Abstract
In this paper, we propose to embed edges instead of nodes using state-of-the-art neural/factorization methods (DeepWalk, node2vec). These methods produce latent representations based on co-ocurrence statistics by simulating fixed-length random walks and then taking bags-of-vectors as the input to the Skip Gram Learning with Negative Sampling (SGNS). We commence by expressing commute times embedding as matrix factorization, and thus relating this embedding to those of DeepWalk and node2vec. Recent results showing formal links between all these methods via the spectrum of graph Laplacian, are then extended to understand the results obtained by SGNS when we embed edges instead of nodes. Since embedding edges is equivalent to embedding nodes in the line graph, we proceed to combine both existing formal characterizations of the line graphs and empirical evidence in order to explain why this embedding dramatically outperforms its nodal counterpart in multi-label classification tasks.
M. A. Lozano, M. Curado and F. Escolano are funded by the project TIN2015-69077-P of the Spanish Government.
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Benson, A.R., Gleich, D.F., Lim, L.: The spacey random walk: a stochastic process for higher-order data. SIAM Rev. 59(2), 321–345 (2017). https://doi.org/10.1137/16M1074023
Breitkreutz, B., et al.: The biogrid interaction database: 2008 update. Nucleic Acids Res. 36, 637–640 (2008). https://doi.org/10.1093/nar/gkm1001
Chung, F.R.K.: Spectral graph theory. In: Conference Board of the Mathematical Sciences (CBMS), number 92. American Mathematical Society (1997)
Curado, M., Escolano, F., Lozano, M.A., Hancock, E.R.: Dirichlet densifiers: beyond constraining the spectral gap. In: Bai, X., Hancock, E., Ho, T., Wilson, R., Biggio, B., Robles-Kelly, A. (eds.) S+SSPR 2018. LNCS, vol. 11004, pp. 512–521. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97785-0_49
Escolano, F., Curado, M., Lozano, M.A., Hancook, E.R.: Dirichlet graph densifiers. In: Robles-Kelly, A., Loog, M., Biggio, B., Escolano, F., Wilson, R. (eds.) S+SSPR 2016. LNCS, vol. 10029, pp. 185–195. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49055-7_17
Evans, T.S., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Phys. Rev. E 80, 016105 (2009). https://doi.org/10.1103/PhysRevE.80.016105
Grover, A., Leskovec, J.: node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, 13–17 August 2016, pp. 855–864 (2016). https://doi.org/10.1145/2939672.2939754
Leskovec, J., Krevl, A.: SNAP datasets: Stanford large network dataset collection, June 2014. http://snap.stanford.edu/data
Levy, O., Goldberg, Y.: Neural word embedding as implicit matrix factorization. In: Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems, 8–13 December 2014, Montreal, pp. 2177–2185 (2014). http://papers.nips.cc/paper/5477-neural-word-embedding-as-implicit-matrix-factorization
Lovász, L.: Random walks on graphs: a survey. In: Miklós, D., Sós, V.T., Szőnyi, T. (eds.) Combinatorics, Paul Erdős is Eighty, vol. 2, pp. 353–398. János Bolyai Mathematical Society, Budapest (1996)
von Luxburg, U., Radl, A., Hein, M.: Hitting and commute times in large random neighborhood graphs. J. Mach. Learn. Res. 15(1), 1751–1798 (2014). http://dl.acm.org/citation.cfm?id=2638591
Mahoney, M.: Large text compression benchmark (2011). http://www.mattmahoney.net/dc/textdata
McAuley, J.J., Leskovec, J.: Learning to discover social circles in ego networks. In: Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems, Proceedings of a Meeting Held 3–6 December 2012, Lake Tahoe, pp. 548–556 (2012). http://papers.nips.cc/paper/4532-learning-to-discover-social-circles-in-ego-networks
Perozzi, B., Al-Rfou, R., Skiena, S.: DeepWalk: online learning of social representations. In: The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2014, New York, 24–27 August 2014, pp. 701–710 (2014). https://doi.org/10.1145/2623330.2623732
Qiu, H., Hancock, E.R.: Clustering and embedding using commute times. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 1873–1890 (2007). https://doi.org/10.1109/TPAMI.2007.1103
Qiu, J., Dong, Y., Ma, H., Li, J., Wang, K., Tang, J.: Network embedding as matrix factorization: unifying DeepWalk, LINE, PTE, and node2vec. In: Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining, WSDM 2018, pp. 459–467. ACM, New York (2018). https://doi.org/10.1145/3159652.3159706
Sen, P., Namata, G., Bilgic, M., Getoor, L., Gallagher, B., Eliassi-Rad, T.: Collective classification in network data. AI Mag. 29(3), 93–106 (2008). http://www.aaai.org/ojs/index.php/aimagazine/article/view/2157
Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., Mei, Q.: LINE: large-scale information network embedding. In: Proceedings of the 24th International Conference on World Wide Web, WWW 2015, Florence, 18–22 May 2015, pp. 1067–1077 (2015). https://doi.org/10.1145/2736277.2741093
Yan, C.: Properties of spectra of graphs and line graphs. Appl. Math. J. Chin. Univ. 17(3), 371–376 (2002). https://doi.org/10.1007/s11766-002-0017-7
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Lozano, M.A., Curado, M., Escolano, F., Hancock, E.R. (2019). Network Embedding by Walking on the Line Graph. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_21
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