Abstract
Fusing or aligning two or more networks is a fundamental building block of many graph mining tasks (e.g., recommendation systems, link prediction, collective analysis of networks). Most past work has focused on formulating pairwise graph alignment as an optimization problem with varying constraints and relaxations. In this paper, we study the problem of multiple graph alignment (collectively aligning multiple graphs at once) and propose HashAlign, an efficient and intuitive hash-based framework for network alignment that leverages structural properties and other node and edge attributes (if available) simultaneously. We introduce a new construction of LSH families, as well as robust node and graph features that are tailored for this task. Our method quickly aligns multiple graphs while avoiding the all-pairwise-comparison problem by expressing all alignments in terms of a chosen ‘center’ graph. Our extensive experiments on synthetic and real networks show that, on average, HashAlign is \(2{\times }\) faster and 10 to 20% more accurate than the baselines in pairwise alignment, and \(2{\times }\) faster while 50% more accurate in multiple graph alignment.
M. Heimann and W. Lee—These authors contributed equally to this work.
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References
COBRE (2012). http://fcon_1000.projects.nitrc.org/indi/retro/cobre.html
Konect: Koblenz network collection (2016). http://konect.uni-koblenz.de/networks/
Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In: FOCS. IEEE (2006)
Bayati, M., Gleich, D.F., Saberi, A., Wang, Y.: Message-passing algorithms for sparse network alignment. ACM TKDD 7(1), 3:1–3:31 (2013)
Bradde, S., Braunstein, A., Mahmoudi, H., Tria, F., Weigt, M., Zecchina, R.: Aligning graphs and finding substructures by a cavity approach. Europhys. Lett. 89, 37009 (2010)
Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.S.: Locality-sensitive hashing scheme based on p-stable distributions. In: SCG, pp. 253–262. ACM (2004)
Ding, C.H.Q., Li, T., Jordan, M.I.: Nonnegative matrix factorization for combinatorial optimization: spectral clustering, graph matching, and clique finding. In: ICDM (2008)
Duan, S., Fokoue, A., Hassanzadeh, O., Kementsietsidis, A., Srinivas, K., Ward, M.J.: Instance-based matching of large ontologies using locality-sensitive hashing. In: Cudré-Mauroux, P., Heflin, J., Sirin, E., Tudorache, T., Euzenat, J., Hauswirth, M., Parreira, J.X., Hendler, J., Schreiber, G., Bernstein, A., Blomqvist, E. (eds.) ISWC 2012. LNCS, vol. 7649, pp. 49–64. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35176-1_4
Goyal, P., Ferrara, E.: Graph embedding techniques, applications, and performance: a survey. arXiv preprint arXiv:1705.02801 (2017)
Heimann, M., Koutra, D.: On generalizing neural node embedding methods to multi-network problems. In: KDD MLG Workshop (2017)
Heimann, M., Shen, H., Koutra, D.: Node representation learning for multiple networks: The case of graph alignment. arXiv preprint arXiv:1802.06257 (2018)
Khan, K.U., Nawaz, W., Lee, Y.K.: Set-based unified approach for attributed graph summarization. In: IEEE BDCC, December 2014. https://doi.org/10.1109/BDCloud.2014.108
Koutra, D., Faloutsos, C.: Individual and collective graph mining: principles, algorithms, and applications. Synth. Lect. Data Min. Knowl. Discov. 9(2), 1–206 (2017)
Koutra, D., Tong, H., Lubensky, D.: Big-align: fast bipartite graph alignment. In: ICDM. IEEE (2013)
Leskovec, J., Sosič, R.: SNAP: a general-purpose network analysis and graph-mining library. ACM TIST 8(1), 1 (2016)
Malmi, E., Chawla, S., Gionis, A.: Lagrangian relaxations for multiple network alignment. Data Mining Knowl. Discov. 31, 1–28 (2017)
Safavi, T., Sripada, C., Koutra, D.: Scalable hashing-based network discovery. In: ICDM. IEEE (2017)
Singh, R., Xu, J., Berger, B.: Global alignment of multiple protein interaction networks with application to functional orthology detection. PNAS 105(35), 12763–12768 (2008)
Zhang, J., Yu, P.S.: Multiple anonymized social networks alignment. In: ICDM. IEEE (2015)
Zhang, S., Tong, H.: Final: Fast attributed network alignment. In: KDD. ACM (2016)
Acknowledgements
This material is based upon work supported in part by the National Science Foundation under Grant No. IIS 1743088, and the University of Michigan. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or other funding parties. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.
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Heimann, M., Lee, W., Pan, S., Chen, KY., Koutra, D. (2018). HashAlign: Hash-Based Alignment of Multiple Graphs. In: Phung, D., Tseng, V., Webb, G., Ho, B., Ganji, M., Rashidi, L. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2018. Lecture Notes in Computer Science(), vol 10939. Springer, Cham. https://doi.org/10.1007/978-3-319-93040-4_57
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