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The Link Prediction Problem in Bipartite Networks

  • Jérôme Kunegis
  • Ernesto W. De Luca
  • Sahin Albayrak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6178)

Abstract

We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the vertices. Common link prediction functions for general graphs are defined using paths of length two between two nodes. Since in a bipartite graph adjacency vertices can only be connected by paths of odd lengths, these functions do not apply to bipartite graphs. Instead, a certain class of graph kernels (spectral transformation kernels) can be generalized to bipartite graphs when the positive-semidefinite kernel constraint is relaxed. This generalization is realized by the odd component of the underlying spectral transformation. This construction leads to several new link prediction pseudokernels such as the matrix hyperbolic sine, which we examine for rating graphs, authorship graphs, folksonomies, document–feature networks and other types of bipartite networks.

Keywords

Bipartite Graph Preferential Attachment Mean Average Precision Link Prediction Bipartite Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Liben-Nowell, D., Kleinberg, J.: The link prediction problem for social networks. In: Proc. Int. Conf. on Information and Knowledge Management, pp. 556–559 (2003)Google Scholar
  2. 2.
    Taskar, B., Wong, M.F., Abbeel, P., Koller, D.: Link prediction in relational data. In: Advances in Neural Information Processing Systems (2003)Google Scholar
  3. 3.
    Gärtner, T., Horváth, T., Le, Q.V., Smola, A., Wrobel, S.: Kernel Methods for Graphs. In: Mining Graph Data. John Wiley & Sons, Chichester (2006)Google Scholar
  4. 4.
    Holme, P., Liljeros, F., Edling, C.R., Kim, B.J.: On network bipartivity. Phys. Rev. E 68, 6653–6673 (2003)Google Scholar
  5. 5.
    Leskovec, J., Backstrom, L., Kumar, R., Tomkins, A.: Microscopic evolution of social networks. In: Proc. Int. Conf. on Knowledge Discovery and Data Mining, pp. 462–470 (2008)Google Scholar
  6. 6.
    Adamic, L., Adar, E.: Friends and neighbors on the web. Social Networks 25, 211–230 (2001)CrossRefGoogle Scholar
  7. 7.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)Google Scholar
  8. 8.
    Zhang, D., Mao, R.: Classifying networked entities with modularity kernels. In: Proc. Conf. on Information and Knowledge Management, pp. 113–122 (2008)Google Scholar
  9. 9.
    Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74 (2006)Google Scholar
  10. 10.
    Chung, F.: Spectral Graph Theory. American Mathematical Society, Providence (1997)MATHGoogle Scholar
  11. 11.
    Rendle, S., Schmidt-Thieme, L.: Online-updating regularized kernel matrix factorization models for large-scale recommender systems. In: Proc. Int. Conf. on Recommender Systems, pp. 251–258 (2008)Google Scholar
  12. 12.
    Kunegis, J., Lommatzsch, A.: Learning spectral graph transformations for link prediction. In: Proc. Int. Conf. on Machine Learning, pp. 561–568 (2009)Google Scholar
  13. 13.
    Ito, T., Shimbo, M., Kudo, T., Matsumoto, Y.: Application of kernels to link analysis. In: Proc. Int. Conf. on Knowledge Discovery in Data Mining, pp. 586–592 (2005)Google Scholar
  14. 14.
    Wu, Y., Chang, E.Y.: Distance-function design and fusion for sequence data. In: Proc. Int. Conf. on Information and Knowledge Management, pp. 324–333 (2004)Google Scholar
  15. 15.
    Kandola, J., Shawe-Taylor, J., Cristianini, N.: Learning semantic similarity. In: Advances in Neural Information Processing Systems, pp. 657–664 (2002)Google Scholar
  16. 16.
    Cardoso, J.R., Leite, F.S.: Computing the inverse matrix hyperbolic sine. In: Vulkov, L.G., Waśniewski, J., Yalamov, P. (eds.) NAA 2000. LNCS, vol. 1988, pp. 160–169. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Hotho, A., Jäschke, R., Schmitz, C., Stumme, G.: BibSonomy: A social bookmark and publication sharing system. In: Proc. Workshop on Conceptual Structure Tool Interoperability, pp. 87–102 (2006)Google Scholar
  18. 18.
    Ziegler, C.N., McNee, S.M., Konstan, J.A., Lausen, G.: Improving recommendation lists through topic diversification. In: Proc. Int. World Wide Web Conf., pp. 22–32 (2005)Google Scholar
  19. 19.
    Emamy, K., Cameron, R.: CiteULike: A researcher’s social bookmarking service. Ariadne (51) (2007)Google Scholar
  20. 20.
    Bizer, C., Cyganiak, R., Auer, S., Kobilarov, G.: DBpedia.org–querying Wikipedia like a database. In: Proc. Int. World Wide Web Conf. (2007)Google Scholar
  21. 21.
    Massa, P., Avesani, P.: Controversial users demand local trust metrics: an experimental study on epinions.com community. In: Proc. American Association for Artificial Intelligence Conf., pp. 121–126 (2005)Google Scholar
  22. 22.
    Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: A constant time collaborative filtering algorithm. Information Retrieval 4(2), 133–151 (2001)MATHCrossRefGoogle Scholar
  23. 23.
    GroupLens Research: MovieLens data sets (October 2006), http://www.grouplens.org/node/73
  24. 24.
    Bennett, J., Lanning, S.: The Netflix prize. In: Proc. KDD Cup, pp. 3–6 (2007)Google Scholar
  25. 25.
    Wikimedia Foundation: Wikimedia downloads (January 2010), http://download.wikimedia.org/
  26. 26.
    Manning, C.D., Raghavan, P., Schütze, H.: Introduction to Information Retrieval. Cambridge University Press, Cambridge (2008)Google Scholar
  27. 27.
    Estrada, E., Rodríguez-Velázquez, J.A.: Spectral measures of bipartivity in complex networks. Phys. Rev. E 72 (2005)Google Scholar
  28. 28.
    Stewart, D.: Social status in an open-source community. American Sociological Review 70 (5), 823–842 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jérôme Kunegis
    • 1
  • Ernesto W. De Luca
    • 1
  • Sahin Albayrak
    • 1
  1. 1.DAI LabTechnische Universität BerlinBerlinGermany

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