Abstract
A triangle is an important building block of social networks, so the study of triangle formation in a network is critical for better understanding of the dynamics of such networks. Existing works in this area mainly focus on triangle counting, or generating synthetic networks by matching the prevalence of triangles in real-life networks. While these efforts increase our understanding of triangle’s role in a network, they have limited practical utility. In this work we undertake an interesting problem relating to triangle formation in a network, which is, to predict the time by which the third link of a triangle appears in a network. Since the third link completes a triangle, we name this task as Triangle Completion Time Prediction (TCTP). Solution to TCTP problem is valuable for real-life link recommendation in social/e-commerce networks, also it provides vital information for dynamic network analysis and community generation study.
An efficient and robust framework (GraNiTE) is proposed for solving the TCTP problem. GraNiTE uses neural networks based approach for learning a representation vector of a triangle completing edge, which is a concatenation of two representation vectors: first one is learnt from graphlet based local topology around that edge and the second one is learnt from time-preserving embedding of the constituting vertices of that edge. A comparison of the proposed solution with several baseline methods shows that the mean absolute error (MAE) of the proposed method is at least one-forth of that of the best baseline method.
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- 1.
GraNiTE is an anagram of the bold letters in Graphlet and Node based Time-conserving Embedding.
- 2.
Code and data for the experiments are available at https://github.com/Vachik-Dave/GraNiTE_solving_triangle_completion_time_prediction.
- 3.
- 4.
- 5.
Note that, by strict definition of local graphlet, g3 and g7 are not local, but we compute their frequencies anyway because these are popular 4-size graphlets.
References
Antal, T., Krapivsky, P., Redner, S.: Social balance on networks: the dynamics of friendship and enmity. Physica D 224, 130–136 (2006)
Bianconi, G., Darst, R.K., Iacovacci, J., Fortunato, S.: Triadic closure as a basic generating mechanism of communities in complex networks. Phys. Rev. E 90(4), 042806 (2014)
Bonner, S., Brennan, J., Kureshi, I., Theodoropoulos, G., McGough, A.S., Obara, B.: Temporal graph offset reconstruction: towards temporally robust graph representation learning. In: IEEE Big Data, pp. 3737–3746 (2018)
Dave, V.S., Ahmed, N.K., Hasan, M.A.: E-clog: counting edge-centric local graphlets. In: IEEE Intternational Conference on Big Data, pp. 586–595, December 2017
Dave, V.S., Al Hasan, M., Reddy, C.K.: How fast will you get a response? Predicting interval time for reciprocal link creation. In: Eleventh International AAAI Conference on Web and Social Media, ICWSM 2017 (2017)
Dave, V.S., Hasan, M.A., Zhang, B., Reddy, C.K.: Predicting interval time for reciprocal link creation using survival analysis. Soc. Netw. Anal. Min. 8(1), 1–20 (2018). https://doi.org/10.1007/s13278-018-0494-1
Dave, V.S., Zhang, B., Al Hasan, M., AlJadda, K., Korayem, M.: A combined representation learning approach for better job and skill recommendation. In: ACM International Conference on Information and Knowledge Management, CIKM 2018, pp. 1997–2005 (2018)
Dave, V.S., Zhang, B., Chen, P.Y., Hasan, M.A.: Neural-brane: neural Bayesian personalized ranking for attributed network embedding. Data Sci. Eng. (2019)
Dong, Y., et al.: Link prediction and recommendation across heterogeneous social networks. In: IEEE International Conference on Data Mining, pp. 181–190 (2012)
Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)
Durak, N., Pinar, A., Kolda, T.G., Seshadhri, C.: Degree relations of triangles in real-world networks and graph models. In: ACM International Conference on Information and Knowledge Management, pp. 1712–1716 (2012)
Grover, A., Leskovec, J.: Node2vec: scalable feature learning for networks. In: KDD 2016, pp. 855–864 (2016)
Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Advances in Neural Information Processing Systems (NIPS), vol. 30, pp. 1024–1034 (2017)
Hasan, M.A., Dave, V.: Triangle counting in large networks: a review. Wiley Interdisc. Rev. Data Min. Knowl. Discov. 8(2), e1226 (2018)
Hasan, M.A., Zaki, M.J.: A survey of link prediction in social networks. In: Aggarwal, C. (ed.) Social Network Data Analytics, pp. 243–275. Springer, Boston (2011). https://doi.org/10.1007/978-1-4419-8462-3_9
Huang, H., Tang, J., Liu, L., Luo, J., Fu, X.: Triadic closure pattern analysis and prediction in social networks. IEEE Trans. Knowl. Data Eng. 27(12), 3374–3389 (2015)
Leskovec, J., Backstrom, L., Kumar, R., Tomkins, A.: Microscopic evolution of social networks. In: KDD 2008, pp. 462–470 (2008)
Nguyen, G.H., Lee, J.B., Rossi, R.A., Ahmed, N.K., Koh, E., Kim, S.: Continuous-time dynamic network embeddings. In: Companion of the Web Conference 2018, pp. 969–976 (2018)
Perozzi, B., Al-Rfou, R., Skiena, S.: DeepWalk: online learning of social representations. In: KDD 2014, pp. 701–710 (2014)
Sala, A., Cao, L., Wilson, C., Zablit, R., Zheng, H., Zhao, B.Y.: Measurement-calibrated graph models for social network experiments. In: ACM International Conference on World Wide Web, pp. 861–870 (2010)
Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., Mei, Q.: Line: large-scale information network embedding. In: International Conference on World Wide Web, pp. 1067–1077 (2015)
Tsitsulin, A., Mottin, D., Karras, P., Müller, E.: Verse: versatile graph embeddings from similarity measures. In: The World Wide Web Conference, pp. 539–548 (2018)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440 (1998)
Zhang, Z., Cui, P., Wang, X., Pei, J., Yao, X., Zhu, W.: Arbitrary-order proximity preserved network embedding. In: KDD 2018, pp. 2778–2786 (2018)
Zhou, L., Yang, Y., Ren, X., Wu, F., Zhuang, Y.: Dynamic network embedding by modeling triadic closure process. In: Conference on Artificial Intelligence (2018)
Zuo, Y., Liu, G., Lin, H., Guo, J., Hu, X., Wu, J.: Embedding temporal network via neighborhood formation. In: ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2857–2866 (2018)
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Dave, V.S., Al Hasan, M. (2020). Triangle Completion Time Prediction Using Time-Conserving Embedding. In: Brefeld, U., Fromont, E., Hotho, A., Knobbe, A., Maathuis, M., Robardet, C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2019. Lecture Notes in Computer Science(), vol 11906. Springer, Cham. https://doi.org/10.1007/978-3-030-46150-8_32
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