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Topology estimation method for telecommunication networks

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Abstract

Network topology specifies the interconnections of nodes and is essential in defining the qualitative network behaviour which is known to be universal with the similar phenomena appearing in many complex networks in diverse application fields. Topology information may be uncertain, or several pieces of inconsistent topology information may exist. This paper studies a method for estimating the network topology directly from node data, and is motivated by mobile telecommunications networks (MTNs). Mutual information based dependency measure is first used to quantify the statistical node dependencies, and the topology estimate is then constructed with multidimensional scaling and distance thresholding. The topology estimate defines the graph structure of a Markov random field (MRF) model, and after model parameter identification, the MRF model can then be used e.g. in analyzing the effect of disturbances to the overall network state of MTN. The method is evaluated with MCMC generated data and is found to work in qualitative network behaviour situations that are practical from the application perspective of MTNs. With the same data, the method yields at least as good results as a typical constrained-based graph estimation method.

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References

  1. Abdallah, S. (2002). Towards music perception by redundancy reduction and unsupervised learning in probabilistic models. Doc. Thesis: King’s College, London.

  2. Abellán, J., Gómez-Olmedo, M., & Moral, S. (2006). Some variations on the PC algorithm. In Proc third European workshop on probabilistic graphical models.

  3. Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.

    Article  Google Scholar 

  4. Basalaj, W. (1999). Incremental multidimensional scaling method for database visualization. In Proc SPIE’99, pp. 149–158.

  5. Bentrem, F. W. (2010). A Q-Ising model application for linear-time image segmentation. Central European Journal of Physics, 8(5), 689–698.

    Article  Google Scholar 

  6. Besag, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological), 36, 192–225.

    Google Scholar 

  7. Besag, J. E. (1975). Statistical analysis of non-lattice systems. The Statistician, 24, 179–195.

    Article  Google Scholar 

  8. Bishop, C. M. (2006). Pattern recognition and machine learning. Berlin: Springer.

    Google Scholar 

  9. Breitbart, Y., Garofalakis, M., Jai, B., Martin, C., Rastogi, R., & Silbershatz, A. (2004). Topology discovery in heterogeneous IP networks: The NetInventory system. IEEE/ACM Transactions on Networking, 12(3), 401–414.

    Article  Google Scholar 

  10. Bromberg, F., Margaritis, D., & Honavar, V. (2006). Efficient Markov network structure discovery using independence tests. In Proceedings of SIAM international conference on data mining, pp. 141–152.

  11. Bromberg, F., & Margaritis, D. (2007). Efficient and robust independence-based Markov network structure discovery. In Proc IJCAI.

  12. Bromberg, F., & Margaritis, D. (2009). Improving the reliability of causal discovery from small data sets using argumentation. JMLR, 10, 301–340.

    Google Scholar 

  13. Brown, P., Cocke, J., Della Pietra, S., Della Pietra, V., Jelinek, F., Mercer, R. (1988). A statistical approach to language translation. In COLING-88, Vol. 1, pp. 71–76.

  14. Butte, A. J., & Kohane, I. S. (2000). Mutual information relevance networks: Functional genomic clustering using pairwise entropy measurements. In Pacific symposium on biocomputing, Vol. 5.

  15. Chen, H., & Varshney, P. (2003). Mutual information-based CT-MR brain image registration using generalized partial volume joint histogram estimation. IEEE Transactions on Medical Imaging, 22(9), 1111–1119.

    Article  Google Scholar 

  16. Cheng, J., Greiner, R., Kelly, J., Bell, D., & Liu, W. (2002). Learning Bayesian networks from data: An information-theory based approach. Artificial Intelligence, 137(1–2), 43–90.

    Article  Google Scholar 

  17. Cover, T. M., & Thomas, J. A. (1991). Elements of information theory (pp. 5–21). Hoboken: Wiley.

    Book  Google Scholar 

  18. Cressie, N. A. C. (1993). Statistics for spatial data (pp. 383–573). Hoboken: Wiley.

    Google Scholar 

  19. De Campos, L. M. (2006). A scoring function for learning Bayesian networks based on mutual information and conditional independence tests. Journal of Machine Learning Research, 7, 2149–2187.

