Advertisement

Management of Control Impacts Based on Maximizing the Spread of Influence

  • Alexander Tselykh
  • Vladislav Vasilev
  • Larisa TselykhEmail author
Research Article

Abstract

The choice of fulcrums for control of socio-economic systems represented by directed weighted signed graphs is a topic of current interest. This article proposes a new method for identifying nodes of impact and influential nodes, which will provide a guaranteed positive system response over the growth model. The task is posed as an optimization problem to maximize the ratio of the norms of the accumulated increments of the growth vector and the exogenous impact vector. The algorithm is reduced to solving a quadratic programming problem with nonlinear restrictions. The selection of the most effective vertices is based on the cumulative gains of the component projections onto the solution vector. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Keywords

Directed weighted graphs control impact spread of influence optimization algorithm growth model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This research was supported by the Russian Foundation for Basic Research (No. 17-01-00076).

References

  1. [1]
    B. Chang, T. Xu, Q. Liu, E. H. Chen. Study on information diffusion analysis in social networks and its applications. International Journal of Automation and Computing, vol. 15, no. 4, pp. 377–401, 2018. DOI: 10.1007/s11633-018-1124-0.CrossRefGoogle Scholar
  2. [2]
    S. C. Peng, A. M. Yang, L. H. Cao, S. Yu, D. Q. Xie. Social influence modeling using information theory in mobile social networks. Information Sciences, vol. 379, pp. 146–159, 2017. DOI: 10.1016/j.ins.2016.08.023.CrossRefGoogle Scholar
  3. [3]
    S. C. Peng, Y. M. Zhou, L. H. Cao, S. Yu, J. W. Niu, W. J. Jia. Influence analysis in social networks: A survey. Journal of Network and Computer Applications, vol. 106, pp. 17–32, 2018. DOI: 10.1016/j.jnca.2018.01.005.CrossRefGoogle Scholar
  4. [4]
    D. Kempe, J. Kleinberg, E. Tardos. Maximizing the spread of influence through a social network. In Proceedings of the 9th International Conference on Knowledge Discovery and Data Mining, ACM, Washington, USA, pp. 105–147, 2003. DOI: 10.1145/956750.956769.Google Scholar
  5. [5]
    M. Granovetter. Threshold models of collective behavior. American Journal of Sociology, vol. 83, no. 6, pp. 1420–1443, 1978. DOI: 10.1086/226707.CrossRefGoogle Scholar
  6. [6]
    J. Goldenberg, B. Libai, E. Muller. Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters, vol. 12, no. 3, pp. 211–223, 2001. DOI: 10.1023/A:1011122126881.CrossRefGoogle Scholar
  7. [7]
    S. Brin, L. Page. The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems, vol. 30, no. 1–7, pp. 107–117, 1998. DOI: 10.1016/ S0169-7552(98)00110-X.CrossRefGoogle Scholar
  8. [8]
    G. R. Chen. Pinning control and controllability of complex dynamical networks. International Journal of Automation and Computing, vol. 14, no. 1, pp. 1–9, 2017. DOI: 10.1007/s11633-016-1052-9.MathSciNetCrossRefGoogle Scholar
  9. [9]
    B. Kosko. Fuzzy cognitive maps. International Journal of Man-Machine Studies, vol. 24, no. 1, pp. 65–75, 1986. DOI: 10.1016/S0020-7373(86)80040-2.CrossRefzbMATHGoogle Scholar
  10. [10]
    W. Pedrycz. Fuzzy Control and Fuzzy Systems, 2nd ed., New York, USA: John Wiley & Sons, 1993.zbMATHGoogle Scholar
  11. [11]
    F. S. Roberts. Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems, Englewood Cliffs, USA: Prentice Hall Press, 1997.Google Scholar
  12. [12]
    W. Yang, X. F. Wang, H. B. Shi. Optimal control nodes selection for consensus in multi-agent systems. IFAC Proceedings Volumes, vol. 47, no. 3, pp. 11697–11702, 2014. DOI: 10.3182/20140824-6-ZA-1003.00946.CrossRefGoogle Scholar
  13. [13]
    M. Y. Zhou, X. S. He, Z. Q. Fu, H. Liao, S. M. Cai, Z. Zhuo. Diffusion inspires selection of pinning nodes in pinning control. Physica A: Statistical Mechanics and its Applications, vol. 446, pp. 120–128, 2016. DOI: 10.1016/j. physa.2015.11.018.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    P. Wu, L. Pan. Scalable influence blocking maximization in social networks under competitive independent cascade models. Computer Networks, vol. 123, pp. 38–50, 2017. DOI: 10.1016/j.comnet.2017.05.004.CrossRefGoogle Scholar
