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Towards Hierarchical Clustering (Extended Abstract)

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Book cover Computer Science – Theory and Applications (CSR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4649))

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Abstract

In the paper, new modified agglomerative algorithms for hierarchical clustering are suggested. The clustering process is targeted to generating a cluster hierarchy which can contain the same items in different clusters. The algorithms are based on the following additional operations: (i) building an ordinal item pair proximity (’distance’) including the usage of multicriteria approaches; (ii) integration of several item pair at each stage of the algorithms; and (iii) inclusion of the same items into different integrated item pairs/clusters. The suggested modifications above are significant from the viewpoints of practice, e.g., design of systems architecture for engineering and computer systems.

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References

  1. Agrawal, P.K., Procopiuc, C.M.: Exact and approximation algorithms for clustering. Algorithmica 33, 201–226 (2002)

    Article  MathSciNet  Google Scholar 

  2. Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, New York (1973)

    MATH  Google Scholar 

  3. Andersen, R., Chung, F., Lang, K.: Local graph partitioning using pagerank vector. In: 47th Annual IEEE Symp. on Foundations of Compter Science FOCS 2006, Berkeley, CA, pp. 475–486 (2006)

    Google Scholar 

  4. Arabie, P., Hubert, L.J., De Soete, G. (eds.): Clustering and Classification. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  5. Augustson, J.G., Minker, J.: Analysis of some graph-theoretical cluster techniques. J. of the ACM 17(4), 575–588 (1970)

    Article  Google Scholar 

  6. Babu, G.P., Murty, M.N.: Clustering with evolution styrategies. Pattern Recognition 27(2), 321–329 (1994)

    Article  Google Scholar 

  7. Bandyopadhyay, S., Coyle, E.J.: An energy efficient hierarchical clustering algorithm for wireless sensor network. In: INFOCOM 2006 (2006)

    Google Scholar 

  8. Biswas, G., Weinberg, J., Li, C.: Conceptual Clustering Method for Knowledge Discovery in Databases. Editions Technip. (1995)

    Google Scholar 

  9. Bournaud, I., Ganascia, J.-G.: Conceptual clustering of complex objects: A generalization space based approach. In: Ellis, G., Rich, W., Levinson, R., Sowa, J.F. (eds.) ICCS 1995. LNCS, vol. 954, pp. 173–187. Springer, Heidelberg (1995)

    Google Scholar 

  10. Capoyleas, V., Rote, G., Woeginger, G.: Geometric clustering. J. of Algorithms 12, 341–356 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Castro, R.M., Coates, M.J., Nowak, R.D.: Likelihood based hierarchical clustering. IEEE Trans. on Signal Processing 52(8), 2308–2321 (2004)

    Article  MathSciNet  Google Scholar 

  12. Chatterjee, M., Das, S.K., Turgut, D.: WCA: a weghted clustering algorithm for mobile Ad Hoc networks. Cluster Computing 5, 193–204 (2002)

    Article  Google Scholar 

  13. Chen, Y.: Multiple Criteria Decision Analysis: Classification Problems and Solutions. PhD Thesis, University of Waterloo, Ontarion (2006)

    Google Scholar 

  14. Cheng, Y., Fu, K.S.: Conceptual clustering in knowledge organization. IEEE Trans. PAMI 7, 592–598 (1985)

    Google Scholar 

  15. Cheng, C.H.: A branch and bound custering algorithm. IEEE Trans. SMC 25, 895–898 (1995)

    Google Scholar 

  16. Du, Q., Faber, V., Gunzburger, M.: Centroidal Voronoi tesselations: applications and algoithms. SIAM Rev. 41, 637–676 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Estvill-Castro, V., Murray, A.T.: Spatial clustering for data mining with genetic algorithms, Technical Report, Queensland Univ. of Technology, Australia (1997)

    Google Scholar 

  18. Garay, G., Chaudhuri, B.B.: A novel genetic algorithm for automatic clustering. Pattern Recognition 25(2), 173–187 (2004)

    Article  Google Scholar 

  19. Garey, M.R., Johnson, D.S.: Computers and Intractability. The Guide to the Theory of NP-Completeness. W.H.Freeman and Company, San Francisco (1979)

