledge in Data Clustering. In: Proc. of the Intern. Conf. on Machine Learning, Sydney, Australia, pp. 307–314 (2002)
Kohonen, T.: Self-Organizing Maps, 2nd edn. Springer, Berlin (1997)
Krishnapuram, R., Keller, J.M.: A Possibilistic Approach to Clustering. IEEE Trans. on Fuzzy Systems 1, 98–110 (1993)
Kulis, B., Basu, S., Dhillon, I., Mooney, R.: Semi-supervised Graph Clustering: A Kernel Approach. Mach. Learn. 74, 1–22 (2009)
Li, R.P., Mukaidono, M.: A Maximum Entropy Approach to Fuzzy Clustering. In: Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems (FUZZ-IEEE/IFES 1995), Yokohama, Japan, March 20-24, pp. 2227–2232 (1995)
Li, R.P., Mukaidono, M.: Gaussian Clustering Method Based on Maximum-fuzzy-entropy Interpretation. Fuzzy Sets and Systems 102, 253–258 (1999)
MacQueen, J.B.: Some Methods of Classification and Analysis of Multivariate Observations. In: Proc. of 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281–297 (1967)
McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, New York (2000)
Miyamoto, S.: Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer, Dordrecht (1990)
Miyamoto, S., Mukaidono, M.: Fuzzy c-means as a Regularization and Maximum Entropy Approach. In: Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA 1997), Prague, Czech, June 25-30, vol. II, pp. 86–92 (1997)
Miyamoto, S.: Introduction to Cluster Analysis, Morikita-Shuppan, Tokyo (1999) (in Japanese)
Miyamoto, S., Nakayama, Y.: Algorithms of Hard c-means Clustering Using Kernel Functions in Support Vector Machines. Journal of Advanced Computational Intelligence and Intelligent Informatics 7(1), 19–24 (2003)
Miyamoto, S., Suizu, D.: Fuzzy c-means Clustering Using Kernel Functions in Support Vector Machines. Journal of Advanced Computational Intelligence and Intelligent Informatics 7(1), 25–30 (2003)
Miyamoto, S., Suizu, D., Takata, O.: Methods of Fuzzy c-means and Possibilistic Clustering Using a Quadratic Term. Scientiae Mathematicae Japonicae 60(2), 217–233 (2004)
Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Springer, Heidelberg (2008)
Miyamoto, S., Terami, A.: Semi-Supervised Agglomerative Hierarchical Clustering Algorithms with Pairwise Constraints. In: Proc. of WCCI 2010 IEEE World Congress on Computational Intelligence, CCIB, Barcelona, Spain, July 18-23, pp. 2796–2801 (2010)
Miyamoto, S., Terami, A.: Constrained Agglomerative Hierarchical Clustering Algorithms with Penalties. In: Proc. of 2011 IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, June 27-30, pp. 422–427 (2011)
Redner, R.A., Walker, H.F.: Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review 26(2), 195–239 (1984)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press (2002)
Schönberg, I.J.: Metric Spaces and Completely Monotone Functions. Annals of Mathematics 39(4), 811–841 (1938)
Shental, N., Bar-Hillel, A., Hertz, T., Weinshall, D.: Computing Gaussian Mixture Models with EM Using Equivalence Constraints. In: Advances in Neural Information Processing Systems, vol. 16 (2004)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
Vapnik, V.N.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (2000)
Vapnik, V.N.: Transductive Inference and Semi-supervised Learning. In: Chapelle, O., et al. (eds.) Semi-Supervised Learning, pp. 453–472. MIT Press, Cambridge (2006)
Wagstaff, K., Cardie, C., Rogers, S., Schroedl, S.: Constrained K-means Clustering with Background Knowledge. In: Proc. of the 9th ICML, pp. 577–584 (2001)
Wang, N., Li, X., Luo, X.: Semi-supervised Kernel-based Fuzzy c-Means with Pairwise Constraints. In: Proc. of WCCI 2008, pp. 1099–1103 (2008)
Zhu, X., Goldberg, A.B.: Introduction to Semi-Supervised Learning. Morgan and Claypool (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Miyamoto, S. (2011). Two Classes of Algorithms for Data Clustering. In: Tang, Y., Huynh, VN., Lawry, J. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2011. Lecture Notes in Computer Science(), vol 7027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24918-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-24918-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24917-4
Online ISBN: 978-3-642-24918-1
eBook Packages: Computer ScienceComputer Science (R0)