Abstract
Recent years have witnessed a widespread interest on methods using both link structure and node information for link prediction on graphs. One of the state-of-the-art methods is Link Propagation which is a new semi-supervised learning algorithm for link prediction on graphs based on the popularly-studied label propagation by exploiting information on similarities of links and nodes. Despite its efficiency and effectiveness compared to other methods, its applications were still limited due to the computational time and space constraints. In this paper, we propose fast and scalable algorithms for the Link Propagation by introducing efficient procedures to solve large linear equations that appear in the method. In particular, we show how to obtain a compact representation of the solution to the linear equations by using a non-trivial combination of techniques in linear algebra to construct algorithms that are also effective for link prediction on dynamic graphs. These enable us to apply the Link Propagation to large networks with more than 400,000 nodes. Experiments demonstrate that our approximation methods are scalable, fast, and their prediction qualities are comparably competitive.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Anderson, C.J., Wasserman, S., Crouch, B.: A p * primer: logit models for social networks. Social Networks 21, 37–66 (1999)
Basilico, J., Hofmann, T.: Unifying collaborative and content-based filtering. In: ICML (2004)
Ben-Hur, A., Noble, W.S.: Kernel methods for predicting protein-protein interactions. Bioinformatics 21(suppl. 1), i38–i46 (2005)
Bishop, C.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2006)
Chu, W., Sindhwani, V., Ghahramani, Z., Keerthi, S.: Relational learning with Gaussian processes. In: NIPS (2007)
Getoor, L., Diehl, C.P.: Link mining: a survey. SIGKDD Explorations 7(2), 3–12 (2005)
Hanneke, S., Xing, E.: Discrete temporal models of social networks. In: Airoldi, E.M., Blei, D.M., Fienberg, S.E., Goldenberg, A., Xing, E.P., Zheng, A.X. (eds.) ICML 2006. LNCS, vol. 4503, pp. 115–125. Springer, Heidelberg (2007)
Hasan, M.A., Chaoji, V., Salem, S., Zaki, M.: Link prediction using supervised learning. In: LinkKDD (2005)
Hayashi, K., Hirayama, J., Ishii, S.: Dynamic Exponential Family Matrix Factorization. In: Theeramunkong, T., Kijsirikul, B., Cercone, N., Ho, T.-B. (eds.) PAKDD 2009. LNCS, vol. 5476, pp. 452–462. Springer, Heidelberg (2009)
Kashima, H., Kato, T., Yamanishi, Y., Sugiyama, M., Tsuda, K.: Link propagation: A fast semi-supervised learning algorithm for link prediction. In: SDM (2009)
Kato, T., Tsuda, K., Asai, K.: Selective integration of multiple biological data for supervised network inference. Bioinformatics 21(10), 2488–2495 (2005)
Laub, A.J.: Matrix Analysis for Scientists and Engineers. Society for Industrial and Applied Mathematics (2005)
Lee, D., Seung, H.: Algorithms for non-negative matrix factorization. In: NIPS, pp. 556–562 (2001)
Liben-Nowell, D., Kleinberg, J.: The link prediction problem for social networks. In: CIKM, pp. 556–559 (2004)
O’Madadhain, J., Hutchins, J., Smyth, P.: Prediction and ranking algorithms for event-based network data. SIGKDD Explorations 7(2), 23–30 (2005)
Oyama, S., Manning, C.D.: Using feature conjunctions across examples for learning pairwise classifiers. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol. 3201, pp. 322–333. Springer, Heidelberg (2004)
Popescul, A., Ungar, L.H.: Statistical relational learning for link prediction. In: IJCAI Workshop on Learning Statistical Models from Relational Data (2003)
Srebro, N.: Learning with Matrix Factorization. PhD thesis, Massachusetts Institute of Technology (2004)
Srebro, N., Rennie, J., Jaakkola, T.: Maximum-margin matrix factorization. In: NIPS, pp. 1329–1336 (2005)
Taskar, B., Wong, M., Abbeel, P., Koller, D.: Link prediction in relational data. In: NIPS (2004)
Tong, H., Papadimitriou, S., Sun, J., Yu, P.S., Faloutsos, C.: Colibri: fast mining of large static and dynamic graphs. In: KDD, pp. 686–694 (2008)
Tong, H., Papadimitriou, S., Yu, P.S., Faloutsos, C.: Fast monitoring proximity and centrality on time-evolving bipartite graphs. Statistical Analysis and Data Mining 1(3), 142–156 (2008)
Vert, J.-P., Yamanishi, Y.: Supervised graph inference. In: NIPS (2005)
Vishwanathan, S.V.N., Borgwardt, K., Schraudolph, N.: Fast computation of graph kernels. In: NIPS (2007)
Wu, M., Schölkopf, B.: Transductive classification via local learning regularization. In: AISTATS (2007)
Yamanishi, Y., Vert, J.-P., Kanehisa, M.: Supervised enzyme network inference from the integration of genomic data and chemical information. Bioinformatics 21, i468–i477 (2005)
Yu, K., Chu, W., Yu, S., Tresp, V., Xu, Z.: Stochastic relational models for discriminative link prediction. In: NIPS (2007)
Zan Huang, H.C., Li, X.: Link prediction approach to collaborative filtering. In: JCDL (2005)
Zhou, D., Bousquet, O., Weston, J., Schölkopf, B.: Learning with local and global consistency. In: NIPS, pp. 321–328 (2004)
Zhou, D., Zhu, S., Yu, K., Song, X., Tseng, B.L., Zha, H., Giles, C.L.: Learning multiple graphs for document recommendations. In: WWW ’08, pp. 141–150. ACM, New York (2008)
Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using Gaussian fields and harmonic functions. In: ICML (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Raymond, R., Kashima, H. (2010). Fast and Scalable Algorithms for Semi-supervised Link Prediction on Static and Dynamic Graphs. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2010. Lecture Notes in Computer Science(), vol 6323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15939-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-15939-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15938-1
Online ISBN: 978-3-642-15939-8
eBook Packages: Computer ScienceComputer Science (R0)