    Google Scholar 

  20. Genkin, A.V., Muchnik, I.B.: Fixed points approach to clustering. J. of Clustering 10, 219–240 (1993)

    MATH  MathSciNet  Google Scholar 

  21. Gonzalez, T.: Clustering to minimize the maximum intercluster distance. Theoret. Comput. Sci. 38, 293–306 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  22. Gordon, A.D.: Classification, 2nd edn. Chapman&Hall/CRC (1999)

    Google Scholar 

  23. Guha, S., Rastogi, R., Shim, K.: ROCK: a robust clustering algorihtm for categorial atributes. Information Systems 25(5), 345–366 (2000)

    Article  Google Scholar 

  24. Fasulo, D.: An Analysis of Recent Work on Clustering Algorithms. Technical Report # 01-03-02, Univ. of Washington (2001)

    Google Scholar 

  25. Fraley, C.: Algorithms for model-based Gaussian hierarchical clustering. SIAM J. on Scientific Computing 20(1), 270–281 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  26. Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniqes. J. of Intelligent Information Systems 17(2-3), 107–145 (2004)

    Google Scholar 

  27. Hartigan, J.A.: Clustering Algorithms. Wiley, New York (1975)

    MATH  Google Scholar 

  28. Hoppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. Wiley, New York (1999)

    Google Scholar 

  29. Hubert, L.J.: Some applications of graph theory to clustering. Psychomerica 39, 283–309 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  30. Jain, A.K., Dubes, R.C.: Algorithms for Custering Data. Prentice Hall, Englewood Cliffs, NJ (1988)

    Google Scholar 

  31. Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Computing Surveys 31(3), 264–323 (1999)

    Article  Google Scholar 

  32. Jonyer, I., Cook, D.J., Holder, L.B.: Discovery and evaluation of graph-based hierarchical conceptual clustering. J. of Machine Learning Research 2, 19–43 (2001)

    Article  Google Scholar 

  33. Jajuqa, K., Sokolovski, A., Bock, H.-H. (eds.): Classification, Clustering and Data Analysis. Recent Advances and Applications. Springer, Heidelberg (2002)

    Google Scholar 

  34. Jardine, N., Sibson, R.: Mathematical Taxonomy. Wiley, London (1971)

    MATH  Google Scholar 

  35. Johnson, S.C.: Hierarchical clustering schemes. Psychometrika 2, 241–254 (1967)

    Article  Google Scholar 

  36. Jones, D., Beltramo, M.A.: Solving partitioning problems with genetic algorithms. In: Proc. of 4th Int. Conf. on Genetic Algorithms, pp. 442–449 (1991)

    Google Scholar 

  37. Kanungo, T., Mount, D.M., Natanyahu, N.S., Piatko, C.D., Silverman, R., Wu, A.Y.: An efficient k-means clustering algorithm: analysis and implementation. IEEE Trans. PAMI 24(7), 881–892 (2002)

    Google Scholar 

  38. Karypis, G., Han, E., Kuma, V.: Chameleon: hierarchical clustering using dynamic modeling. IEEE Computer 32, 68–75 (1999)

    Google Scholar 

  39. Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduciton to Cluster Analysis. John Wiley & Sons, New York (1990)

    Google Scholar 

  40. Kivijarvi, J., Franti, P., Nevalainen, O.: Self-adaptive genetic algorithm for clustering. J. of Heuristics 9(2), 113–129 (2003)

    Article  Google Scholar 

  41. Levin, M.Sh.: Course ’Design of Systems: structural approach (2004...2007), http://www.iitp.ru/mslevin/SYSD.HTM

  42. Levin, M.Sh.: Course ’System design: structural approach. In: DTM 2006. 18th Int. Conf. Design Methodology and Theory, DETC2006-99547 (2006)

    Google Scholar 

  43. Markov, Z.: A lattice-based approach to hierarchical clustering. In: Proc. of the Florida Artificial Intelligence Research Symposium, pp. 389–393 (2001)

    Google Scholar 

  44. Maulik, U., Bandyopadhyay, S.: Genetic algorithm-based clusterign technique. Pattern Recognition 33, 1445–1465 (2000)

    Article  Google Scholar 

  45. Michalski, R.S., Stepp, R.: Revealing conceptual structure in data by inductive inference. In: Hayes, J.E., Michie, D., Pao, Y.-H. (eds.) Machine Intelligence 10, pp. 173–196. Wiley, New York (1982)

