Advertisement

Clustering II: Topics in Clustering

  • Ke-Lin DuEmail author
  • M. N. S. Swamy
Chapter

Abstract

Following Chap.  9, this chapter continues to deal with clustering. We describe many associated topics such as the underutilization problem, robust clustering, hierarchical clustering, and cluster validity. Kernel-based clustering is introduced in Chap.  20.

References

  1. 1.
    Aggarwal, C. C. (2004). A human-computer interactive method for projected clustering. IEEE Transactions on Knowledge and Data Engineering, 16(4), 448–460.CrossRefGoogle Scholar
  2. 2.
    Aggarwal, C. C., &. Yu, P. S. (2000). Finding generalized projected clusters in high dimensional spaces. In Proceedings of the ACM SIGMOD International Conference on Management of Data (pp. 70–81).Google Scholar
  3. 3.
    Aggarwal, C. C., Procopiuc, C., Wolf, J. L., Yu, P. S., & Park, J. S. (1999). Fast algorithms for projected clustering. In Proceedings of the ACM SIGMOD International Conference on Management of Data (pp. 61–72).Google Scholar
  4. 4.
    Aggarwal, C. C., Han, J., Wang, J., & Yu, P. S. (2005). On high dimensional projected clustering of data streams. Data Mining and Knowledge Discovery, 10, 251–273.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Agrawal, R., Gehrke, J., Gunopulos, D., & Raghavan, P. (1998). Automatic subspace clustering of high dimensional data for data mining applications. In Proceedings of the ACM SIGMOD International Conference on Management of Data (pp. 94–105).Google Scholar
  6. 6.
    Ahalt, S. C., Krishnamurty, A. K., Chen, P., & Melton, D. E. (1990). Competitive learning algorithms for vector quantization. Neural Networks, 3(3), 277–290.CrossRefGoogle Scholar
  7. 7.
    Bacciu, D., & Starita, A. (2008). Competitive repetition suppression (CoRe) clustering: A biologically inspired learning model with application to robust clustering. IEEE Transactions on Neural Networks, 19(11), 1922–1941.CrossRefGoogle Scholar
  8. 8.
    Ball, G. H., & Hall, D. J. (1967). A clustering technique for summarizing multivariate data. Behavioral Sciences, 12, 153–155.CrossRefGoogle Scholar
  9. 9.
    Banerjee, A., Merugu, S., Dhillon, I. S., & Ghosh, J. (2005). Clustering with Bregman divergences. Journal of Machine Learning Research, 6, 1705–1749.MathSciNetzbMATHGoogle Scholar
  10. 10.
    Baraldi, A., & Blonda, P. (1999). A survey of fuzzy clustering algorithms for pattern recognition-Part II. IEEE Transactions on Systems, Man, and Cybernetics Part B, 29(6), 786–801.CrossRefGoogle Scholar
  11. 11.
    Bauer, H.-U., Der, R., & Herrmann, M. (1996). Controlling the magnification factor of self-organizing feature maps. Neural Computation, 8, 757–771.CrossRefGoogle Scholar
  12. 12.
    Basu, S., Davidson, I., & Wagstaff, K. L. (2008). Constrained clustering: Advances in algorithms, theory, and applications. New York: Chapman & Hall/CRC.zbMATHGoogle Scholar
  13. 13.
    Bay, S. D., & Schwabacher, M. (2003). Mining distance-based outliers in near linear time with randomization and a simple pruning rule. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 29–38).Google Scholar
  14. 14.
    Bengio, Y., Delalleau, O., Le Roux, N., Paiement, J. F., Vincent, P., & Ouimet, M. (2004). Learning eigenfunctions links spectral embedding and kernel PCA. Neural Computation, 16(10), 2197–2219.zbMATHCrossRefGoogle Scholar
  15. 15.
    Bezdek, J. C., Coray, C., Gunderson, R., & Watson, J. (1981). Detection and characterization of cluster substructure: Fuzzy \(c\)-varieties and convex combinations thereof. SIAM Journal of Applied Mathematics, 40(2), 358–372.Google Scholar
  16. 16.
    Bezdek, J. C., Hathaway, R. J., & Pal, N. R. (1995). Norm-induced shell-prototypes (NIPS) clustering. Neural, Parallel, and Scientific Computations, 3, 431–450.Google Scholar
  17. 17.
    Bouchachia, A., & Pedrycz, W. (2006). Enhancement of fuzzy clustering by mechanisms of partial supervision. Fuzzy Sets and Systems, 157, 1733–1759.MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Bouguessa, M., & Wang, S. (2009). Mining projected clusters in high-dimensional spaces. IEEE Transactions on Knowledge and Data Engineering, 21(4), 507–522.CrossRefGoogle Scholar
  19. 19.
    Bradley, P. S., Mangasarian, O. L., & Steet, W. N. (1996). Clustering via concave minimization. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems (Vol. 8, pp. 368–374). Cambridge: MIT Press.Google Scholar
  20. 20.
    Bruske, J., & Sommer, G. (1995). Dynamic cell structure. In G. Tesauro, D. S. Touretzky, & T. K. Leen (Eds.), Advances in neural information processing systems (Vol. 7, pp. 497–504). Cambridge: MIT Press.Google Scholar
  21. 21.
    Bubeck, S., & von Luxburg, U. (2009). Nearest neighbor clustering: A baseline method for consistent clustering with arbitrary objective functions. Journal of Machine Learning Research, 10, 657–698.MathSciNetzbMATHGoogle Scholar
  22. 22.
    Campello, R. J. G. B., & Hruschka, E. R. (2006). A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Sets and Systems, 157, 2858–2875.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Chatzis, S., & Varvarigou, T. (2009). Factor analysis latent subspace modeling and robust fuzzy clustering using \(t\)-distributions. IEEE Transactions on Fuzzy Systems, 17(3), 505–517.Google Scholar
  24. 24.
    Chen, X., Liu, W., Qiu, H., & Lai, J. (2011). APSCAN: A parameter free algorithm for clustering. Pattern Recognition Letters, 32(7), 973–986.CrossRefGoogle Scholar
  25. 25.
    Cheung, Y. M. (2003). \(k*\)-Means: A new generalized k-means clustering algorithm. Pattern Recognition Letters, 24, 2883–2893.zbMATHCrossRefGoogle Scholar
  26. 26.
    Cheung, Y. M. (2005). On rival penalization controlled competitive learning for clustering with automatic cluster number selection. IEEE Transactions on Knowledge and Data Engineering, 17(11), 1583–1588.CrossRefGoogle Scholar
  27. 27.
    Cheung, Y. M., & Law, L. T. (2007). Rival-model penalized self-organizing map. IEEE Transactions on Neural Networks, 18(1), 289–295.CrossRefGoogle Scholar
  28. 28.
    Choi, D. I., & Park, S. H. (1994). Self-creating and organizing neural network. IEEE Transactions on Neural Networks, 5(4), 561–575.CrossRefGoogle Scholar
  29. 29.
    Choy, C. S. T., & Siu, W. C. (1998). A class of competitive learning models which avoids neuron underutilization problem. IEEE Transactions on Neural Networks, 9(6), 1258–1269.CrossRefGoogle Scholar
  30. 30.
    Chung, F. L., & Lee, T. (1994). Fuzzy competitive learning. Neural Networks, 7(3), 539–551.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Cordeiro, R. L. F., Traina, A. J. M., Faloutsos, C., & Traina, C, Jr. (2013). Halite: Fast and scalable multiresolution local-correlation clustering. IEEE Transactions on Knowledge and Data Engineering, 25(2), 387–401.CrossRefGoogle Scholar
  32. 32.
    Dave, R. N. (1990). Fuzzy shell-clustering and applications to circle detection in digital images. International Journal of General Systems, 16(4), 343–355.MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Dave, R. N. (1991). Characterization and detection of noise in clustering. Pattern Recognition Letters, 12, 657–664.CrossRefGoogle Scholar
  34. 34.
    Dave, R. N., & Bhaswan, K. (1992). Adaptive fuzzy \(C\)-shells clustering and detection of ellipse. IEEE Transactions on Neural Networks, 3(5), 643–662.Google Scholar
  35. 35.
    Dave, R. N., & Krishnapuram, R. (1997). Robust clustering methods: A unified view. IEEE Transactions on Fuzzy Systems, 5(2), 270–293.CrossRefGoogle Scholar
  36. 36.
    Dave, R. N., & Sen, S. (2002). Robust fuzzy clustering of relational data. IEEE Transactions on Fuzzy Systems, 10(6), 713–727.CrossRefGoogle Scholar
  37. 37.
    Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(4), 224–227.CrossRefGoogle Scholar
  38. 38.
    Desieno, D. (1988). Adding a conscience to competitive learning. Proceedings of IEEE International Conference on Neural Networks, 1, 117–124.CrossRefGoogle Scholar
  39. 39.
    Dhillon, I., Mallela, S., & Kumar, R. (2003). A divisive information-theoretic feature clustering algorithm for text classification. Journal of Machine Learning Research, 3(4), 1265–1287.MathSciNetzbMATHGoogle Scholar
  40. 40.
    Dhillon, I. S., Mallela, S., & Modha, D. S. (2003). Information-theoretic co-clustering. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 89–98).Google Scholar
  41. 41.
    Dhillon, I. S., Guan, Y., & Kulis, B. (2007). Weighted graph cuts without eigenvectors: A multilevel approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(11), 1944–1957.CrossRefGoogle Scholar
  42. 42.
    El-Sonbaty, Y., & Ismail, M. (1998). Fuzzy clustering for symbolic data. IEEE Transactions on Fuzzy Systems, 6(2), 195–204.CrossRefGoogle Scholar
  43. 43.
    Ester, M., Kriegel, H. P., Sander, J., & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD) (pp. 226–231). Portland, OR.Google Scholar
  44. 44.
    Forti, A., & Foresti, G. L. (2006). Growing hierarchical tree SOM: An unsupervised neural network with dynamic topology. Neural Networks, 19, 1568–1580.zbMATHCrossRefGoogle Scholar
  45. 45.
    Foss, A., Markatou, M., Ray, B., & Heching, A. (2016). A semiparametric method for clustering mixed data. Machine Learning, 105, 419–458.MathSciNetzbMATHCrossRefGoogle Scholar
  46. 46.
    Franti, P., Virmajoki, O., & Hautamaki, V. (2006). Fast agglomerative clustering using a \(k\)-nearest neighbor graph. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(11), 1875–1881.Google Scholar
  47. 47.
    Frey, B. J., & Dueck, D. (2007). Clustering by passing message between data points. Science, 315, 972–976.MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Frezza-Buet, H. (2008). Following non-stationary distributions by controlling the vector quantization accuracy of a growing neural gas network. Neurocomputing, 71, 1191–1202.CrossRefGoogle Scholar
  49. 49.
    Frigui, H., & Krishnapuram, R. (1999). A robust competitive clustering algorithm with applications in computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(5), 450–465.CrossRefGoogle Scholar
  50. 50.
    Fritzke, B. (1994). Growing cell structures - A self-organizing neural networks for unsupervised and supvised learning. Neural Networks, 7(9), 1441–1460.CrossRefGoogle Scholar
  51. 51.
    Fritzke, B. (1995). A growing neural gas network learns topologies. In G. Tesauro, D. S. Touretzky, & T. K. Leen (Eds.), Advances in neural information processing systems (Vol. 7, pp. 625–632). Cambridge: MIT Press.Google Scholar
  52. 52.
    Fritzke, B. (1995). Growing grid-A self-organizing network with constant neighborhood range and adaptation strength. Neural Processing Letters, 2(5), 9–13.CrossRefGoogle Scholar
  53. 53.
    Fritzke, B. (1997). A self-organizing network that can follow nonstationary distributions. In W. Gerstner, A. Germond, M. Hasler, & J. D. Nicoud (Eds.), Proceedings of International Conference on Artificial Neural Networks, LNCS (Vol. 1327, pp. 613–618). Lausanne, Switzerland. Berlin: Springer.Google Scholar
  54. 54.
    Gath, I., & Geva, A. B. (1989). Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 773–781.zbMATHCrossRefGoogle Scholar
  55. 55.
    Gath, I., & Hoory, D. (1995). Fuzzy clustering of elliptic ring-shaped clusters. Pattern Recognition Letters, 16, 727–741.CrossRefGoogle Scholar
  56. 56.
    Geva, A. B. (1999). Hierarchical unsupervised fuzzy clustering. IEEE Transactions on Fuzzy Systems, 7(6), 723–733.CrossRefGoogle Scholar
  57. 57.
    Gonzalez, J., Rojas, I., Pomares, H., Ortega, J., & Prieto, A. (2002). A new clustering technique for function approximation. IEEE Transactions on Neural Networks, 13(1), 132–142.CrossRefGoogle Scholar
  58. 58.
    Grossberg, S. (1987). Competitive learning: From iterative activation to adaptive resonance. Cognitive Science, 11, 23–63.CrossRefGoogle Scholar
  59. 59.
    Guha, S., Rastogi, R., & Shim, K. (2001). CURE: An efficient clustering algorithm for large databases. Information Systems, 26(1), 35–58.zbMATHCrossRefGoogle Scholar
  60. 60.
    Gustafson, D. E., & Kessel, W. (1979). Fuzzy clustering with a fuzzy covariance matrix. In Proceedings of the IEEE Conference on Decision and Control (pp. 761–766). San Diego, CA.Google Scholar
  61. 61.
    Hamker, F. H. (2001). Life-long learning cell structures–Continuously learning without catastrophic interference. Neural Networks, 14, 551–573.CrossRefGoogle Scholar
  62. 62.
    Hartigan, J. A. (1972). Direct clustering of a data matrix. Journal of the American Statistical Association, 67(337), 123–129.CrossRefGoogle Scholar
  63. 63.
    Hartigan, J. A. (1975). Clustering algorithms. New York: Wiley.zbMATHGoogle Scholar
  64. 64.
    Hathaway, R. J., & Bezdek, J. C. (1994). NERF \(c\)-means: Non-euclidean relational fuzzy clustering. Pattern Recognition, 27, 429–437.CrossRefGoogle Scholar
  65. 65.
    Hathaway, R. J., & Bezdek, J. C. (2000). Generalized fuzzy \(c\)-means clustering strategies using \(L_p\) norm distances. IEEE Transactions on Fuzzy Systems, 8(5), 576–582.CrossRefGoogle Scholar
  66. 66.
    Hathaway, R. J., & Bezdek, J. C. (2001). Fuzzy \(c\)-means clustering of incomplete data. IEEE Transactions on Systems, Man, and Cybernetics Part B, 31(5), 735–744.CrossRefGoogle Scholar
  67. 67.
    Hathaway, R. J., & Hu, Y. (2009). Density-weighted fuzzy \(c\)-means clustering. IEEE Transactions on Fuzzy Systems, 17(1), 243–252.CrossRefGoogle Scholar
  68. 68.
    He, J., Tan, A. H., & Tan, C. L. (2004). Modified ART 2A growing network capable of generating a fixed number of nodes. IEEE Transactions on Neural Networks, 15(3), 728–737.CrossRefGoogle Scholar
  69. 69.
    Hein, M., Audibert, J.-Y., & von Luxburg, U. (2007). Graph Laplacians and their convergence on random neighborhood graphs. Journal of Machine Learning Research, 8, 1325–1370.MathSciNetzbMATHGoogle Scholar
  70. 70.
    Hoeppner, F. (1997). Fuzzy shell clustering algorithms in image processing: Fuzzy \(C\)-rectangular and 2-rectangular shells. IEEE Transactions on Fuzzy Systems, 5(4), 599–613.CrossRefGoogle Scholar
  71. 71.
    Honda, K., Notsu, A., & Ichihashi, H. (2010). Fuzzy PCA-guided robust \(k\)-means clustering. IEEE Transactions on Fuzzy Systems, 18(1), 67–79.CrossRefGoogle Scholar
  72. 72.
    Hornik, K., Feinerer, I., Kober, M., & Buchta, C. (2012). Spherical \(k\)-means clustering. Journal of Statistical Software, 50(10), 1–22.CrossRefGoogle Scholar
  73. 73.
    Hsu, A., & Halgamuge, S. K. (2008). Class structure visualization with semi-supervised growing self-organizing maps. Neurocomputing, 71, 3124–3130.CrossRefGoogle Scholar
  74. 74.
    Huang, J. Z., Ng, M. K., Rong, H., & Li, Z. (2005). Automated variable weighting in \(k\)-means type clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(5), 1–12.CrossRefGoogle Scholar
  75. 75.
    Huang, Z. (1998). Extensions to the \(k\)-means algorithm for clustering large data sets with categorical values. Data Mining and Knowledge Discovery, 2, 283–304.CrossRefGoogle Scholar
  76. 76.
    Hunt, L., & Jorgensen, M. (2011). Clustering mixed data. WIREs Data Mining and Knowledge Discovery, 1, 352–361.CrossRefGoogle Scholar
  77. 77.
    Jing, L., Ng, M. K., & Huang, J. Z. (2007). An entropy weighting \(k\)-means algorithm for subspace clustering of high-dimensional sparse data. IEEE Transactions on Knowledge and Data Engineering, 19(8), 1026–1041.CrossRefGoogle Scholar
  78. 78.
    Karypis, G., Han, E. H., & Kumar, V. (1999). Chameleon: Hierarchical clustering using dynamic modeling cover feature. Computer, 12, 68–75.CrossRefGoogle Scholar
  79. 79.
    Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis. New York: Wiley.zbMATHCrossRefGoogle Scholar
  80. 80.
    Kaymak, U., & Setnes, M. (2002). Fuzzy clustering with volume prototypes and adaptive cluster merging. IEEE Transactions on Fuzzy Systems, 10(6), 705–712.CrossRefGoogle Scholar
  81. 81.
    Kersten, P. R. (1999). Fuzzy order statistics and their application to fuzzy clustering. IEEE Transactions on Fuzzy Systems, 7(6), 708–712.CrossRefGoogle Scholar
  82. 82.
    King, B. (1967). Step-wise clustering procedures. Journal of the American Statistical Association, 69, 86–101.CrossRefGoogle Scholar
  83. 83.
    Krishnapuram, R., Nasraoui, O., & Frigui, H. (1992). The fuzzy \(c\)-spherical shells algorithm: A new approach. IEEE Transactions on Neural Networks, 3(5), 663–671.CrossRefGoogle Scholar
  84. 84.
    Krishnapuram, R., & Keller, J. M. (1993). A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems, 1(2), 98–110.CrossRefGoogle Scholar
  85. 85.
    Krishnapuram, R., Frigui, H., & Nasraoui, O. (1995). Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation: Part 1 & 2. IEEE Transactions on Fuzzy Systems, 3(1), 44–60.CrossRefGoogle Scholar
  86. 86.
    Kruskal, J. (1956). On the shortest spanning subtree and the traveling salesman problem. In Proceedings of the American Mathematical Society (pp. 48–50).Google Scholar
  87. 87.
    Landis, F., Ott, T., & Stoop, R. (2010). Hebbian self-organizing integrate-and-fire networks for data clustering. Neural Computation, 22, 273–288.MathSciNetzbMATHCrossRefGoogle Scholar
  88. 88.
    Leski, J. M. (2003). Generalized weighted conditional fuzzy clustering. IEEE Transactions on Fuzzy Systems, 11(6), 709–715.CrossRefGoogle Scholar
  89. 89.
    Lin, C.-R., & Chen, M.-S. (2005). Combining partitional and hierarchical algorithms for robust and efficient data clustering with cohesion self-merging. IEEE Transactions on Knowledge and Data Engineering, 17(2), 145–159.CrossRefGoogle Scholar
  90. 90.
    Liu, Z. Q., Glickman, M., & Zhang, Y. J. (2000). Soft-competitive learning paradigms. In Z. Q. Liu & S. Miyamoto (Eds.), Soft Computing and Human-Centered Machines (pp. 131–161). New York: Springer.CrossRefGoogle Scholar
  91. 91.
    Luk, A., & Lien, S. (1998). Learning with lotto-type competition. In Proceedings of International Joint Conference on Neural Networks (Vol. 2, pp. 1143–1146). Anchorage, AK.Google Scholar
  92. 92.
