Advertisement

Learning Unknown Graphs

  • Nicolò Cesa-Bianchi
  • Claudio Gentile
  • Fabio Vitale
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5809)

Abstract

Motivated by a problem of targeted advertising in social networks, we introduce and study a new model of online learning on labeled graphs where the graph is initially unknown, and the algorithm is free to choose the next vertex to predict. After observing that natural nonadaptive exploration/prediction strategies (like depth-first with majority vote) badly fail on simple binary labeled graphs, we introduce an adaptive strategy that performs well under the hypothesis that the vertices of the unknown graph (i.e., the members of the social network) can be partitioned into a few well-separated clusters within which labels are roughly constant (i.e., members in the same cluster tend to prefer the same products). Our algorithm is efficiently implementable and provably competitive against the best of these partitions.

Keywords

online learning graph prediction unknown graph  clustering 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Albers, S., Henzinger, M.: Exploring unknown environments. SIAM Journal on Computing 29(4), 1164–1188 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blum, A., Chawla, S.: Learning from labeled and unlabeled data using graph mincuts. In: Proc. 18th ICML. Morgan Kaufmann, San Francisco (2001)Google Scholar
  3. 3.
    Blum, A., Lafferty, J., Rwebangira, M., Reddy, R.: Semi-supervised learning using randomized mincuts. In: Proc. 21st ICML. ACM Press, New York (2004)Google Scholar
  4. 4.
    Bryant, D., Berry, V.: A Structured family of clustering and tree construction methods. Advances in Applied Mathematics 27, 705–732 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Balcan, N., Blum, A., Vempala, S.: A discriminative framework for clustering via similarity functions. In: Proc. 40th STOC. ACM Press, New York (2008)Google Scholar
  6. 6.
    Cesa-Bianchi, N., Gentile, C., Vitale, F.: Fast and optimal prediction of a labeled tree. In: Proc. 22nd COLT. Omnipress (2009)Google Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)zbMATHGoogle Scholar
  8. 8.
    Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. In: Proc. 31st FOCS, pp. 355–361. IEEE Press, Los Alamitos (1990)Google Scholar
  9. 9.
    Hanneke, S.: An analysis of graph cut size for transductive learning. In: Proc. 23rd ICML, pp. 393–399. ACM Press, New York (2006)Google Scholar
  10. 10.
    Hebster, M., Pontil, M.: Prediction on a graph with the Perceptron. In: NIPS, vol. 19, pp. 577–584. MIT Press, Cambridge (2007)Google Scholar
  11. 11.
    Herbster, M.: Exploiting cluster-structure to predict the labeling of a graph. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds.) ALT 2008. LNCS (LNAI), vol. 5254, pp. 54–69. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Herbster, M., Lever, G., Pontil, M.: Online prediction on large diameter graphs. In: NIPS, vol. 22. MIT Press, Cambridge (2009)Google Scholar
  13. 13.
    Herbster, M., Pontil, M., Rojas-Galeano, S.: Fast prediction on a tree. In: NIPS, vol. 22. MIT Press, Cambridge (2009)Google Scholar
  14. 14.
    Herbster, M., Lever, G.: Predicting the labelling of a graph via minimum p-seminorm interpolation. In: Proc. 22nd COLT. Omnipress (2009)Google Scholar
  15. 15.
    Joachims, T.: Transductive Learning via Spectral Graph Partitioning. In: Proc. 20th ICML, pp. 305–312. AAAI Press, Menlo Park (2003)Google Scholar
  16. 16.
    Kondor, I., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: Proc. 19th ICML, pp. 315–322. Morgan Kaufmann, San Francisco (2002)Google Scholar
  17. 17.
    Pelckmans, J., Shawe-Taylor, J., Suykens, J., De Moor, B.: Margin based transductive graph cuts using linear programming. In: Proc. 11th AISTAT. JMLR Proceedings Series, pp. 360–367 (2007)Google Scholar
  18. 18.
    Remy, J., Souza, A., Steger, A.: On an online spanning tree problem in randomly weighted graphs. Combinatorics, Probability and Computing 16, 127–144 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Smola, A., Kondor, I.: Kernels and regularization on graphs. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 144–158. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Yang, W.S., Dia, J.B.: Discovering cohesive subgroups from social networks for targeted advertising. Expert Systems with Applications 34, 2029–2038 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nicolò Cesa-Bianchi
    • 1
  • Claudio Gentile
    • 2
  • Fabio Vitale
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoItaly
  2. 2.Dipartimento di Informatica e ComunicazioneUniversità dell’InsubriaVareseItaly

Personalised recommendations