  15. [15]
    C. Budak, D. Agrawal, A. El Abbadi. Limiting the spread of misinformation in social networks. In Proceedings of the 20th International Conference on World Wide Web, ACM, Hyderabad, India, pp. 665–674, 2011. DOI: 10.1145/ 1963405.1963499.Google Scholar
  16. [16]
    J. Ding, Y. Z. Lu, J. Chu. Studies on controllability of directed networks with extremal optimization. Physica A: Statistical Mechanics and its Applications, vol. 392, no. 24, pp. 6603–6615, 2013. DOI: 10.1016/j.physa.2013.09.004.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J. Ding, P. Tan, Y. Z. Lu. Optimizing the controllability index of directed networks with the fixed number of control nodes. Neurocomputing, vol. 171, pp. 1524–1532, 2016. DOI: 10.1016/j.neucom.2015.07.102.CrossRefGoogle Scholar
  18. [18]
    Y. Y. Liu, J. J. Slotine, A. L. Barabasi. Controllability of complex networks. Nature, vol. 473, no. 7346, pp. 161–173, 2011. DOI: 10.1038/nature10011.CrossRefGoogle Scholar
  19. [19]
    N. Cai. On quantitatively measuring controllability of complex networks. Physica A: Statistical Mechanics and its Applications, vol. 474, pp. 282–292, 2017. DOI: 10.1016/ j.physa.2017.01.053.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    P. Bonacich, P. Lloyd. Eigenvector-like measures of centrality for asymmetric relations. Social Networks, vol. 23, no. 3, pp. 191–201, 2001. DOI: 10.1016/S0378-8733(01) 00038-7.CrossRefGoogle Scholar
  21. [21]
    R. A. Horn, C. R. Johnson. Matrix Analysis, 2nd ed., New York, USA: Cambridge University Press, 2013.zbMATHGoogle Scholar
  22. [22]
    G. E. P. Box, G. M. Jenkins, G. C. Reinsel. Time Series Analysis: Forecasting and Control, Englewood Cliffs, USA: Prentice Hall, 1994.zbMATHGoogle Scholar
  23. [23]
    C. Chatfield. The Analysis of Time Series: An Introduction, London, UK: Chapman & Hall, 1996.zbMATHGoogle Scholar
  24. [24]
    A. N. Tselykh, V. S. Vasilev, L. A. Tselykh, S. A. Barkovskii. Method maximizing the spread of influence in directed signed weighted graphs. Advances in Electrical and Electronic Engineering, vol. 15, no. 2, pp. 203–214, 2017. DOI: 10.15598/aeee.v15i2.1950.CrossRefGoogle Scholar
  25. [25]
    P. Lancaster, M. Tismenetsky. The Theory of Matrices, Orlando, USA: Academic Press, 1985.zbMATHGoogle Scholar
  26. [26]
    D. P. Bertsekas. Constrained Optimization and Lagrange Multiplier Methods, Belmont, USA: Athena Scientific, 1996.zbMATHGoogle Scholar
  27. [27]
    A. Tselykh, L. Tselykh. Methodology for comparative cognitive modeling based on the analysis of fuzzy target and control factors. Izvestiya SFedU.Engineering sciences, vol. 168, no. 7, pp. 101–115, 2015.Google Scholar
  28. [28]
    A. H. Karanashev, A. G. Karasheva, L. B. Baysultanova, L. A. Tselykh, E. A. Panfilova. Comparative cognitive corporate culture modeling of the Kabardino-Balkaria republic′s enterprises recreational sphere. Mediterranean Journal of Social Sciences, vol. 6, no. 3 S4, pp. 37–43, 2015. DOI: 10.5901/mjss.2015.v6n3s4p37.Google Scholar
  29. [29]
    N. Abramova, Z. Avdeeva, S. Kovriga, D. Makarenko. Subject-formal Methods Based on Cognitive Maps and the Problem of Risk Due to the Human Factor, Vienna, Austria: InTech, pp. 35–63, 2010. DOI: 10.5772/7118.Google Scholar
  30. [30]
    D. H. Kim. Cognitive maps of policy makers on financial crises of South Korea and Malaysia: A comparative study. International Review of Public Administration, vol. 9, no. 2, pp. 31–38, 2004. DOI: 10.1080/12294659.2005.10805047.MathSciNetCrossRefGoogle Scholar
  31. [31]
    A. Tikhonov, V. Arsenin. Solutions of Ill-Posed Problems, New York, USA: Wiley, 1977.zbMATHGoogle Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Computer Technologies and Information SafetySouthern Federal UniversityRostov-on-DonRussia
  2. 2.Department of Economics and BusinessRostov State University of EconomicsRostov-on-DonRussia

Personalised recommendations