    Luk, A., & Lien, S. (1999). Lotto-type competitive learning and its stability. In Proceedings of International Joint Conference on Neural Networks (Vol. 2, pp. 1425–1428). Washington, DC.Google Scholar
  93. 93.
    Ma, J., & Wang, T. (2006). A cost-function approach to rival penalized competitive learning (RPCL). IEEE Transactions on Systems, Man, Cybernetics Part B, 36(4), 722–737.CrossRefGoogle Scholar
  94. 94.
    Maji, P., & Pal, S. K. (2007). Rough set based generalized fuzzy \(C\)-means algorithm and quantitative indices. IEEE Transactions on Systems, Man, Cybernetics Part B, 37(6), 1529–1540.CrossRefGoogle Scholar
  95. 95.
    Man, Y., & Gath, I. (1994). Detection and separation of ring-shaped clusters using fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(8), 855–861.CrossRefGoogle Scholar
  96. 96.
    Mao, J., & Jain, A. K. (1996). A self-organizing network for hyperellipsoidal clustering (HEC). IEEE Transactions on Neural Networks, 7(1), 16–29.CrossRefGoogle Scholar
  97. 97.
    Marshland, S., Shapiro, J., & Nehmzow, U. (2002). A self-organizing network that grows when required. Neural Networks, 15, 1041–1058.CrossRefGoogle Scholar
  98. 98.
    Ng, R. T., & Han, J. (1994). Efficient and effective clustering methods for spatial data mining. In Proceedings of the 20th International Conference on Very Large Data Bases (pp. 144–155). Santiago, Chile.Google Scholar
  99. 99.
    Ng, R. T., & Han, J. (2002). CLARANS: A method for clustering objects for spatial data mining. IEEE Transactions on Knowledge and Data Engineering, 14(5), 1003–1016.CrossRefGoogle Scholar
  100. 100.
    Ning, H., Xu, W., Chi, Y., Gong, Y., & Huang, T. S. (2010). Incremental spectral clustering by efficiently updating the eigen-system. Pattern Recognition, 43(1), 113–127.zbMATHCrossRefGoogle Scholar
  101. 101.
    Ontrup, J., & Ritter, H. (2006). Large-scale data exploration with the hierarchically growing hyperbolic SOM. Neural Networks, 19, 751–761.zbMATHCrossRefGoogle Scholar
  102. 102.
    Pal, N. R., Pal, K., Keller, J. M., & Bezdek, J. C. (2005). A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy Systems, 13(4), 517–530.CrossRefGoogle Scholar
  103. 103.
    Pedrycz, W. (1998). Conditional fuzzy clustering in the design of radial basis function neural networks. IEEE Transactions on Neural Networks, 9(4), 601–612.CrossRefGoogle Scholar
  104. 104.
    Prim, R. (1957). Shortest connection networks and some generalization. Bell System Technical Journal, 36, 1389–1401.CrossRefGoogle Scholar
  105. 105.
    Procopiuc, C. M., Jones, M., Agarwal, P.K., & Murali, T. M. (2002). A Monte Carlo algorithm for fast projective clustering. In Proceedings of the ACM SIGMOD International Conference on Management of Data (pp. 418–427).Google Scholar
  106. 106.
    Rizzo, R., & Chella, A. (2006). A comparison between habituation and conscience mechanism in self-organizing maps. IEEE Transactions on Neural Networks, 17(3), 807–810.CrossRefGoogle Scholar
  107. 107.
    Rodrigues, P. P., Gama, J., & Pedroso, J. P. (2008). Hierarchical clustering of time series data streams. IEEE Transactions on Knowledge and Data Engineering, 20(5), 615–627.CrossRefGoogle Scholar
  108. 108.
    Rose, K., Gurewitz, E., & Fox, G. C. (1990). A deterministic annealing approach to clustering. Pattern Recognition Letters, 11(9), 589–594.zbMATHCrossRefGoogle Scholar
  109. 109.
    Rumelhart, D. E., & Zipser, D. (1985). Feature discovery by competititve learning. Cognitive Sciences, 9, 75–112.CrossRefGoogle Scholar
  110. 110.
