Journal of Systems Science and Complexity

, Volume 31, Issue 5, pp 1128–1145 | Cite as

Distributed Consensus-Based K-Means Algorithm in Switching Multi-Agent Networks

  • Peng LinEmail author
  • Yinghui Wang
  • Hongsheng Qi
  • Yiguang Hong


This paper discusses a distributed design for clustering based on the K-means algorithm in a switching multi-agent network, for the case when data are decentralized stored and unavailable to all agents. The authors propose a consensus-based algorithm in distributed case, that is, the double-clock consensus-based K-means algorithm (DCKA). With mild connectivity conditions, the authors show convergence of DCKA to guarantee a distributed solution to the clustering problem, even though the network topology is time-varying. Moreover, the authors provide experimental results on various clustering datasets to illustrate the effectiveness of the fully distributed algorithm DCKA, whose performance may be better than that of the centralized K-means algorithm.


Consensus-based algorithm distributed K-means clustering multi-agent network switching topology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Nedic A and Ozdaglar A, Distributed subgradient methods for multi-agent optimization, IEEE Trans. Automatic Control, 2009, 54(1): 48–61.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Lou Y C, Hong Y G, and Shi G D, Target aggregation of second-order multi-agent systems with switching interconnection, Journal of Systems Science and Complexity, 2012, 25(3): 430–440.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Yi P and Hong Y G, Stochastic sub-gradient algorithm for distributed optimization with random sleep scheme, Control Theory and Technology, 2015, 13(4): 333–347.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Lou Y C, Hong Y G, and Wang S Y, Distributed continuous-time approximate projection protocols for shortest distance optimization problems, Automatica, 2016, 69: 289–297.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Liu X Y, Sun J, Dou L H, et al., Leader-following consensus for discrete-time multi-agent systems with parameter uncertainties based on the event-triggered strategy, Journal of Systems Science and Complexity, 2017, 30(1): 30–45.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Fayyad U M, Piatetsky-Shapiro G, Smyth P, et al., Advances in Knowledge Discovery and Data Mining, AAAI Press, Menlo Park, California, 1996.Google Scholar
  7. [7]
    Basu S, Davidson I, and Wagstaff K, Constrained Clustering: Advances in Algorithms, Theory, and Applications, CRC Press, Boca Raton, USA, 2008.zbMATHGoogle Scholar
  8. [8]
    Jain A K and Dubes R C, Algorithms for Clustering Data, Prentice-Hall, Inc., 1988.zbMATHGoogle Scholar
  9. [9]
    Jain A K, Data clustering: 50 years beyond K-means, Pattern Recognition Letters, 2010, 31(8): 651–666.CrossRefGoogle Scholar
  10. [10]
    Lloyd S, Least squares quantization in PCM, IEEE Trans. Information Theory, 1982, 28(2): 129–137.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Bottou L and Bengio Y, Convergence properties of the K-means algorithms, Advances in Neural Information Processing Systems, 1995, 25(2): 585–592.Google Scholar
  12. [12]
    Ostrovsky R, Rabani Y, Schulman L J, et al., The effectiveness of lloyd-type methods for the Kmeans problem, Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, Berkeley, 2006.Google Scholar
  13. [13]
    Gu D B, Distributed em algorithm for gaussian mixtures in sensor networks, IEEE Transactions on Neural Networks, 2008, 19(7): 1154–1166.CrossRefGoogle Scholar
  14. [14]
    Greenhill S and Venkatesh S, Distributed query processing for mobile surveillance, Proceedings of the 15th ACM International Conference on Multimedia, Augsburg, 2007.Google Scholar
  15. [15]
    Considine J, Li F F, Kollios G, et al., Approximate aggregation techniques for sensor databases, Proceedings of the 20th Conference on Data Engineering, Boston, 2004.Google Scholar
