Combinatorial clustering: Literature review, methods, examples

  • M. Sh. LevinEmail author
Information Technology in Engineering Systems


The paper addresses clustering problems from combinatorial viewpoints. A systemic survey is presented. The list of considered issues involves the following: (1) literature analysis of basic combinatorial methods and clustering of very large data sets/networks; (2) quality characteristics of clustering solutions; (3) multicriteria clustering models; (4) graph based clustering methods (minimum spanning tree based clustering methods, clique based clustering as detection of cliques/quasi-cliques, correlation clustering, detection of network communities); and (5) fast clustering approaches. Mainly, the presented material is targeted to networking. Numerical examples illustrate models, methods and applications.


clustering classification combinatorial optimization multicriteria decision making heuristics network applications 


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  1. 1.
    J. Abello, M. G. C. Resende, and S. Sudarsky, “Massive quasi-clique detection,” in Lecture Notes in Computer Science (LNCS), Vol. 2573: Proc. 5th Latin American Symp. on Theoretical Informatics (LATIN 2002), Cancun, Mexico, Apr. 3–6, 2002, Ed. By Rajsbaum (Springer-Verlag, Berlin, 2002). pp. 598–612.Google Scholar
  2. 2.
    E. Achtert, C. Bohm, H.-P. Kriegel, P. Kroger, and A. Zimek, “Robust, complete, and efficient correlation clustering,” in Proc. 7th SIAM Int. Conf. on Data Mining (SDM), Minneapolis, MN, 2007 (SIAM, 2007). pp. 413–418.CrossRefGoogle Scholar
  3. 3.
    E. Achtert, C. Bohm, J. David, P. Kroger, and A. Zimek, “Global correlation clustering based on the hough transform,” Stat. Anal. Data Mining, 1, 111–127 (2008).MathSciNetCrossRefGoogle Scholar
  4. 4.
    G. Agarwal and D. Kempe, “Modularity maximizing network communitites using mathematical programming,” Eur. Phys J. 66, 4009–418 (2008).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Data Streams: Models and Algorithms, Ed. by C. C. Aggarwal (Springer, New York, 2007).Google Scholar
  6. 6.
    R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan, “Automatic subspace clustering of high dimensional data,” Data Mining Knowl. Discov. 11 (5), 5–33, (2005).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms (Addison Wesley, Reading, MA, 1974).zbMATHGoogle Scholar
  8. 8.
    N. Ailon, M. Charikar, and A. Newman, “Aggregating inconsistent information: Ranking and clustering,” J. ACM 55 (5), art. No. 23, (2008).Google Scholar
  9. 9.
    E. Akkoyunlu, “The enumeration of maximal cliques of large graph,” SIAM J. Comput. 2 (1), 1–6 (1973).MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    N. Alon, M. Krivelevich, and B. Sudakov, “Finding a large hidden clique in a random graph,” in Proc. 9th, Ann. ACM-SIAM Symp. on Discr. Alg., San Francisco, CA, 1998 (ACM, 1998). pp. 594–598.Google Scholar
  11. 11.
    C. J. Augeri and H. H. Ali, “New graph-based algorithms for partitioning VLSI circuits,” in Proc. IEEE Int. Symp. on Cirquits and Systems (ISCAS’04), Vancouver, Canada, May 23–26, 2004 (IEEE, New York, 2004). Vol. 4, pp. 521–524.Google Scholar
  12. 12.
    H. Ayad and M. S. Kamel, “On voting-based consensus of cluster ensembles,” Pattern Recogn. 43, 1943–1953 (2010).zbMATHCrossRefGoogle Scholar
  13. 13.
    L. Babel, “A fast algorithm for the maximum weight clique problem,” Computing 52, 31–38 (1994).MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    G. Babu and M. Nurty, “Clustering with evolution strategy,” Pattern Recogn. Lett. 14, 763–769, (1993).zbMATHCrossRefGoogle Scholar
  15. 15.
    S. Bagon and M. Galun, “Optimizing large scale correlation clustering,” Electr. Prepr., 9 p., Dec. 13, (2011). http://arxivorg/abs/1112.2903 [cs.CV]Google Scholar
  16. 16.
    E. Balas, V. Chvatal, and J. Nesetril, “On the maximum weight clique problem,” Math., Oper. Res. 12, 522–535 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    N. Bansal, A. Blum, and S. Chawla, “Correlation clustering,” in Proc. 43rd Symp. on Foundations of Computer Science (FOCS 2002), Vancouver, BC, Canada, Nov. 16–19, 2002 (IEEE, New York, 2002). pp. 238–250.Google Scholar
  18. 18.
    N. Bansal, A. Blum, and S. Chawla, “Correlation clustering,” Mach. Learn. 56, 89–113 (2004).zbMATHCrossRefGoogle Scholar
  19. 19.
    V. Batagelj and M. Zavershik, “An O(m) algorithm for cores decomposition of networks,” Electr. Prepr., 10 p., Oct. 25, (2003). http://arxivorg/abs/0310.0049 [cs.DS]Google Scholar
  20. 20.
    A. Ben-Dor, R. Shamir, and Z. Yakhini, “Clustering gene expression patterns,” J. Comput. Biology 6, 281–292, (1999).CrossRefGoogle Scholar
  21. 21.
    P. Berkhin, “A survey of clustering data mining techniques,” in Grouping Multidimensional Data, (Springer-Verlag, New York, 2006). 25–71.CrossRefGoogle Scholar
  22. 22.
    V. D. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre, “Fast unfolding of communities in large networks,” Electr. Prepr., 12 p., July 25, 2008; http://arxivorg/abs/0803.0476 [physicssoc-ph]Google Scholar
  23. 23.
    V. D. Blondel, M. Esch, C. Chan, F. Clerot, P. Deville, E. Huens, F. Morlot, Z. Smoreda, and C. Ziemlicki, “Data for development the d4d challenge on mobile phone data,” Electr. Prepr., 10 p., Jan. 28, (2012). http://arxivorg/abs/1210.0137 [cs.CY]Google Scholar
  24. 24.
    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex netwoprks: Structure and dynamics,” Phys. Rep. 424, 175–208 (2006).MathSciNetCrossRefGoogle Scholar
  25. 25.
    D. Boley, M. Gini, R. Gross, S. Han, K. Hastings, G. Kapyris, V. Kumar, B. Mobasher, and J. Moor, “Partitioning-based clustering of web document categorization,” Decision Support Syst. (DSS) 27, 329–341 (1999).CrossRefGoogle Scholar
  26. 26.
    I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo, “The maximum clique problem,” in Handbook of Combinatorial Optimization, Ed. by D.-Z. Du and P. M. Pardalos (Springer, New York, 1999). (Suppl. vol. A), pp. 659–729.Google Scholar
  27. 27.
