Advertisement

Spread Sampling and Its Applications on Graphs

  • Yu WangEmail author
  • Bortik Bandyopadhyay
  • Vedang Patel
  • Aniket Chakrabarti
  • David Sivakoff
  • Srinivasan Parthasarathy
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

Efficiently finding small samples with high diversity from large graphs has many practical applications such as community detection and online survey. This paper proposes a novel scalable node sampling algorithm for large graphs that can achieve better spread or diversity across communities intrinsic to the graph without requiring any costly pre-processing steps. The proposed method leverages a simple iterative sampling technique controlled by two parameters: infection rate, that controls the dynamics of the procedure and removal threshold that affects the end-of-procedure sampling size. We demonstrate that our method achieves very high community diversity with an extremely low sampling budget on both synthetic and real-world graphs, with either balanced or imbalanced communities. Additionally, we leverage the proposed technique for a very low sampling budget (only 2%) driven treatment assignment in Network A/B Testing scenario, and demonstrate competitive performance concerning baseline on both synthetic and real-world graphs.

Keywords

Graph sampling Social network analysis 

Notes

Acknowledgments

This paper is funded by NSF grants DMS-1418265, IIS-1550302, and IIS-1629548.

References

  1. 1.
    Andersen, R., Chung, F., Lang, K.: Local graph partitioning using pagerank vectors. In: FOCS 2006, pp. 475–486 (2006)Google Scholar
  2. 2.
    Backstrom, L., Kleinberg, J.: Network bucket testing. In: Proceedings of the 20th International Conference on World Wide Web, pp. 615–624. ACM (2011)Google Scholar
  3. 3.
    Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  4. 4.
    Chiericetti, F., Dasgupta, A., Kumar, R., Lattanzi, S., Sarlós, T.: On sampling nodes in a network. In: Proceedings of the 25th International Conference on World Wide Web, pp. 471–481. International World Wide Web Conferences Steering Committee (2016)Google Scholar
  5. 5.
    Chung, F.: Graph theory in the information age. Not. AMS 57(6), 726–732 (2010)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Karrer,B., Eckles, D., Ugander, J.: Design and analysis of experiments in networks: reducing bias from interference (2014)Google Scholar
  7. 7.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Walking in Facebook: a case study of unbiased sampling of OSNs. In: 2010 Proceedings IEEE Infocom, pp. 1–9. IEEE (2010)Google Scholar
  10. 10.
    Gui, H., Xu, Y., Bhasin, A., Han, J.: Network A/B testing: from sampling to estimation. In: Proceedings of the 24th International Conference on World Wide Web, pp. 399–409. ACM (2015)Google Scholar
  11. 11.
    Hand, D.J.: Statistical analysis of network data: methods and models by Eric D. Kolaczyk. Int. Stat. Rev. 78(1), 135–135 (2010)CrossRefGoogle Scholar
  12. 12.
    Handcock, M.S., Gile, K.J.: Modeling social networks from sampled data. Ann. Appl. Stat. 4(1), 5 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hansen, M.H., Hurwitz, W.N.: On the theory of sampling from finite populations. Ann. Math. Stat. 14(4), 333–362 (1943)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Katzir, L., Liberty, E., Somekh, O.: Framework and algorithms for network bucket testing. In: Proceedings of the 21st International Conference on World Wide Web, WWW 2012, pp. 1029–1036. ACM, New York (2012)Google Scholar
  16. 16.
    Kloumann, I.M., Kleinberg, J.M.: Community membership identification from small seed sets. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1366–1375. ACM (2014)Google Scholar
  17. 17.
    Kohavi, R., Deng, A., Frasca, B., Walker, T., Xu, Y., Pohlmann, N.: Online controlled experiments at large scale. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2013, pp. 1168–1176. ACM, New York (2013)Google Scholar
  18. 18.
    Kohavi, R., Deng, A., Longbotham, R., Xu, Y.: Seven rules of thumb for web site experimenters. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2014, pp. 1857–1866. ACM, New York (2014)Google Scholar
  19. 19.
    Koutra, D., Shah, N., Vogelstein, J.T., Gallagher, B., Faloutsos, C.: D elta C on: principled massive-graph similarity function with attribution. ACM Trans. Knowl. Discov. Data (TKDD) 10(3), 28 (2016)Google Scholar
  20. 20.
    Leskovec, J. Faloutsos, C.: Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 631–636. ACM (2006)Google Scholar
  21. 21.
    Leskovec, J., Sosič, R.: SNAP: a general-purpose network analysis and graph-mining library. ACM Trans. Intell. Syst. Technol. (TIST) 8(1), 1 (2016)CrossRefGoogle Scholar
  22. 22.
    Lohr, S.: Sampling: Design and Analysis. Nelson Education, Toronto (2009)zbMATHGoogle Scholar
  23. 23.
    Maiya, A.S., Berger-Wolf, T.Y.: Expansion and search in networks. In: Proceedings of the 19th ACM International Conference on Information and Knowledge Management, pp. 239–248. ACM (2010)Google Scholar
  24. 24.
    Maiya, A.S., Berger-Wolf, T.Y.: Sampling community structure. In: Proceedings of the 19th International Conference on World Wide Web, pp. 701–710. ACM (2010)Google Scholar
  25. 25.
    McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Ann. Rev. Sociol. 27(1), 415–444 (2001)CrossRefGoogle Scholar
  26. 26.
    Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953) CrossRefGoogle Scholar
  27. 27.
    Middleton, J.A., Aronow, P.M.: Unbiased estimation of the average treatment effect in cluster-randomized experimentsGoogle Scholar
  28. 28.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: bringing order to the web. Technical report, Stanford InfoLab (1999)Google Scholar
  29. 29.
    Ribeiro, B., Towsley, D.: Estimating and sampling graphs with multidimensional random walks. In: Proceedings of the 10th ACM SIGCOMM Conference on Internet Measurement, pp. 390–403. ACM (2010)Google Scholar
  30. 30.
    Ruan, Y., Fuhry, D., Liang, J., Wang, Y., Parthasarathy, S.: Community discovery: simple and scalable approaches. In: User Community Discovery, pp. 23–54. Springer (2015)Google Scholar
  31. 31.
    Rubin, D.B.: Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol. 66(5), 688 (1974)CrossRefGoogle Scholar
  32. 32.
    Saveski, M., Pouget-Abadie, J., Saint-Jacques, G., Duan, W., Ghosh, S., Xu, Y., Airoldi, E.M.: Detecting network effects: randomizing over randomized experiments. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1027–1035. ACM (2017)Google Scholar
  33. 33.
    Ugander, J., Karrer, B., Backstrom, L., Kleinberg, J.: Graph cluster randomization: network exposure to multiple universes. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2013, pp. 329–337. ACM, New York (2013)Google Scholar
  34. 34.
    Wang, D., Li, Z., Xie, G.: Towards unbiased sampling of online social networks. In: 2011 IEEE International Conference on Communications (ICC), pp. 1–5. IEEE (2011)Google Scholar
  35. 35.
    Wang, Y.: Revisiting network sampling. Ph.D. thesis, The Ohio State University (2019)Google Scholar
  36. 36.
    Wang, Y., Chakrabarti, A., Sivakoff, D., Parthasarathy, S.: Fast change point detection on dynamic social networks. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence, pp. 2992–2998. AAAI Press (2017)Google Scholar
  37. 37.
    Wang, Y., Chakrabarti, A., Sivakoff, D., Parthasarathy, S.: Hierarchical change point detection on dynamic networks. In: Proceedings of the 2017 ACM on Web Science Conference, pp. 171–179. ACM (2017)Google Scholar
  38. 38.
    Whang, J.J., Gleich, D.F., Dhillon, I.S.: Overlapping community detection using seed set expansion. In: CIKM, pp. 2099–2108. ACM (2013)Google Scholar
  39. 39.
    Yang J., Leskovec, J.: Structure and overlaps of communities in networks. arXiv preprint arXiv:1205.6228 (2012)

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Yu Wang
    • 1
    Email author
  • Bortik Bandyopadhyay
    • 1
  • Vedang Patel
    • 1
  • Aniket Chakrabarti
    • 2
  • David Sivakoff
    • 1
  • Srinivasan Parthasarathy
    • 1
  1. 1.The Ohio State UniversityColumbusUSA
  2. 2.Microsoft Inc.HyderabadIndia

Personalised recommendations