Skip to main content
Log in

On dynamic combinatorial clustering

Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract

The paper addresses dynamic combinatorial clustering. First, a systematic literature survey on dynamic/online clustering is presented (problems, methods, applications). Second, restructuring approach to clustering is described (one-stage clustering, multi-stage clustering, sorting). Third, two network application examples of dynamic/multistage clustering are examined: (a) multi-stage connection of users to access points, (b) partition coloring problem in optical networks (wavelength routing and assignment).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. Aaron, D. E. Tamir, N. D. Rishe, and A. Kandel, “Dynamic incremental k-means clustering,” in Proc. 2014 Int. Conf. on Computational Science and Computational Intelligence (CSCI’14), Las Vegas, March 10–13, 2014 (Am. Council on Science and Education (ACSE), 2014), pp. 308–313.

    Google Scholar 

  2. A. A. Abbasi and M. Younis, “A survey on clustering algorithms for wireless sensor networks,” Comp. Commun. 30 (14–15), 2826–2841 (2007).

    Article  Google Scholar 

  3. C. C. Aggarwal et al., “A framework for clustering evolving data streams,” in Proc. 29th Int. Conf. on Very Large Data Bases, Berlin, Sept. 12–13, 2003, (VLDB, Berlin, 2003). pp. 81–92.

    Google Scholar 

  4. C. C. Aggarwal (Ed.), Data Streams: Models and Algorithms (Springer-Verlag, 2007).

    MATH  Google Scholar 

  5. C. C. Aggarwal, Outlier Analysis (Springer-Verlag, NewYork, 2013).

    Book  MATH  Google Scholar 

  6. B. M. Ahamed Shafeeq and K. S. Hareesha, “Dynamic clustering of data with modified k-means algorithm,” in Proc. Int. Conf. on Information and Computer Networks (ICICN 2012), 2012 (IACSIT Press, Singapore, 2012), Vol. 27, pp. 221–225.

    Google Scholar 

  7. J. Azorin-Lopez, M. Saval-Calvo, and A. Fuster- Guillo, “A predictive model for recognizing human behaviour based on trajectrory representation,” in Proc. Int. Joint Conf. on Neural Networks, 2014 (IEEE, New York, 2014), pp. 1494–1501.

    Google Scholar 

  8. L. Bahiense, Y. Frota, N. Maculan, T. F. Noronha, and C. C. Ribeiro, “A branch-and-cut algorithm for the equitable coloring problem using a formulation by representatives,” Disc. Appl. Math. 164, pp. 34–46 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Bandyopadhyay, C. Giennella, U. Maulik, H. Kargupta, K. Liu, and S. Datta, “Clustering distributed data streams in peer-to-peer environment,” Inf. Sci. 176 (14), 1952–1985 (2006).

    Article  Google Scholar 

  10. S. Banerjee and S. Khuller, “A clustering scheme for hierarchical control in multihop wireless networks,” Proc. IEEE INFOCOM, 1028–1037 (2001).

    Google Scholar 

  11. W. Barbakh and C. Fife, “Online clustering algorithms,” Int. J. Neural Systems 18 (03), 185–194 (2008).

    Article  Google Scholar 

  12. A. Benslimane, T. Taleb, and R. Sivaraj, “Dynamic clustering-based adaptive mobile gateway management in integrated VANET-3G heterogeneous wireless networks,” IEEE J. on Selected Areas in Commun. 29, 559–570 (2011).

    Article  Google Scholar 

  13. J. Beringer and E. Hullermaier, “Online clustering of parallel data streams,” Data and Knowledge Engineering, 58, 180–204, (2006).

    Article  Google Scholar 

  14. T. Campbell, M. Liu, B. Kulis, J.P. How, and L. Carin, “Dynamic clustering via asymptotics of dependent Dirichlet process mixture,” Electron. Preprint, Nov. 1 (2013). http://arxiv.org/abs/1305.6659 [cs.LG].

  15. F. Cao, M. Ester, W. Qian, and A. Zhou, “Densitybased clustering over an evolving data stream with noise,” in SDM, (SIAM, 2006), Vol. 6, pp. 328–339.

    Google Scholar 

  16. D. Cavendish and M. Gerla, “Rouitng optimizaiton in communication networks,” in Combinatorial Optimization in Communication Networks, Ed. by M. X. Cheng, Y. Li, D.-Z. Du, (Springer-Verlag, 2006), pp. 505–547.

    Chapter  Google Scholar 

  17. T. M. Chan and H. Zarrabi-Zadeh, “A randomized algorithm for online unit clustering,” in Approximation and Online Algorithms (Springer-Verlag, 2007), pp. 121–131.