    U. Brandes, D. Delling, M. Gaertler, R. Gorke, M. Hoefer, Z. Nikolosk, and D. Wagner, “On modularity clustering,” IEEE Trans. Knowl. Data Eng. 20, 172–188, (2008).CrossRefGoogle Scholar
  28. 28.
    C. Bron and J. Kerbosch, “Algorithm 457: Finding all cliques of an undirected graph,” Commun. ACM 16, 575–577, (1973).zbMATHCrossRefGoogle Scholar
  29. 29.
    D. Brown and C. Huntley, “A practical application of simulated annealing to clustering,” Pattern Recogn. 25, 401–412, (1992).CrossRefGoogle Scholar
  30. 30.
    S. Butenko and W. Wilhelm, “Clique-detection models in computational biochemistry and genomics,” Eur. J. Operat. Res. (EJOR) 173 (1), 1–17, (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Z. Cai, M. Lu, and X. Wang, “Channel access-based self-organized clustering in ad hoc networks,” IEEE Trans. Mobile Comput. 2, 102–113 (2003).CrossRefGoogle Scholar
  32. 32.
    M. Charikar, V. Guruswami, and A. Wirth, “Clustering with quantitative information,” in Proc. 44th Symp. on Foundations of Computer Science (FOCS 2003), Cambridge, MA, USA, Oct. 11–14, 2003, (IEEE, New York, 2003). pp. 524–533.Google Scholar
  33. 33.
    M. Charikar, V. Guruswami, and A. Wirth, “Clustering with quantitative information,” J. Comput. Syst. Sci. 71, 360–383 (2005).MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    I. Charon and O. Hundry, “Optimal clustering in multipartite graph,” Disc. Appl. Math. 156, 1330–1347 (2008).zbMATHCrossRefGoogle Scholar
  35. 35.
    C.-Y. Chen and F. Ye, “Particle swam optimization algorithm and its application to cluster analysis,” in Proc. 2004 IEEE Int. Conf. on Networking, Sensing and Control, Taipei, Mar. 21–23, 2004 (IEEE, New York, 2004). vol. 2, 789–794.Google Scholar
  36. 36.
    Y. P. Chen and A. L. Liestman, “Maintaining weaklyconnected dominating sets for clustering ad hoc networks,” Ad Hoc Netw. 3, 629–642 (2005).CrossRefGoogle Scholar
  37. 37.
    P. Chen and S. Redner, “Community structure of the physical review citation network,” J. Informetrics 4, 278–290 (2010).CrossRefGoogle Scholar
  38. 38.
    C. H. Cheng, “A branch-and-bound clustering algorithm,” IEEE Trans. Syst. Man Cybern. 25, 895–898 (1995).CrossRefGoogle Scholar
  39. 39.
    A. Clauset, M. E. J. Newman, and C. Moore, “Finding community structure in very large networks,” Phys. Review E 70, No. 066111, 2004.Google Scholar
  40. 40.
    J. Coble, D. J. Cook, and L. B. Holder, “Structure discovery in sequentially-connected data streams,” Int. J. Artif. Intell. Tools 15, 917–944 (2006).CrossRefGoogle Scholar
  41. 41.
    C. Cobos, M. Mendoza, and Leon E., “A hyper-heuristic approach to design and tuning heuristic methods for web document clustering,” in Proc. 2011 IEEE Cong. on Evolutionary Computation (CEC), New Orleans, USA, June 5–8, 2011 (IEEE, New York, 2011). pp. 1350–1358.Google Scholar
  42. 42.
    D. Cokuslu, K. Erciyes, and O. Dagdeviren, “A dominating set based clustering algorithm for mobile ad hoc networks,” in Lecture Notes in Computer Science (LNCS), Vol. 3991: Proc. 6th Int. Conf. on Computational Science (ICCS’2006), Reading, UK, May 28–31, 2006, Ed. by V. N. Alexandrov, et al. (Springer-Verlag, Berlin, 2006). pp. 571–578.Google Scholar
  43. 43.
    D. Cokuslu and K. Erciyes, “A hierarchical connected dominating set based clustering algorithm for mobile ad hoc networks,” in Proc. 15th Int. Symp. on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS’07), Istanbul, Turkey, Oct. 2007 (IEEE, New York, 2007). pp. 60–66.CrossRefGoogle Scholar
  44. 44.
    A. Condon and R. M. Karp, “Algorithms for graph partitining on the planted partition model,” Random Struct. Alg. 18, 116–140 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, 3rd ed. (MIT Press, Cambridge, 2009).zbMATHGoogle Scholar
  46. 46.
    D. G. Corneil and Y. Perl, “Clustering and domination in perfect graphs,” Disc. Appl. Math. 9, 27–39, 1984.MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    M. C. Cowgill, R. J. Harvey, and L. T. Watson, “A genetic algorithm approach to cluster analysis,” Comput. Math. Appl. 37 (7), 99–108, (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    M. Dawande, P. Keskinocak, J. M. Swaminathan and S. Tayur, “On bipartite and multipartite clique problems,” J. Algorithms 41, 388–403 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    S. G. de Amorim, J.-P. Barthelemy, and C. C. Ribeiro, “Clustering and clique partitioning: Simulated anealing and tabu search approaches,” J. Classif. 9 (1), 17–41 (1992).CrossRefGoogle Scholar
  50. 50.
    E. D. Demaine and N. Immorlica, “Correlation clusteirng with partial information,” in Approximation, Randomization, and Combinatorial Optimization (Algorithms and Techniques, Springer-Verlag, 2003). pp. 1–13.Google Scholar
  51. 51.
    E. D. Demaine, D. Emanuel, A. Fiat, and N. Immorlica, “Correlation clustering in general weighted graphs,” Theor. Comp. Sci. 361, 172–187 (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    C. H. Q. Ding, X. He, H. Zha, M. Gu, and H. D. Simon, “A min-max algorithm for graph partitioning and data clustering,” in Proc. IEEE Int. Conf. on Data Mining (ICDM’01), San Jose, Nov. 2001 (IEEE, New York, 2001). pp. 107–111.CrossRefGoogle Scholar
  53. 53.
    H. N. Djidjev, “A scalable multilevel algorithm for graph clustering and community structure detection,” in Lecture Notes in Computer Science (LNCS), Vol. 4936: Proc. 4th Int. Workshop on Algorithms and Models for the Web-Graph (WAW’06), Banff, Canada, Nov. 30–Dec. 1, 2006, Ed. by W. Aiello et al. (Springer, Berlin, 2008). pp. 117–128.Google Scholar
  54. 54.
    D. Duan, Y. Li, R. Li, and Z. Lu, “Incremantal K-clique clustering in dynamic social networks,” Artif. Intell. Rev. 38, 129–147 (2012).CrossRefGoogle Scholar
  55. 55.
    J. Duch and A. Arenas, “Community detection in complex networks using extremal optimization,” Phys. Rev. E 72, 027104 (2005).CrossRefGoogle Scholar
  56. 56.
    M. Elsner and W. Schudy, “Bounding and comparing methods for correlation clustering beyond ILP,” in Proc. NAACL HLT Workshop on Integer Linear Programming for Natural Language Processing, Boulder, Co, May 31–June 5, 2009 (North Am. Chap. Ass. Comput. Linguistics, 2009). pp. 19–27.Google Scholar
  57. 57.
    D. Emanuel and A. Fiat, “Correlation clustering minimizing disagreements on arbitrary weighted graphs,” in Proc. 11th Ann. Eur. Symp. on Algorithms, ESA-2003, Budapest, Hungary, Sept., 2003 (SpringerVerlag, Berlin, 2003). pp. 208–220.Google Scholar
  58. 58.
    G. Even, J. Naor, S. Rao, and B. Schieber, “Fast approximate graph partitioning algorithms,” SIAM J. Comput. 28, 2187–2214 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    U. Feige and R. Krauthgamer, “Finding and certifying a large clique in a semi-random graph,” Random Struc. Alg. 16, 195–208, (2000).MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    D. Feldman and M. Langberg, “A unified framework for approximating and clustering data,” in Proc. 43rd ACM Symp. on Theory of Computing, (STOC 2011), San Jose, CA, USA, June 6–8, 2011 (ACM, 2011). pp. 569–578.Google Scholar
  61. 61.
    A. E. Feldman and L. Foschini, “Balanced partitions of trees and applications,” Algorithmica 71, 354–376 (2015).MathSciNetCrossRefGoogle Scholar
  62. 62.
    M. R. Fellows, J. Guob, C. Komusiewicz, R. Niedermeier and J. Uhlmann, “Graph-based data clustering with overlaps,” Disc. Optim. 8, 2–17 (2011).zbMATHCrossRefGoogle Scholar
  63. 63.
    S. Fortunato, “Community detection in graphs,” Electr. Prepr., 103 p., Jan. 25, (2010). http://arxivorg/abs/0906.0612v2 [physicssoc-ph]Google Scholar
  64. 64.
    G. Frahling and C. Sohler, “Coresets in dynamic geometric data streams,” in Proc. 37th ACM Symp. on Theory of Computing (STOC 2005), Baltimore, MD, USA, May 22–24, 2005 (ACM, 2005). pp. 209–217.Google Scholar
  65. 65.
    E. M. Furems, “Dominance-based extension of STEPCLASS for multiattribute nominal classification,” Int. J. Inform. Technol. Dec. Making 12, 905–925 (2013).CrossRefGoogle Scholar
  66. 66.
    H. N. Gabow, Z. Galil, T. Spencer, and R. E. Tarjan, “Efficient algorithms for finding minimum spanning trees in undirected and directed graphs,” Combinatorica 6, 109–122 (1986).MathSciNetzbMATHCrossRefGoogle Scholar
  67. 67.
    M. R. Garey and D. S. Johnson, Computers and Intractability. The Guide to the Theory of NP-Completeness (W. H. Freeman, San Francisco, 1979).Google Scholar
  68. 68.
    I. Giotis and V. Guruswami, “Correlation clustering with a fixed number of clusters,” in Proc. 17th Ann. ACM-SIAM Symp. on Discrete Algorithms (SODA’06), Miami, FL, Jan. 22–26, 2006 (SIAM, New York, 2006). pp. 1167–1176.Google Scholar
  69. 69.
    M. Girvan and M. E. J. Newman, “Community structure in social an biological networks. Community structure in social and biological networks,” Proc. Natl. Acad. Sci. USA (PNAS) 99, 8271–8276 (2002).MathSciNetCrossRefGoogle Scholar
  70. 70.
    J. Gramm, J. Guo, F. Huffner, and R. Niedermeier, “Graph-modeled data clustering: Fixed-parameter algorithm for clique generation,” Theory Comput. Syst. 38, 373–392 (2005).MathSciNetzbMATHCrossRefGoogle Scholar
  71. 71.
    J. Goldberger and T. Tassa, “A hierarchical clustering algorithm based on the Hungarian method,” Pattern Recogn. Lett. 29, 1632–1638 (2008).CrossRefGoogle Scholar
  72. 72.
    B. Goldengorin, D. Krushinsky, and P. M. Pardalos, Cell Formation in Industrial Engineering: Theory, Algorithms and Experiments (Springer-Verlag, New York, 2013).CrossRefGoogle Scholar
  73. 73.
    P. K. Gopalan and D. M. Blei, “Efficient discovery of overlapping communites in massive networks,” Proc. Natl. Acad. Sci. USA (PNAS) 110, 14534–14539 (2013).MathSciNetzbMATHCrossRefGoogle Scholar
  74. 74.
    J. Gower and G. Ross, “Minimum spanning trees and single linkage cluster analysis,” J. Royal Stat. Soc., Ser. C: Appl. Stat. 18, 54–64 (1969).MathSciNetGoogle Scholar
  75. 75.
    O. Grygorash, Y. Zhou, and Z. Jorgensen, “Minimum spanning tree based clustering algorithms,” in Proc. 18th IEEE Int. Conf. in Tools with Artificial Intelligence (ICTAI’06), Arlington, VA, USA, Nov. 13–15, 2006 (IEEE, New York, 2006). pp. 73–81.Google Scholar
  76. 76.
    A. Guenoche, “Consensus partitions: a constructive approach,” Adv. Data Anal., Classif. 5, 215–229 (2011).MathSciNetzbMATHCrossRefGoogle Scholar
  77. 77.
    S. Guha, N. Mishra, R. Motwani, and L. O’Callagham, “Clustering data streams,” in Proc. 41st Ann. Symp. Foundations of Computer Science (FOCS), Redondo Beach, CA, Nov. 12–14, 2000 (IEEE Computer Society, 2000). pp. 359–366.Google Scholar
  78. 78.
    R. Guimera, L. Dadon, A. Diaz-Guilera, F. Giralt, and A. Arenas, “Self-similar community structure in a network of human interactions,” Phys. Rev. E 68, 065103 (2003).CrossRefGoogle Scholar
  79. 79.
    R. Guimera, M. Sales-Pardo, and L. A. N. Amaral, “Modularity from fluctuations in random graphs and complex networks,” Phys. Rev. E 70, 025101 (2004).CrossRefGoogle Scholar
  80. 80.
    I. Gunes and H. Bingol, “Coomunity detection in complex networks using agents,” Electr. Prepr., 5 p., Oct. 23, (2006). arXiv:cs/0610129 [cs.MA]Google Scholar
  81. 81.