    Google Scholar 

  46. Michalski, R.S., Stepp, R.: Learning from observation. In: Michalski, R.S., carbonell, J.C., Mitchell, T.M. (eds.) Machine Learning: An Artificial Intelligence Approach, Palo Alto, CA, Tioga, pp. 163–190 (1983)

    Google Scholar 

  47. Mirkin, B.: Approximation clustering: a mine of semidefinite programming problems. In: Pardalos, P., WOlkowich, H. (eds.) Topics in Semidefinite and Interior Point Methods. Fields Institute Communication Series, pp. 167–180. AMS, Providence (1997)

    Google Scholar 

  48. Mirkin, B., Muchnik, I.: Combinatorial optimization in clustering. In: Du, D.-Z., Pardalos, P. (eds.) Handbook on Combinatorial Optimization, vol. 2, pp. 261–329. Kluwer, Boston, MA (1998)

    Google Scholar 

  49. Mirkin, B.G.: Clustering for Data Mining: A Data Recovery Approach. Chapman & Hall / CRC (2005)

    Google Scholar 

  50. Murtagh, F.: A survey of recent advances in hierarchical clustering algorithms. The Computer Journal 26, 354–359 (1993)

    Google Scholar 

  51. Pal, N.R., Bezdek, J.C., Tsao, E.C.-J.: Generalized clsutering networks are Kohonen’s self-organizing scheme. IEEE Trans. Neural Networks 4, 549–557 (1993)

    Article  Google Scholar 

  52. Pareto, V.: Manual of Political Economy. Reprint ed., New York (1971)

    Google Scholar 

  53. Pavan, M., Pellilo, M.: Dominant sets and pairwise clustering. IEEE Trans. on PAMI 29(1), 167–172 (2007)

    Google Scholar 

  54. Ramanathan, K., Guan, S.U.: Clustering and combinatorial optimization in recursive supervised learning. J. of Combinatorial Optimization 13(2), 137–152 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  55. Rasmussen, E.: Clustering algorithm. In: Information Retrieval, Printice Hall, Englewood Cliffs (1992)

    Google Scholar 

  56. Roy, B.: Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht (1996)

    MATH  Google Scholar 

  57. Sethi, I., Jain, A.K. (eds.): Artificial Neural Networks and Pattern Recognition: Old and New Connections. Elsevier, New York (1991)

    MATH  Google Scholar 

  58. Shekar, B., Murty, N.M., Krishna, G.: A knowledge-based clustering scheme. Pattern Recognition Letters 5(4), 253–259 (1987)

    Article  Google Scholar 

  59. Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy. Freeman, San Francisco (1973)

    MATH  Google Scholar 

  60. Stepp, R.E., Michalski, R.S.: Conceptual clustering of structured objects: a goal oriented approach. Artificial Intelligence 28(1), 43–69 (1986)

    Article  Google Scholar 

  61. Van Ryzin, J. (ed.): Classification and Clustering. Academic Press, New York (1977)

    Google Scholar 

  62. Willet, P.: Recent trends in hierarchical document clustering: a critical review. Information Processing & Management 24(5), 577–597 (1988)

    Article  Google Scholar 

  63. Zahn, C.T.: Graph-theoretic method for detecting and describing gestalt clusters. IEEE Trans. Comput. 20, 68–86 (1971)

    Article  MATH  Google Scholar 

  64. Zait, M., Messatfa, H.: A comparative study of clustering methods. Future Generation Computer Systems 13, 149–159 (1997)

    Article  Google Scholar 

  65. Zaponunidis, C., Doumpos, M.: Multicriteria classification and sorting methods: A literacy review. Eur. J. of Oper. Res. 138(2), 229–246 (2002)

    Article  Google Scholar 

  66. Zhang, T., Ramakrishnan, R., Livny, M.: BIRCH: a new data clustering algorithm and its applications. Data Mining and Knowledge Discovery 1(2), 141–182 (1997)

    Article  Google Scholar 

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Volker Diekert Mikhail V. Volkov Andrei Voronkov

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Levin, M.S. (2007). Towards Hierarchical Clustering (Extended Abstract). In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_22

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  • DOI: https://doi.org/10.1007/978-3-540-74510-5_22

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