    Chapter  Google Scholar 

  18. A. Chattopadhyay, B. Blaszczyszyn, and E. Altman, “Cell planning for mobility management in heterogeneous cellular networks,” Electron. Preprint, May 24, (2016). http://arxiv.org/abs/1605.07341 [cs.NI].

    Google Scholar 

  19. W.-P. Chen, J. C. Hou, and L. Sha, “Dynamic clustering for acoustic target tracking in wireless sensor networks,” IEEE Trans. Mobile Comput. 3, 258–271 (2004).

    Article  Google Scholar 

  20. C. Chinrungrueng and C.H. Sequin, “Optimal adaptive k-means algorithm with dynamic adjustment of learning rate,” TR-91-017, Dept. of Electrical Eng. and CS (Univ. of California, Berkeley, 1991).

  21. G. Cormode and S. Muthikrishnan, “Space eficient mining of multigraph streams,” in Proc. 24th ACM SIGMOD- SIGACT-SIGART Symp. on Principles of Database Systems PODS, 2005 (ACM, 2005), pp. 271–282.

    Google Scholar 

  22. F. G. da Costa, R. A. Rios, and R. F. de Mello, “Using dynamical systems tools to detect concept drift in data streams,” Expert Systems with Appl. (ESwA) 60, 39–50, (2016).

    Article  Google Scholar 

  23. F. Crespo and R. Weber, “A methodology for dynamic data mining based on fuzzy clustering,” Fuzzy Sets Systems 150, 267–284, (2005).

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Csirik, L. Epstein, C. Imreh, and A. Levin, “Online clustering with variable sized clusters,” Algorithmica 65, 251–274 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  25. J. C. da Silva, C. Giennella, R. Bhargava, H. Kargupta, and M. Klusch, “Distributed data mining and agents,” Eng, Appl. AI, 18 (1), 791–807 (2005).

    Article  Google Scholar 

  26. J. Darmont, C. Fromantin, L. Gruenwald, and M. Schneoder, “Dynamic clustering in object-oriented databases: An advocacy for simplicity,” Electron. Preprint, 15 pp., May (2007). http://arxiv.org/abs/0705.0281.

    Google Scholar 

  27. S. Datta, C. Giannella, and H. Kargupta, “K-means clustering over a large, dynamic networks,” in Proc. SIAM Conf. SDM'06, 2006, pp. 153–164.

    Google Scholar 

  28. E. Diday, “The dynamic cluster method in non-hierarchical clustering,” J. Comput. Inf. Sci. 2, 61–88 (1973).

    Article  MATH  Google Scholar 

  29. A. Eckstein, “Automated flight track taxonomy for measuring benefits from performance based navigation,” in Proc. Integrated Communications, Navigation and Surveillance Conf., (ICNS) 2009 (IEEE, New York, 2009).

    Google Scholar 

  30. M. Enriquez, “Identifying temporally persistent flow in the terminal airspace via spectral clustering,” in Proc. 10th USA/Europe Air Trac management Research and Development Seminar ATM’13, Chicago, 2013 (ATM, Chicago, 2013).

    Google Scholar 

  31. M. Enriquez and C. Kurcz, “A simple and robust flow detection algorithym based on spectral clustering,” in Proc. 5th Int. Conf. on Research in Air Transportation (ICRAT 2012), May 22–25, 2012 (Univ. Berkley, California, 2012).

    Google Scholar 

  32. Y. Fan, Q. Xu, Y. Guo, and S. Liang, “Visualization on agglomerative information bottleneck based trajectory clustering,” in Proc. 19th Int. Conf. Information Visualization (IV), 2015, pp. 557–560.

  33. N. Fereora, J. T. Klosowski, C. E. Scheidegger, and C. T. Silva, “Vector field k-means: Clustering trajectories by fitting multiple vector fields,” Electr. Preprint, Aug. 2012. http://arxiv/abs/1208.5801.

    Google Scholar 

  34. A. Fernandez-Caballero, J. C. Castillo, and J. M. Rodriguez-Sabchez, “Human activity monitoring by local and global finite state machines,” ESwA 39, 6982–6993 (2012).

    Google Scholar 

  35. S. Fomin and A. Zelevinsky, “Cluster algebras I: Foundations,” J. Am. Math. Soc. 15, 497–520 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  36. Y. Frota, N. Maculan, T. F. Noronha, and C. Ribeiro, “A branch-and-cut algorithm for partition coloring,” Networks, 55, 194–204 (2010).