    Google Scholar 

  20. Drees, B. L., Thorsson, V., Carter, G. W., Rives, A. W., Raymond, M. Z., Avila-Campillo, I., et al. (2005). Derivation of genetic interaction networks from quantitative phenotype data. Genome Biology, 6, R38.

    Article  Google Scholar 

  21. Everitt, B. S., & Rabe-Hesketh, S. (1997). Kendall’s library of statistics 4: The analysis of proximity data (pp. 11–68). London: Arnold.

    Google Scholar 

  22. Friedman, N., & Koller, D. (2003). Being Bayesian about network structure: A Bayesian approach to structure discovery in Bayesian networks. Machine Learning, 50, 95–126.

    Article  Google Scholar 

  23. Gandhi, P., Bromberg, F., & Margaritis, D. (2008). Learning markov network structure using few independence tests. In Proceedings of SIAM international conference on data mining, pp. 680–691.

  24. Gower, J. C. (1975). Generalized procrustes analysis. Psychometrika, 40(1), 33–51.

    Article  Google Scholar 

  25. Hellebrandt, M., Mathar, R., & Scheibenbogen, M. (1997). Estimating position and velocity of mobiles in a cellular radio network. IEEE Transactions on Vehicular Technology, 46(1), 65–71.

    Article  Google Scholar 

  26. Horn, R. A., & Johnson, C. R. (1990). Norms for vectors and matrices. Matrix analysis (Ch. 5). Cambridge: Cambridge University Press.

  27. Ising, E. (1925). Beitrag zur Theorie des Ferromagnetismus. Zeitschrift fũr Physik, 31, 253–258.

    Article  Google Scholar 

  28. Kalisch, M., & Bühlmann, P. (2007). Robustification of the PC-algorithm for directed acyclic graphs. Journal of Computational and Graphical Statistics, 17(4), 773–789.

    Article  Google Scholar 

  29. Kishino, H., & Waddell, P. J. (2000). Correspondence analysis of genes and tissue types and finding genetic links from microarray data. Genome Informatics, 11, 83–95.

    Google Scholar 

  30. Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.

    Article  Google Scholar 

  31. Kruskal, J. B. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115–129.

    Article  Google Scholar 

  32. Lee, S.-I., Ganapahthi, V., & Koller, D. (2007). Efficient structure learning of Markov networks using \(L_{1}\)-regularization. In Advances in neural information processing systems.

  33. Lenz, W. (1920). Beitrag zum Verständnis der magnetishen Erscheinungen in festen Körpern. Zeitschrift fũr Physik, 21, 613–615.

    Google Scholar 

  34. Li, F. (2007). Structure learning with large sparse undirected graphs and its applications. Doc. Thesis, Carnegie Mellon University, USA.

  35. Lo, W. S., & Pelcovits, R. A. (1990). Ising model in a time-dependent magnetic field. Physical Review A, 42(12), 7471–7474.

    Article  Google Scholar 

  36. MacKay, D. (2003). Information theory, inference and learning algorithms (pp. 357–421). Cambridge: Cambridge University Press.

    Google Scholar 

  37. Margaritis, D., & Bromberg, F. (2009). Efficient Markov network discovery using particle filter. Computational Intelligence, 25(4), 367–394.

    Article  Google Scholar 

  38. Margaritis, D., & Thrun, S. (1999). Bayesian network induction via local neighbourhoods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 832–834.

    Google Scholar 

  39. Martín-Merino, M., & Muñoz, A. (2004). A new MDS algorithm for textual data analysis. In Proc ICONIP’04. LNCS, Vol. 3316, pp. 860–867.