    B. Han and W. Jia, “Clustering wireless ad hoc networks with weakly connected dominating set,” J. Parall. Distr. Comput. 67, 727–737 (2007).zbMATHCrossRefGoogle Scholar
  82. 82.
    P. Hansen and N. Mladenovic, “Variable neighborhood search for the p-median,” Location Sci. 5, 207–226 (1997).zbMATHCrossRefGoogle Scholar
  83. 83.
    P. Hansen, J. Brimberg, D. Urosevic, and N. Mladenovic, “Data Clustering using Large p-Median Models and Primal-Dual Variable Neighborhood Search,” Les Cahiers du GERAD, G-2007-41, June (2007).Google Scholar
  84. 84.
    P. Hansen, J. Brimberg, D. Urosevic, and N. Mladenovic, “Primal-dual variable neighborhood search for the simple plant-location problem,” INFORMS J. Comput. 19, 552–564 (2007).MathSciNetzbMATHCrossRefGoogle Scholar
  85. 85.
    P. Hansen, J. Brimberg, D. Urosevic, and N. Mladenovic, “Solving large p-median clustering problems by primal-dual variable neighborhood search,” Data Min. Knowl. Discov. 19, 351–375 (2009).MathSciNetCrossRefGoogle Scholar
  86. 86.
    S. Har-Peled and S. Mazumdar, “On coresets for kmean and k-median clustering,” in Proc. 36th Annual ACM Symp. on Theory of Computing, Chicago, IL, USA, June 13–16, 2004 (ACM, 2004). pp. 291–300.Google Scholar
  87. 87.
    J. Hopcroft, O. Khan, B. Kulis, and B. Selman, “Natural communities in large linked networks,” in Proc. 9th ACM SIGKDD Int. Conf. on Knowl. Discov. Data Mining (KDD’03), New York, NY, USA, 2003 (ACM, New York, 2003). pp. 541–546.Google Scholar
  88. 88.
    J. Hopcroft, O. Khan, B. Kulis, and B. Selman, “Tracking evolving communities in large linked networks,” Proc. Natl. Acad. Sci. USA 101 (Suppl. 1), 5249–5353 (2004).CrossRefGoogle Scholar
  89. 89.
    T. C. Hou and T.-J. Tsai, “An access-based clustering protocol for multihop wireless ad hoc networks,” IEEE J. Selec. Areas Commun. 19, 1201–1210 (2001).CrossRefGoogle Scholar
  90. 90.
    E. R. Hruschka, R. G. B. Campello, A. A. Freitas, and A. P. L. Carvalho, “A survey of evolutionary algorithms for clustering,” IEEE Trans. Syst. Man Cybern., Part C 39 (2), 133–155 (2009).CrossRefGoogle Scholar
  91. 91.
    Z. Huang, “Extensions to the k-means algorithm for clustering large data sets with categorical values,” Data Mining Knowl. Discov. 2, 283–304 (1998).CrossRefGoogle Scholar
  92. 92.
    R. K. R. Indukuri and S. V. Penumathsa, “Dominating sets and spanning tree based clustering algorithms for mobile ad hoc networks,” Int. J. Adv. Comput. Sci. Appl. 2, 75–81 (2011).Google Scholar
  93. 93.
    A. S. Ivanov, A. I. Lyakhov, and E. M. Khorov, “Analytical model of batch flow multihop transmission in wireless networks with channel reservation,” Autom. Remote Control, 76 (7), 1179–1192 (2015).MathSciNetCrossRefGoogle Scholar
  94. 94.
    A. K. Jain, “Data clustering: 50 years beyond k-means,” Pattern Recogn. Lett. 31, 651–666 (2010).CrossRefGoogle Scholar
  95. 95.
    A. K. Jain and R. C. Dubes, Algorithms for Clustering Data (Prentice Hall, Upper Saddle River, 1988).Google Scholar
  96. 96.
    A. K. Jain, M. N. Murty, and P. J. Flynn, “Data clustering: a review,” ACM Comput. Surv. 31, 264–323 (1999).CrossRefGoogle Scholar
  97. 97.
    T. Joachims and J. Hopcroft, “Error bounds for correlation clustering,” in Proc. 22nd Int. Conf. on Machine Learning (ICML’05), Bonn, Germany, Aug. 7–11, 2005 (ACM, 2005). pp. 385–392.Google Scholar
  98. 98.
    DIMACS Ser. in Disc. Math, and Theor. Comp. Sci., Vol. 26: Cliques, Coloring, and Satisfiability, Ed. by D. S. Johnson and M. A. Trick (AMS, Providence, 1996).Google Scholar
  99. 99.
    R. Jovanovic, M. Tuba, and S. Voss, “An ant colony optimization algorithm for partitioning graphs with supply and demand,” Electr. prep. 21 p., March 3 (2015). http://arxivorg/abs/1503.00899 [cs.AI]Google Scholar
  100. 100.
    I. Kargin, E. Khorov, and A. Lyakhov, “A mathematical method to estimate packet loss ratio for a multipath route with error correlation” Probl. Inform. Transmission, (2015).(in press).Google Scholar
  101. 101.
    R. M. Karp, “Reducibility among combinatorial problems,” in Complexity of Computer Computations, Ed. by R. E. Miller and J. W. Thatcher (Plenum, New York, 1972). pp. 85–103.CrossRefGoogle Scholar
  102. 102.
    B. Kernigham and S. Lin, “An efficient heuristic procedure for partitioning graphs,” Bell Syst. Techn. J. 49, 291–307 (1970).CrossRefGoogle Scholar
  103. 103.
    E. Khorov, A. Lyakhov, A. Krotov, and A. Guschin, “A survey on IEEE 802.11ah: an enabling networking technology for smart cities,” Comput. Commun. 58, 53–69 (2015).CrossRefGoogle Scholar
  104. 104.
    E. M. Khorov, A. G. Kiruanov, A. A. Kureev, and A. Lyakhov, “Study of mechanism for building a logical network topology in MANET,” J. Commun. Technol. Electron. 60 (12), (2015). (In Press)Google Scholar
  105. 105.
    E. Khorov, A. Krotov, and A. Lyakhov, “Modeling machine type communication in IEEE 802.11ah network,” in Proc. IEEE Int. Conf. on CommunicationsWorkshop on 5G & Beyond Enabling Technologies and Applications, London, UK, June, 2015 (IEEE, New York, 2015).Google Scholar
  106. 106.
    S. Kim, S. Nowozin, P. Kohli, and C. D. Yoo, “Higher-order correlation clustering for image segmentation,” in Adv. Neural Inf. Process. Syst. 25, 1530–1538 (2011).Google Scholar
  107. 107.