    Runkler, T. A., & Bezdek, J. C. (1999). Alternating cluster estimation: A new tool for clustering and function approximation. IEEE Transactions on Fuzzy Systems, 7(4), 377–393.CrossRefGoogle Scholar
  111. 111.
    Runkler, T. A., & Palm, R. W. (1996). Identification of nonlinear systems using regular fuzzy \(c\)-elliptotype clustering. In Proceedings of the 5th IEEE Conference on Fuzzy Systems (pp. 1026–1030).Google Scholar
  112. 112.
    Sander, J., Ester, M., Kriegel, H.-P., & Xu, X. (1998). Density-based clustering in spatial databases: The algorithm GDBSCAN and its applications. Data Mining and Knowledge Discovery, 2, 169–194.CrossRefGoogle Scholar
  113. 113.
    Shen, F., & Hasegawa, O. (2006). An adaptive incremental LBG for vector quantization. Neural Networks, 19, 694–704.zbMATHCrossRefGoogle Scholar
  114. 114.
    Shi, J., & Malik, J. (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888–905.CrossRefGoogle Scholar
  115. 115.
    Sneath, P. H. A., & Sokal, R. R. (1973). Numerical taxonomy. London: Freeman.zbMATHGoogle Scholar
  116. 116.
    Song, Q., Yang, X., Soh, Y. C., & Wang, Z. M. (2010). An information-theoretic fuzzy \(C\)-spherical shells clustering algorithm. Fuzzy Sets and Systems, 161, 1755–1773.MathSciNetzbMATHCrossRefGoogle Scholar
  117. 117.
    Staiano, A., Tagliaferri, R., & Pedrycz, W. (2006). Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering. Neurocomputing, 69, 1570–1581.CrossRefGoogle Scholar
  118. 118.
    Su, M. C., & Chou, C. H. (2001). A modified version of the \(K\)-means algorithm with a distance based on cluster symmetry. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6), 674–680.CrossRefGoogle Scholar
  119. 119.
    Su, M. C., & Liu, Y. C. (2005). A new approach to clustering data with arbitrary shapes. Pattern Recognition, 38, 1887–1901.zbMATHCrossRefGoogle Scholar
  120. 120.
    Thulasiraman, K., & Swamy, M. N. S. (1992). Graphs: Theory and algorithms. New York: Wiley.zbMATHCrossRefGoogle Scholar
  121. 121.
    Tishby, N., Pereira, F., & Bialek, W. (1999). The information bottleneck method. In Proceedings of the 37th Annual Allerton Conference on Communication, Control, and Computing (pp. 368–377).Google Scholar
  122. 122.
    Tjhi, W.-C., & Chen, L. (2009). Dual fuzzy-possibilistic coclustering for categorization of documents. IEEE Transactions on Fuzzy Systems, 17(3), 532–543.CrossRefGoogle Scholar
  123. 123.
    Tseng, V. S., & Kao, C.-P. (2007). A novel similarity-based fuzzy clustering algorithm by integrating PCM and mountain method. IEEE Transactions on Fuzzy Systems, 15(6), 1188–1196.CrossRefGoogle Scholar
  124. 124.
    Vesanto, J., & Alhoniemi, E. (2000). Clustering of the self-organizing map. IEEE Transactions on Neural Networks, 11(3), 586–600.CrossRefGoogle Scholar
  125. 125.
    Wang, J. H., & Rau, J. D. (2001). VQ-agglomeration: A novel approach to clustering. IEE Proceedings - Vision, Image and Signal Processing, 148(1), 36–44.CrossRefGoogle Scholar
  126. 126.
    Wang, W., & Zhang, Y. (2007). On fuzzy cluster validity indices. Fuzzy Sets and Systems, 158, 2095–2117.MathSciNetzbMATHCrossRefGoogle Scholar
  127. 127.
    Wang, C.-D., & Lai, J.-H. (2011). Energy based competitive learning. Neurocomputing, 74, 2265–2275.CrossRefGoogle Scholar
  128. 128.
    Wang, X., Wang, X., & Wilkes, D. M. (2009). A divide-and-conquer approach for minimum spanning tree-based clustering. IEEE Transactions on Knowledge and Data Engineering, 21(7), 945–958.CrossRefGoogle Scholar
  129. 129.
    Wu, K.-L., Yang, M.-S., & Hsieh, J.-N. (2009). Robust cluster validity indexes. Pattern Recognition, 42, 2541–2550.zbMATHCrossRefGoogle Scholar
  130. 130.
    Xie, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(8), 841–847.CrossRefGoogle Scholar
  131. 131.
    Xu, L. (2007). A unified perspective and new results on RHT computing, mixture based learning and multi-learner based problem solving. Pattern Recognition, 40, 2129–2153.zbMATHCrossRefGoogle Scholar
  132. 132.
    Xu, L., Krzyzak, A., & Oja, E. (1993). Rival penalized competitive learning for clustering analysis, RBF net, and curve detection. IEEE Transactions on Neural Networks, 4(4), 636–649.CrossRefGoogle Scholar
  133. 133.
    Yair, E., Zeger, K., & Gersho, A. (1992). Competitive learning and soft competition for vector quantizer design. IEEE Transactions on Signal Processing, 40(2), 294–309.CrossRefGoogle Scholar
  134. 134.
    Yang, T. N., & Wang, S. D. (2004). Competitive algorithms for the clustering of noisy data. Fuzzy Sets and Systems, 141, 281–299.MathSciNetzbMATHCrossRefGoogle Scholar
  135. 135.
    Yang, M.-S., Chiang, Y.-H., Chen, C.-C., & Lai, C.-Y. (2008). A fuzzy \(k\)-partitions model for categorical data and its comparison to the GoM model. Fuzzy Sets and Systems, 159, 390–405.MathSciNetzbMATHCrossRefGoogle Scholar
  136. 136.
    Yip, K. Y., Cheung, D. W., & Ng, M. K. (2004). HARP: A practical projected clustering algorithm. IEEE Transactions on Knowledge and Data Engineering, 16(11), 1387–1397.CrossRefGoogle Scholar
  137. 137.
    Yiu, M. L., & Mamoulis, N. (2005). Iterative projected clustering by subspace mining. IEEE Transactions on Knowledge and Data Engineering, 17(2), 176–189.CrossRefGoogle Scholar
  138. 138.
    Zahn, C. T. (1971). Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Transactions on Computers, 20(1), 68–86.zbMATHCrossRefGoogle Scholar
  139. 139.
    Zalik, K. R. (2010). Cluster validity index for estimation of fuzzy clusters of different sizes and densities. Pattern Recognition, 43(10), 3374–3390.zbMATHCrossRefGoogle Scholar
  140. 140.
    Zhang, Y. J., & Liu, Z. Q. (2002). Self-splitting competitive learning: A new on-line clustering paradigm. IEEE Transactions on Neural Networks, 13(2), 369–380.CrossRefGoogle Scholar
  141. 141.
    Zhang, J.-S., & Leung, Y.-W. (2004). Improved possibilistic c-means clustering algorithms. IEEE Transactions on Fuzzy Systems, 12(2), 209–217.CrossRefGoogle Scholar
  142. 142.
    Zhang, T., Ramakrishnan, R., & Livny, M. (1996). BIRCH: An efficient data clustering method for very large databases. In Proceedings of ACM SIGMOD Conference on Management of Data (pp. 103–114). Montreal, Canada.Google Scholar
  143. 143.
    Zhang, T., Ramakrishnan, R., & Livny, M. (1997). BIRCH: A new data clustering algorithm and its applications. Data Mining and Knowledge Discovery, 1, 141–182.CrossRefGoogle Scholar
  144. 144.
    Zheng, G. L., & Billings, S. A. (1999). An enhanced sequential fuzzy clustering algorithm. International Journal of Systems Science, 30(3), 295–307.zbMATHCrossRefGoogle Scholar
  145. 145.
    Zhong, S. (2005). Efficient online spherical \(k\)-means clustering. In Proceedings of International Joint Conference on Neural Networks (IJCNN) (pp. 3180–3185). Montreal, Canada.Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada
  2. 2.Xonlink Inc.HangzhouChina

Personalised recommendations