    MathSciNet  MATH  Google Scholar 

  37. M. M. Gaber, A. Zaslavsky, and S. Krishnaswamy, “Mining data streams: A review” ACM SIGMOD Record, 34 (2), 18–26 (2005).

  38. M. M. Gaber, A. Zaslavsky, and S. Krishnaswamy, “Data streams mining,” in Data Mining and Knowledge Discovery Hanbook, Part 6, 759–787 (2010).

    MATH  Google Scholar 

  39. S. Gaffney and P. Smyth, “Trajectory clustering with mixtures of regression models,” in Proc. 5th Int. Conf. on Knowledge Discovery and Data Mining ACM SIGKDD KDD'99, pp. 63–72, (ACM, 1999).

    Google Scholar 

  40. J. Gama and M. M. Gaber, Learning from Data Streams (Springer, Berlin, 2007).

    Book  MATH  Google Scholar 

  41. J. Gama, Knowledge Discovery from Data Streams (Chapman & Hall/CRC, Boca Raton, FL, 2010).

    Book  MATH  Google Scholar 

  42. M. Gariel, A. N. Srivastava, and E. Feron, “Trajectory clustering and an application to airspace monitoring,” IEEE Trans. on Intell. Transport. Syst. 12, 1511–1524, (2011).

    Article  Google Scholar 

  43. M. Gekhtman, M. Shapiro, and A. Vainshtein, “Higher pentagram maps, wieghted directed networks, and cluster dynamics,” Electronic Preprint, (Jan. 2, 2012). http://arxiv.org/abs/1110.0472 [math.QA].

    MATH  Google Scholar 

  44. M. Glick, “The pentagram map and Y-patterns,” Electronic Preprint, (Apr. 15, 2011). http://arxiv.org/abs/1005.0598 [math.CO].

    MATH  Google Scholar 

  45. S. Guha, N. Mishra, R. Motwani, and L. O’Callaghan, “Clustering data streams,” in Proc. 41st Annual IEEE Symp. on Foundations of Computer Science (FOCS), 2000 (IEEE, New York, 2000), pp. 359–366.

    Chapter  Google Scholar 

  46. S. Guha, N. Koudas, and K. Shim, “Data streams and histograms,” in Proc. ACM STOC, 2001, pp. 471–475.

  47. J. Hopcroft, O. Khan, B. Kulis, and B. Selman, “Tracking evolving communities in large linked networks” Proc. Nat. Acad. Sci. USA 101 (Suppl 1), 5249–5353 (2004).

    Article  Google Scholar 

  48. E. A. Hoshino, Y. A. Frota, and C. C. de Souza, “A branch-and-price approach for the partition coloring problem,” Oper. Res. Lett. 39 (2), 132–137 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  49. J. Jedrzejowicz and P. Jedrzejowicz, “Distance-based online classifiers,” ESwA 60, 249–257 (2016).

    MATH  Google Scholar 

  50. M. Roriz Junior, M. Endler, and F. Jose da Silva e Silva, “An on-line algorithm for cluster detection of mobile nodes through complex event processing,” Inform. Syst. (2016) (in press).

    Google Scholar 

  51. P. Kalnis and N. Mamaoulis, “On discovering moving clusters in spatio-temporal data,” in Proc. of the 9th Int. Symp. on Spatial and Temporal Databases, 2005 (Springer, 2005), pp. 364–381.

    Google Scholar 

  52. K. Kaneko, “Relevance of dynamic clustering to biological networks,” Phys. D: Nonlinear Phenomena 75, 55–73 (1994).

    Article  MATH  Google Scholar 

  53. G. Karypis, E.-H. Han, and V. Kumar, “Chamaleon: hierarchical clustering using dynamical modeling,” IEEE Computer, 68–75 (1999).

    Google Scholar 

  54. E. A. Khalil and B. Attea, “Energy-aware evolutionary routing protocol for dynamic clustering of wireless sensor networks,” Swarm and Evolutionary Comput. 1 (4), 195–203 (2011).

    Article  Google Scholar 

  55. N. Kim, J. Heo, H. S. Kim, and W. H. Kwon, “Reconfiguration of clusterheads for load balancing in wireless sensor networks,” Comput. Commun. 31 (1), 153–159 (2008).

    Article  Google Scholar 

  56. G. Kreml, I. Zliobaite, D. Brzezinski, E. Hullermeier, M. Last, V. Lemaire, et al., “Open challenges for data stream mining research,” ACM SIGKDD Explorations Newsletter, 16 (1), 1–10 (2014).

    Article  Google Scholar 

  57. R. Krishnan and D. Starobinski, “Efficient clustering algorithms for self-organizing wireless sensor networks,” Ad Hoc Netwokrs 4 (1), 36–59 (2006).