    J. M. Kleinberg, C. Papadimitriou, and P. Raghavan, “Segmentation problems,” in Proc. 30th ACM Symp. on Theory of Computing (STOC’1998), New York, NY, USA, 1998 (ACM, New York, 1998). 473–482 (1998).Google Scholar
  108. 108.
    D. E. Knuth and A. Raghunathan, “The problem of compatible representatives,” SIAM J. on Disc. Math. 5, 422–427 (1992).MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    G. Kochenberg, F. Glover, B. Alidaee, and H. Wang, “Clustering of microarray data via clique partitioning,” J. Combin. Optim. 10, 77–92 (2005).CrossRefGoogle Scholar
  110. 110.
    H.-P. Kriegel, P. Kroger, E. Schubert, and A. Zimek, “A general framework for increasing the robustness of PCA-based correlation clustering algorithms,” in Proc. 20th Int. Conf. Scientific and Statistical Database Management (SSDBM), Hong Kong, China, 2008 (Springer-Verlag, Berlin, 2008). pp. 418–435.Google Scholar
  111. 111.
    H.-P. Kriegel, P. Kroger, and A. Zimek, “Clustering high dimensional data: A survey on subspace clustering, pattern-based clustering, and correlation clustering,” ACM Trans. on Knowledge Discovery from Data (KDD) 3 (1), 1–58 (2009).CrossRefGoogle Scholar
  112. 112.
    D. P. Kroese, R. Y. Rubinstein, and T. Taimre, “Application of the cross-entropy method for clustering and vector quantization,” J. Global Optim. 37 (1), 137–157 (2007).zbMATHCrossRefGoogle Scholar
  113. 113.
    V. Kumar, M. Steinbach, and P.-N. Tan, Introduction to Data Mining (Addison-Wesley, 2005).Google Scholar
  114. 114.
    A. C. Kumari and K. Srinivas, Software module clustering using a fast multi-objective hyper-heuristic evolutionary algorithm,” Int. J. of Appl. Inform. Syst. 5 (6), 12–18 (2012).CrossRefGoogle Scholar
  115. 115.
    M. Kyperountas, A. Tefas, and I. Pitas, “Dynamic training using multistage clustering for face recognition,” Pattern Recogn. 41, 894–905 (2008).zbMATHCrossRefGoogle Scholar
  116. 116.
    Y. C. Lai, P. Lin, W. Liao, and C. M. Chen, “A regionbased clustering mechanism for channel access in vehicular ad hoc networks,” IEEE J. Selec. Areas Commun. 29, 83–93 (2011).CrossRefGoogle Scholar
  117. 117.
    J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney, “Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters,” Internet Math. 6, 29–123 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  118. 118.
    M. Sh. Levin, Combinatorial Engineering of Decomposable Systems (Kluwer, Dordrecht, 1998).zbMATHCrossRefGoogle Scholar
  119. 119.
    M. Sh. Levin, Composite Systems Decisions (SpringerVerlag, New York, 2006).Google Scholar
  120. 120.
    M. Sh. Levin, “Aggregation of composite solutions: strategies, models, examples,” Electr. Prepr., 72 p., (Nov. 29, 2011); http://arxivorg/abs/llll.6983 [cs.SE]Google Scholar
  121. 121.
    M. Sh. Levin, “Multiset estimates and combinatorial synthesis,” Electr. prep., 30 p. (May 9, 2012); http://arxivorg/abs/1205.2046 [cs.SY]Google Scholar
  122. 122.
    M. Sh. Levin, “Clique-based fusion of graph streams in multi-function system testing,” Informatica 23, 391–404 (2012).Google Scholar
  123. 123.
    M. Sh. Levin, Modular System Design and Evaluation (Springer-Verlag, New York, 2015).CrossRefGoogle Scholar
  124. 124.
    M. Sh. Levin, “Towards combinatorial clustering: preliminary research survey,” Electr. Prepr., 102 pp., (May 28, 2015); http://arxivorg/abs/1505.07872 [cs.AI]Google Scholar
  125. 125.
    N. P. Lin, C.-I. Chang, H.-E. Chueh, H.-J. Chen, and W.-H. Hao, “A deflected grid-based algorithm for clustering analysis,” WSEAS Trans. Comput. 3 (7), 125–132 (2007).Google Scholar
  126. 126.
    X. Liu, D. Li, S. Wang, and Z. Tao, “Effective algorithm for detecting community structure in complex networks based on GA and clustering,” in Proc. 7th Int. Conf. on Comput. Sci. ICCS’07, Beijing, China, May 27–30, 2007, Ed. by Y. Shi et. al. (Springer-Verlag, Berlin, 2007).Google Scholar
  127. 127.
    X. Liua and T. Murata, “Detecting communities in k-partite k-uniform (hyper)networks,” J. Comput. Sci. Technol. 26, 778–791 (2011).CrossRefGoogle Scholar
  128. 128.
    X. Liua, T. Murata, and K. Wakita, “Extending modularity by capturing the similarity attraction feature in the null model,” Electr. Prepr., 10 p., (Feb. 12, 2013); http://arxivorg/abs/1210.4007 [cs.SI]Google Scholar
  129. 129.
    Y. Lu, Y. Sun, G. Xu, and G. Liu, “A grid-based clustering algorithm for high-dimensional data streams,” in Lecture Notes in Computer Science (LNCS), Vol. 3584: Advanced Data Mining and Applications (Proc. 1st Int. Conf. ADMA, Wuhan, China, July 22–24, 2005) (Springer-Verlag, Berlin, 2005). pp. 824–831.Google Scholar
  130. 130.
    C. Mathieu and W. Schudy, “Correlation clustering with noisy input,” in Proc. 21st Ann. ACM-SIAM Symp. on Discrete Algorithms, Austin, TX, USA, Jan., 2010 (SIAM, 2010). pp. 712–728.Google Scholar
  131. 131.
    A. Mehrotra and M. A. Trick, “Cliques and clustering: A combinatorial approach,” Oper. Res. Lett. 22 (1), 1–12 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  132. 132.
    A. Medius, G. Acuna, and C. O. Dorso, “Detection of community strcuture in networks via global optimization,” Physica A 358, 396–405 (2005).Google Scholar
  133. 133.
    S. Mimaroglu and M. Yagci, “CLICOM: Cliques for combining multiple clusterings,” Expert Syst. Appl. 39, 1889–1901 (2012).CrossRefGoogle Scholar
  134. 134.
    B. Mirkin and I. Muchnik, “Combinatorial optimization in clustering,” in Handbook of Combinatorial Optimization, Ed. by D.-Z. Du and P. M. Pardalos (Springer-Verlag, New York, 1999) Vol. 2, pp. 261–329.Google Scholar
  135. 135.
    M. Mitchell, “Complex systems: Network thinking,” Artif. Intell. 179, 1194–1212 (2006).CrossRefGoogle Scholar
  136. 136.
