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.
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References
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)
Taskar, B., Wong, M.F., Abbeel, P., Koller, D.: Link prediction in relational data. In: Advances in Neural Information Processing Systems (2003)
Gärtner, T., Horváth, T., Le, Q.V., Smola, A., Wrobel, S.: Kernel Methods for Graphs. In: Mining Graph Data. John Wiley & Sons, Chichester (2006)
Holme, P., Liljeros, F., Edling, C.R., Kim, B.J.: On network bipartivity. Phys. Rev. E 68, 6653–6673 (2003)
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)
Adamic, L., Adar, E.: Friends and neighbors on the web. Social Networks 25, 211–230 (2001)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Zhang, D., Mao, R.: Classifying networked entities with modularity kernels. In: Proc. Conf. on Information and Knowledge Management, pp. 113–122 (2008)
Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74 (2006)
Chung, F.: Spectral Graph Theory. American Mathematical Society, Providence (1997)
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)
Kunegis, J., Lommatzsch, A.: Learning spectral graph transformations for link prediction. In: Proc. Int. Conf. on Machine Learning, pp. 561–568 (2009)
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)
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)
Kandola, J., Shawe-Taylor, J., Cristianini, N.: Learning semantic similarity. In: Advances in Neural Information Processing Systems, pp. 657–664 (2002)
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)
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)
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)
Emamy, K., Cameron, R.: CiteULike: A researcher’s social bookmarking service. Ariadne (51) (2007)
Bizer, C., Cyganiak, R., Auer, S., Kobilarov, G.: DBpedia.org–querying Wikipedia like a database. In: Proc. Int. World Wide Web Conf. (2007)
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)
Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: A constant time collaborative filtering algorithm. Information Retrieval 4(2), 133–151 (2001)
GroupLens Research: MovieLens data sets (October 2006), http://www.grouplens.org/node/73
Bennett, J., Lanning, S.: The Netflix prize. In: Proc. KDD Cup, pp. 3–6 (2007)
Wikimedia Foundation: Wikimedia downloads (January 2010), http://download.wikimedia.org/
Manning, C.D., Raghavan, P., Schütze, H.: Introduction to Information Retrieval. Cambridge University Press, Cambridge (2008)
Estrada, E., Rodríguez-Velázquez, J.A.: Spectral measures of bipartivity in complex networks. Phys. Rev. E 72 (2005)
Stewart, D.: Social status in an open-source community. American Sociological Review 70 (5), 823–842 (2005)
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Kunegis, J., De Luca, E.W., Albayrak, S. (2010). The Link Prediction Problem in Bipartite Networks. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_39
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DOI: https://doi.org/10.1007/978-3-642-14049-5_39
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