    Article  Google Scholar 

  58. M. Last, “Online classication of nonstationary data streams,” Intell. Data Analysis, 6, 129–147 (2002).

    MATH  Google Scholar 

  59. J.-G. Lee, J. Han, and K. Y. Whang, “Trajectory clustering: A partition-and-group framework,” in Proc. 2007 ACM SIGMOD Int. Conf. on Management of Data, 2007 (ACM, New York, 2007), pp. 593–604.

    Google Scholar 

  60. J.-G. Lee, J. Han, and X. Li, “A unifying framework of mining trajectory patterns of various temporal tightness,” IEEE Trans. Knowl. Data Eng. 27, 1478–1490 (2015).

    Article  Google Scholar 

  61. M. Sh. Levin, “Towards communication network development (structural system issues, combinatorial models),” in Proc. 2010 IEEE Region 8 Int. Conf. SIBIRCON-2010, Baikal-Hotel, Irkutsk, Russia, July 11–15, 2010 (IEEE, New York, 2010), Vol. 1, pp. 204–208.

    Google Scholar 

  62. M. Sh. Levin, “Clique-based fusion of graph streams in multi-function system testing,” Informatica 23, 391–404 (2012).

    MathSciNet  Google Scholar 

  63. M. Sh. Levin, Modular System Design and Evaluation (Springer, 2015).

    Book  Google Scholar 

  64. M. Sh. Levin, “Towards combinatorial clustering: preliminary research survey,” Electron. Preprint., (May 28, 2015). http://arxiv.org/abs/1505.07872 [cs.AI].

  65. M. Sh. Levin, “On combinatorial clustering: literature review, methods, examples,” J. Commun. Technol. Electron. 60, 1403–1428, (2015).

  66. M. Sh. Levin, “Towards integrated glance to restructuring in combinatorial optimization,” Electron. Preprint., (Dec. 20, 2015). http://arxiv.org/abs/1512.06427 [cs.AI].

  67. M. Sh. Levin, “Towards bin packing (preliminary problem survey, models with multiset estimates),” Elec. Preprint, (May 24, 2016). http://arxiv.org/abs/1605.07574 [cs.AI].

  68. M. Sh. Levin and M. Petukhov, “Multicriteria assignment problem (selection of access points),” in Proc. IEA/AIE, LNCS 6097, Cordoba, Spain, 2010, (Springer, Cordoba, Spain, 2010), part II, pp. 277–287.

    Google Scholar 

  69. G. Li and R. Simha, “The partition coloring problem and its application to wavelength routing and assignment,” in Proc. First Workshop on Optical Networks, CDROM, Dallas, 2000, p. 1.

    Google Scholar 

  70. W. Liu, Z. Wang, and J. Feng, “Continuous clustering of moving objects in spatial networks,” in Proc. 12th Int. Conf. on Knowledge-Based Intelligent Information and Engineering Systems (KES'08), 2008 (Springer, Berlin, 2008), Part II, 543–550.

    Chapter  Google Scholar 

  71. Z. Liu, W. Guo, Q. Shi, W. Hu, and M. Xia, “Sliding scheduled lightpath provisioning by mixed partition coloring in WDM optical networks,” Opt. Switching and Networking 10 (1), 44–53, (2013).

    Article  Google Scholar 

  72. S. Luhr and M. Lazarescu, “Incremental clustering of dynamic data streams using connectivity based representative points,” Data Knowledge Eng. 68 (1), 1–27 (2009).

    Article  Google Scholar 

  73. D. Menas-Torres and J. Aguilar-Ruiz, “A similaritybased approach for data stream classification,” ESwA 41, 4224–4234 (2014).

    Google Scholar 

  74. M. Millan-Giraldo, J. S. Sanchez, and V. J. Traver “On-line learning from streaming data with delayed attributes: a comparison of classifiers and strategies,” Neural Comput. Appl. 20, 935–944 (2011).

    Article  Google Scholar 

  75. S. Muthukrishnan, Data Streams: Algorithms and Applications (Now Publishers Inc., 2005).

    MATH  Google Scholar 

  76. T. M. Nguyen and Q. M. J. Wu, “Dynamic fuzzy clustering and its application in motion segmentation,” IEEE Trans. on Fuzzy Systems 21, 1019–1031 (2013).

    Article  Google Scholar 

  77. T. F. Noronha and C. C. Ribeiro, “Routing and wavelength assignment by partition coloring,” Eur. J. Operat. Res. (EJOR) 171, 797–810 (2006).