  16. [16]
    Greenwald M B and Khanna S, Power-conserving computation of order-statistics over sensor networks, Proceedings of the 23rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Madison, 2004.Google Scholar
  17. [17]
    Lewis F L, Wireless Sensor Networks, John Wiley & Sons, Inc., 2005.Google Scholar
  18. [18]
    Corbett J C, Dean J, Epstein M, et al., Spanner: Google’s globally distributed database, ACM Tran. Computer Systems, 2013, 31(3): 251–264.Google Scholar
  19. [19]
    Joshi M N, Parallel K-means algorithm on distributed memory multiprocessors, Computer, 2003, 9: 3–15.Google Scholar
  20. [20]
    Dhillon I S and Modha D S, A data-clustering algorithm on distributed memory multiprocessors, Large-Scale Parallel Data Mining, Springer, 2002, 245–260.Google Scholar
  21. [21]
    Hajiee M, A new distributed clustering algorithm based on K-means algorithm, Proceedings of the 3rd International Conference on Advanced Computer Theory and Engineering, Chengdu, 2010.Google Scholar
  22. [22]
    Vaidya J and Clifton C, Privacy-preserving K-means clustering over vertically partitioned data, Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, 2003.Google Scholar
  23. [23]
    Jagannathan G and Wright R N, Privacy-preserving distributed K-means clustering over arbitrarily partitioned data, Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Chicago, 2005.Google Scholar
  24. [24]
    Datta S, Giannella C, and Kargupta H, K-means clustering over a large, dynamic network, Proceedings of the 2006 SIAM International Conference on Data Mining, Bethesda, 2006.Google Scholar
  25. [25]
    Datta S, Giannella C, and Kargupta H, Approximate distributed K-means clustering over a peer-to-peer network, IEEE Trans. Knowledge and Data Engineering, 2009, 21(10): 1372–1388.CrossRefGoogle Scholar
  26. [26]
    Forero P A, Cano A, and Giannakis G B, Distributed clustering using wireless sensor networks, IEEE Journal of Selected Topics in Signal Processing, 2011, 5(4): 707–724.CrossRefGoogle Scholar
  27. [27]
    Khedr A M and Bhatnagar R K, New algorithm for clustering distributed data using K-means, Computing & Informatics, 2014, 33(4): 943–964.Google Scholar
  28. [28]
    Oliva G, Setola R, and Hadjicostis C N, Distributed K-means algorithm, arXiv:1312.4176, 2013.zbMATHGoogle Scholar
  29. [29]
    Liu Q H, Fu W M, Qin J H, et al., Distributed K-means algorithm for sensor networks based on multi-agent consensus theory, Proceedings of 2016 IEEE International Conference on Industrial Technology, Taipei, China, 2016.Google Scholar
  30. [30]
    West D B, Introduction to Graph Theory, 2nd Edition, Prentice Hall, Inc. Upper Saddle River, 2001.Google Scholar
  31. [31]
    Forero P A, Cano A, and Giannakis G B, Distributed feature-based modulation classification using wireless sensor networks, Proceedings of IEEE Military Communications Conference, San Diego, 2008.Google Scholar
  32. [32]
    Hartigan J A and Wong M A, Algorithm as 136: A K-means clustering algorithm, Applied Statistics, 1979, 28(1): 100–108.CrossRefzbMATHGoogle Scholar
  33. [33]
    Arthur D and Vassilvitskii S, K-means++: The advantages of careful seeding, Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, 2007.Google Scholar
  34. [34]
    Yuan D M, Ho D W, and Xu S Y, Zeroth-order method for distributed optimization with approximate projections, IEEE Trans. Neural Networks and Learning Systems, 2016, 27(2): 284–294.MathSciNetCrossRefGoogle Scholar
  35. [35]
    Franti P, et al., Clustering datasets, 2015, Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Peng Lin
    • 1
    • 2
    Email author
  • Yinghui Wang
    • 1
    • 2
  • Hongsheng Qi
    • 1
    • 2
  • Yiguang Hong
    • 1
    • 2
  1. 1.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations