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Statistical Selection of Relevant Features to Classify Random, Scale Free and Exponential Networks

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Part of the book series: Advances in Soft Computing ((AINSC,volume 44))

Abstract

In this paper a statistical selection of relevant features is presented. An experiment was designed to select relevant and not redundant features or characterization functions, which allow quantitatively discriminating among different types of complex networks. As well there exist researchers given to the task of classifying some networks of the real world through characterization functions inside a type of complex network, they do not give enough evidences of detailed analysis of the functions that allow to determine if all are necessary to carry out an efficient discrimination or which are better functions for discriminating. Our results show that with a reduced number of characterization functions such as the shortest path length, standard deviation of the degree, and local efficiency of the network can discriminate efficiently among the types of complex networks treated here.

This research was supported in part by CONACYT and DGEST.

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References

  1. Barabási, A.L. Albert R. Jeong, H. “Mean-Field theory for scale-free random networks”. Physica A, vol. 272, pp 173–189, 1999.

    Article  Google Scholar 

  2. Albert, R. Barabási, A.L. “Statistical Mechanics of Complex Networks”. Reviews of Modern Physics, vol. 74, pp 47–97, 2002.

    Article  MathSciNet  Google Scholar 

  3. Adamic, L.A., Lukose, R.M., Puniyani, A.R., Huberman, B.A.: “Search in power law network”. Physical Review E, vol. 64, pp 046135-1–046135-8, 2001.

    Article  Google Scholar 

  4. Costa, L., Rodrigues, F.A., Travieso, G., Villas, P.R. “Characterization of Complex Networks: A survey of measurements.” http://arxiv.org/PS_cache/cond-mat/pdf/0505/0505185v5.pdf (2007)

    Google Scholar 

  5. Bollobás, B. Riordan, O.M.: Mathematical results on scale-free random graphs. Handbook of Graphs and Networks. Wiley-VCH. Berlin. (2002). 1–32.

    Chapter  Google Scholar 

  6. Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature. Vol. 506. (2000). 5234–5237.

    Google Scholar 

  7. Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationship on the internet topology. ACM SIGCOMM. Vol. 29, No. 4. (1999). 251–262.

    Article  Google Scholar 

  8. Newman, M.E.J.: The structure and function of complex networks. SIAM Review. Vol. 45, No. 2. (2003). 167–256.

    Article  MATH  MathSciNet  Google Scholar 

  9. Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small world networks. PNAS. Vol. 97, No. 21. (2000) 11149–11152.

    Article  Google Scholar 

  10. Sen, P., Dasgupta, S., Chatterjee, A., Sreeram, P.A., Mukherjee, G., Manna, S. S.: Small-world properties of the Indian Railway network. Physical Review E. Vol. 67. (2003).

    Google Scholar 

  11. Barabási, A.L. Albert, R.: Emergence of Scaling in Random Networks. Science. (1999). 509–512

    Google Scholar 

  12. Liu, Z., Lai, Y., Ye, N., Dasgupta, P.: Connectivity distribution and attack tolerance of general networks with both preferential and random attachments. Physics Letters A. Vol. 303. (2003). 337–344.

    Article  Google Scholar 

  13. Montgomery, D.C.: Diseño y Análisis de Experimentos. Limusa Wiley. (2004)

    Google Scholar 

  14. Jonhson, D.E.: Métodos multivariados aplicados al análisis de datos. International Thomson Editores. (2000)

    Google Scholar 

  15. Guyon, I., Elisseeff, A.: An Introduction to Variable and Feature Selection. Journal of Machine Learning Research. Vol. 3. (2003) 1157–1182.

    Article  MATH  Google Scholar 

  16. Singhi, S.K., Liu, H.: Feature Subset Selection Bias for Classification Learning. Proceedings of the 23rd ICML. ACM ICPS. Vol. 148. (2006). 849–856.

    Google Scholar 

  17. Airoldi, E.M., Carley, K.M.: Sampling algorithms for pure network topologies: a study on the stability and the separability of metric embeddings. ACM SIGKDD Explorations Newsletter. Vol. 7, No. 2. (2005). 13–22.

    Article  Google Scholar 

  18. Middendorf, M., Ziv, E., Adams, C., Hom, J., Koytcheff, R., Levovitz, C., Woods G., Chen, L., Wiggins, C.: Discriminative Topological Features Reveal Biological Network Mechanisms. BMC Bioinformatics 2004. Vol 5, No. 181 (2004).

    Google Scholar 

  19. Ziv, E., Koytcheff, R., Middendrof, M., Wiggins, C.: Systematic Identification of statistically significant network measures. http://arxiv.org/PS_cache/cond-mat/pdf/0306/0306610v3.pdf (2005)

    Google Scholar 

  20. Ali, W., Mondragón, R.J., Alavi, F.: Extraction of topological features from communication network topological patterns using self-organizing feature maps.

    Google Scholar 

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Reyes, L.C., Conde, E.M., López, T.T., Santillán, C.G.G., Izaguirre, R.O. (2007). Statistical Selection of Relevant Features to Classify Random, Scale Free and Exponential Networks. In: Corchado, E., Corchado, J.M., Abraham, A. (eds) Innovations in Hybrid Intelligent Systems. Advances in Soft Computing, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74972-1_59

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  • DOI: https://doi.org/10.1007/978-3-540-74972-1_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74971-4

  • Online ISBN: 978-3-540-74972-1

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