    J. W. Moon and L. Moser, “On cliques in graphs,” Israel J. Math. 3 (1), 23–28 (1965).MathSciNetzbMATHCrossRefGoogle Scholar
  137. 137.
    E. Muller, I. Assent, S. Gunnemann, R. Krieger, and T. Seidl, “Relevant subspace clustering: Mining the most interesting non-redundent concepts in high dimensional data,” in Proc. 9th IEEE Int. Conf. on Data Mining, Miami, Florida, USA, Dec. 6–9, 2009 (IEEE, New York, 2009). pp. 377–386.Google Scholar
  138. 138.
    A. C. Muller, S. Nowozin, and C. H. Lampert, “Information theoretic clustering using minimum spanning trees,” in Lecture Notes in Computer Science, Vol. 7476: Proc. Joint 34th DAGM & 36th OAGM Symp. Pattern Recognition, Graz, Aug., 2012, Ed. by A. Pinz et al. (Springer-Verlag, Berlin, 2012). pp. 205–215.Google Scholar
  139. 139.
    T. Murata, “Detecting communities from tripartite networks,” in Proc. World Wide Web. Conf. (WWW’2010), Raleigh, North Carolina, USA, Apr. 26–30, 2010, (Springer-Verlag, Berlin, 2010). pp. 1159–1160.Google Scholar
  140. 140.
    T. Murata, “Modularity for heterogeneous networks,” in Proc. 21th ACM Conf. on Hypertext and Hypermedia (HyperText’2010), Toronto, Canada, June 13–16, 2010 (ACM, 2010). pp. 129–134.Google Scholar
  141. 141.
    L. M. Naeni, R. Berretta, and P. Moscano, “MA-Net: A reliable memetic algorithm for community detection by modularity optimization,” in Proc. 18th Asia Pac. Symp. on Intell. & Evol. Syst. Nov. 2014, Ed. by H. Handa et. al., (Springer-Verlag, 2015). Vol. 1, pp. 311–323.Google Scholar
  142. 142.
    M. E. J. Newman, “Fast algorithm for detecting community structure in networks,” Electr. Prepr., 5 p., (Sep. 22, 2003); http://arxivorg/abs/0309508 [condmatstat-mech]Google Scholar
  143. 143.
    M. E. J. Newman, “Detecting community structure in networks,” Eur. Phys. J. B 38(2), 321–330 (2004).CrossRefGoogle Scholar
  144. 144.
    M. E. J. Newman, “Modularity and community structure in networks,” Proc. Natl. Acad. Sci. USA 103, 8577–8582 (2006).CrossRefGoogle Scholar
  145. 145.
    M. E. J. Newman, Networks: an Introduction (Oxford Univ. Press, Oxford, 2010).CrossRefGoogle Scholar
  146. 146.
    M. E. J. Newman and M. Girvan, “Finding and evaluating community structure in networks,” Electr. Prepr., 16 p., (Aug. 11, 2003); http:// arxivorg/abs/0308217 [cond-matstat-mech]Google Scholar
  147. 147.
    A. Noack and R. Rotta, “Multi-level algorithms for modularity clustering,” Electr. Prepr., 12 p., (Dec. 22, 2008); http://arxivorg/abs/0812.4073 [cs.DC]Google Scholar
  148. 148.
    M. Oosten, J. G. C. Rutten, and F. C. R. Spieksma, “The clique partioning problem: Facets and patching facets,” Networks 38, 209–226 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  149. 149.
    I. H. Osman and N. Christofides, “Capacitated clustering problems by hybrid simulated annealing and tabu search,” Int. Trans, Oper. Res. 1, 317–336 (1994).zbMATHCrossRefGoogle Scholar
  150. 150.
    R. E. Osteen and J. T. Tou, “A clique-detection algorithm based on neighborhoods in graphs,” Int. J. Comput. Inf. Sci. 2, 257–268 (1973).MathSciNetzbMATHCrossRefGoogle Scholar
  151. 151.
    P. R. J. Ostergard, “A new algorithm for the maximumweight clique problem,” in Proc. Electr. Notes in Disc. Math., 6th Twente Workshop on Graphs and Combinatorial Optimization, 1999 (Univ. Twente, Enschede, Netherlands, 1999). Vol. 3, pp. 153–156.MathSciNetGoogle Scholar
  152. 152.
    M. Ovelgonne and A. Geyer-Schulz, “A comparison of agglomerative hierarchical algorithms for modularity clustering,” in Challenges at the Interface of Data Analysis, Computer Science, and Optimization, 2012 (Springer-Verlag, Berlin, 2012). pp. 225–232.CrossRefGoogle Scholar
  153. 153.
    T. Ozyer and R. Alhajj, “Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer,” Appl. Intell. 31, 318–331 (2009).CrossRefGoogle Scholar
  154. 154.
    N. Paivinen, “Clustering with a minimum spanning tree of scale-free-like structure,” Pattern Recogn. Lett. 26, 921–930 (2005).CrossRefGoogle Scholar
  155. 155.
    P. M. Pardalos and J. Xue, “The maximum clique problem,” J. Global Optim. 4, 301–328 (1994).MathSciNetzbMATHCrossRefGoogle Scholar
  156. 156.
    P. Pardalos, M. Batzyn, and E. Maslov, “Cliques and quasi-cliques in large graphs: theory and applications,” in Proc. Int. Conf. on Disc. Optim. & Oper. Res. DOOR-2013, Novosibirsk, June 24–28, 2013 (Sobolev Inst. Math., Novosibirsk, 2013).Google Scholar
  157. 157.
    N. H. Park and W. S. Lee, “Statistical grid-based clustering over data streams,” ACM SIGMOD Record 33, 32–37 (2004).CrossRefGoogle Scholar
  158. 158.
    M. Pavan and M. Pelillo, “Dominant sets and pairwise clustering,” IEEE Trans. Pattern. Anal. Mach. Intell. 29, 167–172 (2007).CrossRefGoogle Scholar
  159. 159.
    W. Pedrycz, Knowledge-Based Clustering: From Data to Information Granules (Wiley, Hoboken, NJ, 2005).CrossRefGoogle Scholar
  160. 160.
    S. J. Peter and S. P. Victor, “A novel algorithm for dual similarity clusters using minimum spanning tree,” J. Theor. Appl. Inform. Technol. 14, 60–66 (2010).Google Scholar
  161. 161.
    S. Pettie and V. Ramashandran, “An optimal minimum spanning tree algorithm,” J. ACM 49, 16–34 (2002).MathSciNetCrossRefGoogle Scholar
  162. 162.
    P. Pons and M. Latapy, “Computing communities in large networks using random works,” J. Graph. Alg. Appl. 10, 191–218 (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  163. 163.