    Article  MATH  Google Scholar 

  78. O. Ossama, H. M. O. Mokhtar, and M. E. El-Sharkawi, “An extended k-means technique for clustering moving objects.” Egyptian Inf. J. 12 (1), 45–51 (2011).

  79. O. Ossama, H. M. O. Mokhtar, and M. E. El-Sharkawi, “Dynamic k-means: a clustering technique for moving object trajectories,” Int. J. Intell. Inf. Database Syst., 6, 307–327 (2012).

    Google Scholar 

  80. S. K. Pal and S. Mitra, “Fuzzy dynamic clustering algorithm,” Pattern Recogn. Lett. 11, 525–535 (1990).

    Article  MATH  Google Scholar 

  81. A. Papadogiannis, D. Gesbert, and E. Hardouin, “A dynamic clustering approach in wireless networks with multi-cell cooperative processing,” in Proc. IEEE Int. Conf. on Communications (ICC'08), 2008, (IEEE, New York, 2008), pp. 4033–4037.

    Google Scholar 

  82. C. M. Pereira and R. F. de Mello, “Ts-stream: clustering time series on data streams,” J. Intell. Inform. Syst., 42, 531–566, (2014).

    Google Scholar 

  83. U. Pferschy, R. Rudolf, and G. J. Woeginger, “Some geometric clustering problems,” Nordic J. Comput. 1, 246–263 (1994).

    MathSciNet  Google Scholar 

  84. C. Piciarelli, G. I. Foresti, and L. Suidara, “Trajectory clustering and its applications for video surveillance,” in IEEE Conf. on Advanced Video and Signal Based Surveillance AVSS 2005, (IEEE, New York, 2005), pp. 40–45.

    Chapter  Google Scholar 

  85. S. Pramod and O. P. Vyas, “Data stream mining: A review on windowing approach,” Global J. Computer Sci. Technol. Software and Data Engineering, 12 (11), 26–30 (2012).

    Google Scholar 

  86. M. Sato-Ilic, “Dynamic fuzzy clustering using fuzzy cluster loading,” Int. J. General Syst. 35 (2), 209–230, (2006).

    Article  MathSciNet  MATH  Google Scholar 

  87. A. Shaker and E. Hullermeier, “IBL streams: A system for instance-based classification and regression on data streams,” Evolving Syst. 3 (4), 235–249 (2013).

    Article  Google Scholar 

  88. Y. Shi and A. Zhang, “Dynamic clustering and indexing of multi-dimensional datasets,” in Proc. 4th Int. Conf. on Informaiton Fusion, 2001.

    Google Scholar 

  89. B. Wang, H. B. Lim, and D. Ma, “A coverage-aware clustering protocol for wireless sensor networks,” Computer Networks 56, 1599–1611 (2012).

    Article  Google Scholar 

  90. D. Yang, E. A. Rundensteiner, and M. O. Ward, “Mining neighbor-based patterns in data streams,” Inform. Syst., 38, 331–350 (2013).

    Article  Google Scholar 

  91. O. Younis, M. Krunz, and S. Ramasubramanian, “Node clustering in wireless sensor networks: Recent developments and deployment challenges,” IEEE Networks, 20–25, May/June (2006).

    Google Scholar 

  92. M. Yu, K. K. Leung, and A. Malvankar, “A dynamic clustering and energy eficient routing technique for sensor networks,” IEEE Trans. Wireless Commun. 6, 3069–3079 (2007).

    Article  Google Scholar 

  93. K. R. Zalik and B. Zalik, “A sweep-line algorithm for spatial clustering,” Adv. Engineering Software 40, 445–451 (2009).

    Article  MATH  Google Scholar 

  94. O. Zamir and O. Etzioni, “Grouper: a dynamic clustering interface to Web search results,” Computer Networks 31, 1361–1374 (1999).

    Article  Google Scholar 

  95. D. Zhang, and Y. Dong, “Semantic, hierarchical, online clustering of web search results,” in Advanced Web Technologies and Applications (Springer-Verlag, 2004), pp. 69–78.

    Chapter  Google Scholar 

  96. C. Zopounidis and M. Doumpos, “Multicriteria classification and sorting methods: a literature review,” Eur. J. Operat. Res. 138, 229–246 (2002).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Sh. Levin.

Additional information

Published in Russian in Informatsionnye Protsessy, 2016, Vol. 16, No. 2, pp. 177–193

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Levin, M.S. On dynamic combinatorial clustering. J. Commun. Technol. Electron. 62, 718–730 (2017). https://doi.org/10.1134/S1064226917060122

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226917060122

Keywords

Navigation