  40. Mathiassen, J., Skavhaug, A., & Bø, K. (2002). Texture similarity measure using Kullback–Leibler divergence between Gamma distributions. In A. Heyden et al. (Eds.), ECCV 2002 Part III, LNCS, Vol. 2352, pp. 133–147.

  41. McCoy, B. M., & Wu, T. T. (2014). The two-dimensional Ising model. Courier Corporation.

  42. Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45(2), 167–256.

    Article  Google Scholar 

  43. Niu, C., & Grimson, E. (2006). Recovering non-overlapping network topology using far-field vehicle tracking data. In Proc ICPR’06, pp. 944–949.

  44. Potts, R. B. (1952). Some generalized order-disorder transformations. Proceedings of the Cambridge Philosophical Society, 48, 106–109.

    Article  Google Scholar 

  45. Press, W., Flannery, B., Teukolsky, S., & Vetterling, W. (1986). Numerical recipes: The art of scientific computation (pp. 476–481). Cambridge: Cambridge University Press.

    Google Scholar 

  46. Rajala, M. (2009). Data-based modelling and analysis of coherent networked systems with applications to mobile telecommunications networks. Doc. Thesis, Tampere University of Technology, Finland. http://dspace.cc.tut.fi/dpub/handle/123456789/6056(24.3.2016).

  47. Rajala, M., & Ritala, R. (2006). Mutual information and multidimensional scaling as means to reconstruct network topology. In Proc SICE-ICCAS’06, pp. 1398–1403.

  48. Rajala, M., & Ritala, R. (2006). Statistical model describing networked systems phenomena. In Proc ISCC’06, pp. 647–654.

  49. Rajala, M., & Ritala, R.(2007). A method to estimate the graph structure for a large MRF model. In J. Marques de Sá et al. (Eds.), ICANN 2007 Part II, LNCS, Vol. 4669, pp. 836–849.

  50. Rue, H., & Held, L. (2005). Gaussian Markov random fields: Theory and applications. Boca Raton: CRC.

    Book  Google Scholar 

  51. Schlüter, F. (2014). A survey on independence-based Markov networks learning. Artificial Intelligence Review, 42(4), 1069–1093.

    Article  Google Scholar 

  52. Schroeder, D.V. (1999). An introduction to thermal physics. Reading: Addison-Wesley.

  53. Seber, G. (1984). Multivariate observations (pp. 235–256). Hoboken: Wiley.

    Book  Google Scholar 

  54. Solé, R. V., Ferrer, R., Gonzàlez-Garcìa, I., Quer, J., & Domingo, E. (1999). Red queen dynamics, competition and critical points in a model of RNA virus quasispecies. Journal of Theoretical Biology, 198, 47–59.

    Article  Google Scholar 

  55. Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction, and search. Cambridge, MA: The MIT Press.

    Google Scholar 

  56. Szabó, G., & Kádár, G. (1998). Magnetic hysteresis in an Ising-like dipole–dipole model. Physical Review B, 58(9), 5584–5587.

    Article  Google Scholar 

  57. Thompson, C. J. (1972). Mathematical statistical mechanics. Princeton: Princeton University Press.

    Google Scholar 

  58. Vanderwalle, N., Boveroux, P., Minguet, A., & Ausloos, M. (1998). The crash of October 1987 seen as a phase transition: Amplitude and universality. Physica A, 255, 201–210.

    Article  Google Scholar 

  59. Winkler, G. (2003). Image analysis, random fields and Markov chain Monte Carlo methods (2nd ed.). Berlin: Springer.

    Book  Google Scholar 

  60. Yang, C. N. (1952). The spontaneous magnetization of a two-dimensional Ising model. Physical Review, 85(5), 808–816.

    Article  Google Scholar 

  61. Young, F. W. (2013). Multidimensional scaling: History, theory, and applications. Hove: Psychology Press.

    Google Scholar 

Download references

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Rajala, M., Ritala, R. Topology estimation method for telecommunication networks. Telecommun Syst 68, 745–759 (2018). https://doi.org/10.1007/s11235-018-0422-8

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