    M. A. Porter, J.-P. Onnela, and P. J. Mucha, “Communities in networks”. Notices AMS 56, 1082–1097, 1164 (2009).MathSciNetzbMATHGoogle Scholar
  164. 164.
    J. Reichardt and S. Bornholdt, “Statistical mechanics of community detection,” Phys. Rev. E 74, 016110, (2006).MathSciNetCrossRefGoogle Scholar
  165. 165.
    C. Rocha, L. C. Dias, and I. Dimas, “Multicriteria classification with unknown categories: A clusteringsorting approach and an application to conflict management,” J. Multi-Cri. Dec. Anal. 20, 13–27 (2013).CrossRefGoogle Scholar
  166. 166.
    C. Rocha and L. C. Dias, “MPOC an agglomerative algorithm for multicriteria partially ordered clustering,” Quart. J. Operat. Res. (4OR) 11, 253–273 (2013).MathSciNetzbMATHCrossRefGoogle Scholar
  167. 167.
    M. Rosvall and C. T. Bergstrom, “An information-theoretic framework for resolving community structure in complex networks,” Proc. Natl. Acad. Sci. USA (PNAS) 104, 7327–7331 (2007).CrossRefGoogle Scholar
  168. 168.
    B. Roy, Multicriteria Methodology for Decision Aiding (Kluwer, Dordrecht, 1996).zbMATHCrossRefGoogle Scholar
  169. 169.
    R. Y. Rubinstein, “Cross-entropy and rare-events for maximal cut and partition problems,” ACM Trans. Model. Comput. Simul. 12 (1), 27–53 (2002).CrossRefGoogle Scholar
  170. 170.
    F. Saeed, N. Salim, and A. Abdo, “Voting-based consensus clustering for combining multiple clusterings of chemical structures,” J. Cheminf. 4 (37), 1–8 (2012).zbMATHGoogle Scholar
  171. 171.
    J. Salzmann, R. Behnke, M. Gag, and D. Timmermann, “4-MASCLE improved coverage aware clustering with self healing abilities,” in Proc. IEEE Symp. & Workshops on Ubiquitous, Autonomic and Trusted Computing (UIC-ATC’09), Brisbane, Australia, July 7–9, 2009 (IEEE, New York, 2009). pp. 537–543.CrossRefGoogle Scholar
  172. 172.
    S. E. Schaeffer, “Graph clustering,” Comput. Sci. Rev. 1, 27–64 (2007).zbMATHCrossRefGoogle Scholar
  173. 173.
    A. Schenker, M. Last, H. Bunke, and A. Kandel, “Classification of web documents using graph matching,” Int. J. Pattern Recognit. Artif. Intell. 18, 475–496 (2004).CrossRefGoogle Scholar
  174. 174.
    S. Selim and K. Alsultan, “A simulated annealing algorithm for the clustering problems,” Pattern Recogn. 24, 1003–1008 (1991).MathSciNetCrossRefGoogle Scholar
  175. 175.
    H. M. Selim, R. G. Askin, and A. J. Vakharia, “Cell formation in group technology: review, evaluation and direction for future research,” Comput. Ind. Eng. 34 (1), 3–20 (1998).CrossRefGoogle Scholar
  176. 176.
    R. Shamir, R. Sharan, and D. Tsur, “Cluster graph modification problems,” in Lecture Notes in Computer Science, Vol. 2573: Proc. 28th Int. Workshop on GraphTheoretic Concepts in Computer Science, Cesky Krumlov, Czech Republic, June 13-15, 2002 (Springer-Verlag, Berlin, 2002). pp. 379–316.Google Scholar
  177. 177.
    R. Shamir, R. Sharan, and D. Tsur, “Cluster graph modification problems,” Disc. Appl. Math. 144, 173–182 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  178. 178.
    G. Sheikholeslami, C. Chattterjee, and A. Zhang, “WaveCluster: a wavelet-based clustering approach for spatial data in very large databases,” The VLDB J. 8, 289–304 (2000).CrossRefGoogle Scholar
  179. 179.
    H. Shiokawa, Y. Fujiwara, and M. Onizuka, “Fast algorithm for modularity-based graph clustering,” in Proc. 27th AAAI Conf. on Artificial Intelligence (AAAI 2013), Bellevue, WA, USA 2013 (AAAI, 2013). 1170–1176.Google Scholar
  180. 180.
    D. A. Spielman and S.-H. Teng, “A local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning,” SIAM J. Comput. 42, 1–26 (2013).MathSciNetzbMATHCrossRefGoogle Scholar
  181. 181.
    G. Srinivasan, “A clustering algorithm for machine cell formation in group technology using minimum spanning tree,” Int. J. Prod. Res. 32, 2149–2158 (1994).zbMATHCrossRefGoogle Scholar
  182. 182.
    C. S. Sung and H. W. Jin, “A Tabu-search-based heuristic for clustering,” Pattern Recogn. 33, 849–858 (2000).CrossRefGoogle Scholar
  183. 183.
    C. Swamy, “Correlation clustering: maximizing agreements via semidifinite programming,” in 15th Ann. ACM-SIAM Symp. on Discrete Algorithms (SODA), New Orleans, LA, Jan., 2004 (SIAM, 2004). pp. 526–527.Google Scholar
  184. 184.
    J. Tabor and P. Spurek, “Cross-entropy clustering,” Pattern Recogn. 47, 3046–3059 (2014).CrossRefGoogle Scholar
  185. 185.
    J. Tillet, R. Rao, and F. Sahin, “Cluster-head identification in ad hoc sensor networks using particle swam optimization,” in Proc. 2002 IEEE Int. Conf. on Personal Wireless Commun., New Delhi, India, Dec. 2002 (IEEE, Piscataway, 2002). pp. 201–205.Google Scholar
  186. 186.
    A. Trifunovic and W. J. Knottenbelt, “Parallel multilevel algorithms for hypergraph partitioning,” J. Paral. Distr. Comput. 68, 563–581 (2008).zbMATHCrossRefGoogle Scholar
  187. 187.
    C.-F. Tsai and C.-C. Yen, “ANGEL: a new effective and efficient hybrid clustering techniques for large databases,” in Lecture Notes in Computer Science, Vol. 4426: Proc. 11th Pacific-Asia Conf. on Knowledge Discovery and Data Mining (PAKDD’2007), Nanjing, China, May 22–25, 2007, Ed. by Z.-H. Zhou et. al. (Springer-Verlag, Berlin, 2007). pp. 817–824.Google Scholar
  188. 188.
    C.-F. Tsai, H.-F. Yeh, J.-F. Chang, and N.-H. Liu, “PHD: an efficient data clustering scheme using partition space technique for knowledge discovery in large databases,” Appl. Intell. 33 (1), 39–53 (2010).CrossRefGoogle Scholar
  189. 189.
    C.-W. Tsai, H.-J. Song, and M.-C. Chiang, “A hyperheuristic clustering algorithm,” in Proc. 2012 IEEE Int. Conf. on Systems, Man, Cybernetics (SMC’2012) Seoul, Korea (South), Oct. 14–17, 2012 (IEEE, New York, 2012). pp. 2839–2844.Google Scholar
  190. 190.
    L. Y. Tseng and S. B. Yang, “A genetic approach to the automatic clustering problem,” Pattern Recogn. 34, 415–424 (2001).zbMATHCrossRefGoogle Scholar
  191. 191.
    K. Tsuda and T. Kudo, “Clustering graphs by wieghted substructure mining,” in Proc. 23rd Int. Conf. on Mach. Learn., Pittsburgh, Pennsylvania, USA, June 25–29, 2006 (Carnegie Mellon Univ., Pittsburgh, 2006). pp. 953–960.Google Scholar
  192. 192.
    K. Turner and A. K. Agogino, “Ensemble clustering with voting active clusters,” Pattern Recogn. Lett. 29, 1947–1953 (2008).CrossRefGoogle Scholar
  193. 193.
    D. W. Van der Merwe and A. P. Engelbrecht, “Data clustering using particle swam optimization,” in Proc. 2003 IEEE Congr. on Evolutionary Computation (CEC’2003), Newport Beach, California, June, 2003 (IEEE, New York, 2003). Vol. 1, pp. 215–220.CrossRefGoogle Scholar
  194. 194.
    A. Vashist, C. A. Kulikowsky, and I. Muchnik, “Orthlog clustering on a multipartite graph,” IEEE/ACM Trans. Comput. Biology Bioinform. 4, 17–27 (2007).CrossRefGoogle Scholar
  195. 195.
    S. Vega-Pons and J. Ruiz-Schulcloper, “A survey of clustering ensemble algorithms,” Int. J. Pattern Recogn. Artif. Intell. 25, 337–372 (2011).CrossRefGoogle Scholar
  196. 196.
    K. Wakita and T. Tsusumi, “Finding community structure in mega-scale social networks,” Electr. Prepr., 9 p., Fev. 8 (2007). http://arxivorg/abs/0702.2048 [cs.CY]Google Scholar
  197. 197.
    X. Wang, X. Wang, and X. Wikes, “A divide-and-conquer approach for minimum spanning tree-based clustering,” IEEE Trans. Knowledge Data Eng. (KDE) 21, 945–958 (2009).CrossRefGoogle Scholar
  198. 198.
    Q. Wang and E. Fleury, “Overlapping community structure and modular overlaps in complex networks,” in Lecture Notes in Social Networks, Part: Mining Social Networks and Security Informatics, Ed. by T. Ozyer et al. (Springer, Berlin, 2013). pp. 15–40.CrossRefGoogle Scholar
  199. 199.
    S. White and P. Smyth, “A spectral clustering approach to finding communities in graph,” in Proc. SIAM Data Mining Conf., Trondheim, Norway, Aug. 30–Sept. 2, 2005 (SIAM, 2005). pp. 76–84.Google Scholar
  200. 200.
    J. Xie, S. Kelley, and B. K. Szymanski, “Overlapping community detection in networks: The state-of-theart and comparative study,” ACM Comp. Surv. 45 (4) art. 443 (2013).CrossRefGoogle Scholar
  201. 201.
    Y. Xu, V. Olman, and D. Xu, “Minimum spanning trees for gene expression data clustering,” Genome Inf. 12, 24–33 (2001).Google Scholar
  202. 202.
    X. Xu, N. Yuruk, Z. Feng, and T. A. J. Schweiger, “SCAN: a structural clustering algorithm for networks,” in Proc. Int. Conf. on Knowledge Discovery and Data Mining (SIGKDD-07), San Jose, Aug. 2007 (ACM, 2007). 824–833.Google Scholar
  203. 203.
    B. Yan and S. Gregory, “Detecting communities in networks by merging cliques,” in Proc. 2nd Int. Conf. on Interaction Sciences: Information Technology, Culture and Human (ICIS 2009), Seoul, Korea (South), Nov. 24–26, 2009 (IEEE, New York, 2009). 832–836.Google Scholar
  204. 204.
    Y. Yang and M. S. Kamel, “An aggregated clustering approach using multi-ant colonies algorithms,” Pattern Recogn. 39, 1278–1289 (2006).zbMATHCrossRefGoogle Scholar
  205. 205.
    J. Yang and J. Leskovec, “Overlapping community detection at scale: A nonnegative matrix factorization approach,” in Proc. 6th ACM Int. Conf. on Web Search and Data Mining (WSDM’2013), Rome, Feb. 4–8, 2013 (ACM, 2013). 587–596.Google Scholar
  206. 206.
    J. Yang and J. Leskovec, “Overlapping communities explain core-periphery organization of networks,” Proc. IEEE 102, 1892–1902 (2014).CrossRefGoogle Scholar
  207. 207.
    J. Yang and J. Leskovec, “Structure and overlaps of ground-truth communities in networks,” ACM Trans. Intell. Syst. Technol. (TIST) 15 (2), art. 26 (2014).Google Scholar
  208. 208.
    J. Yang and J. Leskovec, “Designing and evaluation network communities based on ground-truth,” Knowl. Inf. Syst. 42 (1), 181–213 (2015).CrossRefGoogle Scholar
  209. 209.
    A. C. Yao, “E loglog V ) algorithm for finding minimum spanning trees,” Inf. Process. Lett. 4 (1), 21–23 (1975).zbMATHCrossRefGoogle Scholar
  210. 210.
    D. Y. Yeh, “A dynamic programming approach to the complete set partitioning problem,” BIT Numer. Math. 26, 467–474 (1986).zbMATHCrossRefGoogle Scholar
  211. 211.
    O. Younis, M. Krunz, and S. Ramasubramanian, “Node clustering in wireless sensor networks: Recent developments and deployment challenges,” IEEE Networks 20 (3), 20–25 (2006).CrossRefGoogle Scholar
  212. 212.
    W. W. Zachary, “An information flow model for conflict and fission in small groups,” J. Anthropol. Res. 33, 452–473 (1977).Google Scholar
  213. 213.
    E. Ziv, M. Middendorf, and C. Wiggins, “Information-theoretic approach to network modularity,” Phys. Rev. E 71, 046117 (2005).MathSciNetCrossRefGoogle Scholar
  214. 214.
    C. Zopounidis and M. Doumpos, “Multicriteria classification and sorting methods: a literature review,” Eur. J. Operat. Res. (EJOR) 138, 229–246 (2002).MathSciNetzbMATHCrossRefGoogle Scholar

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© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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