Abstract
In real-world scenarios, dynamic signed networks are ubiquitous where edges have positive and negative types and evolve over time. Graph neural networks have achieved impressive performance in node representation learning, facilitating various downstream tasks, i.e., link prediction. However, employing existing methods to learn dynamic signed network embedding faces the following challenges. First, it is hard to encode the dynamics and sign semantics of network simultaneously. Positive and negative edges have different sign semantics and the graph structure is dynamically changing with time. Second, it is non-trivial to alleviate over-smoothing and construct the deeper dynamic signed network due to the learning of network dynamics. In this paper, we propose Dynamic Signed Network Embedding (DynamiSE) to tackle the above problems. DynamiSE effectively integrates the balance theory and ordinary differential equation into node representation learning to encode the dynamics of network and capture sign semantics between neighbors. Specifically, we design the dynamic sign collaboration unit to construct a deeper dynamic signed graph neural network, which models the evolution patterns and simulates the propagation and aggregation of sign semantics. The complex sign influence between nodes formed by different semantics of positive and negative edges is captured by the sign semantics aggregation unit. Extensive experiments on real-world dynamic signed networks show that DynamiSE outperforms most state-of-the-art methods in link prediction task.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
Datasets used in this paper are publicly available. The bitcoin-otc, bitcoin-alpha, wiki-RfA and Epinions datasets: http://snap.stanford.edu/data/.
Code availability
Not Applicable.
Notes
http://www.btc-alpha.com
http://www.bitcoin-otc.com.
http://snap.stanford.edu/data/wiki-RfA.html.
http://epinions.com/
References
Cartwright, D., & Harary, F. (1956). Structural balance: a generalization of Heider’s theory. Psychological Review, 63(5), 277.
Chakraborty, R., Das, R., & Chandra, J. (2023). SigGAN: Adversarial model for learning signed relationships in networks. ACM Transactions on Knowledge Discovery from Data, 17(1), 1–20.
Dang, Q.-V., & Ignat, C.-L. (2018). Link-sign prediction in dynamic signed directed networks. In 2018 IEEE 4th international conference on collaboration and internet computing (CIC), pp. 36–45.
De Brouwer, E., Simm, J., Arany, A., & Moreau, Y. (2019). GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series. Advances in Neural Information Processing Systems, 32.
Derr, T., Ma, Y., & Tang, J. (2018). Signed graph convolutional networks. In International conference on data mining, pp. 929–934.
Duan, P., Zhou, C., & Liu, Y. (2023). Dynamic graph representation learning via coupling-process model. IEEE Transactions on Neural Networks and Learning Systems. https://doi.org/10.1109/TKDE.2021.3103193
Fan, Z., Liu, Z., Zhang, J., Xiong, Y., Zheng, L., & Yu, P.S. (2021). Continuous-time sequential recommendation with temporal graph collaborative transformer. In Proceedings of the 30th ACM international conference on information & knowledge management, pp. 433–442.
Fang, H., Li, X., & Zhang, J. (2022). Integrating social influence modeling and user modeling for trust prediction in signed networks. Artificial Intelligence, 302, 103628.
He, D., Wang, T., Zhai, L., Jin, D., Yang, L., Huang, Y., & Yu, P. (2021). Adversarial representation mechanism learning for network embedding. IEEE Transactions on Knowledge and Data Engineering. https://doi.org/10.1109/TKDE.2021.3103193
Huang, J., Shen, H., Cao, Q., Tao, S., & Cheng, X. (2021). Signed bipartite graph neural networks. In ACMN international conference on information and knowledge management (pp. 740–749).
Huang, J., Shen, H., Hou, L., & Cheng, X. (2019). Signed graph attention networks. In International conference on artificial neural networks (pp. 566–577).
Huang, J., Shen, H., Hou, L., & Cheng, X. (2021). SDGNN: Learning node representation for signed directed networks. In Proceedings of the AAAI conference on artificial intelligence (Vol. 35, pp. 196–203).
Huang, Z., Silva, A., & Singh, A. (2021). Pole: Polarized embedding for signed networks. arXiv preprint arXiv:2110.09899.
Islam, M. R., Prakash, B. A., & Ramakrishnan, N. (2018). Signet: Scalable embeddings for signed networks. In PAKDD (Vol. 10938, pp. 157–169). Springer.
Javari, A., Derr, T., Esmailian, P., Tang, J., & Chang, K.C.-C. (2020). Rose: Role-based signed network embedding. In International world wide web conferences (www), pp. 2782–2788.
Jiao, P., Guo, X., Jing, X., He, D., Wu, H., Pan, S., & Wang, W. (2021). Temporal network embedding for link prediction via vae joint attention mechanism. IEEE Transactions on Neural Networks and Learning Systems, 33, 7400.
Kim, J., Park, H., Lee, J.-E., & Kang, U. (2018). Side: Representation learning in signed directed networks. In Proceedings of the 2018 world wide web conference, pp. 509–518.
Kipf, T.N., & Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907.
Kumar, S., Spezzano, F., Subrahmanian, V., & Faloutsos, C. (2016). Edge weight prediction in weighted signed networks. In International conference on data mining, pp. 221–230.
Li, Y., Qu, M., Tang, J., Chang, Y. (2023). Signed Laplacian graph neural networks. In Proceedings of the AAAI conference on artificial intelligence (Vol. 37, pp. 4444–4452).
Li, Y., Tian, Y., Zhang, J., & Chang, Y. (2020). Learning signed network embedding via graph attention. In Proceedings of the AAAI conference on artificial intelligence (Vol. 34, pp. 4772–4779).
Lin, W., & Li, B. (2022). Status-aware signed heterogeneous network embedding with graph neural networks. IEEE Transactions on Neural Networks and Learning Systems. https://doi.org/10.1109/TNNLS.2022.3151046
Liu, H. (2022). LightSGCN: Powering signed graph convolution network for link sign prediction with simplified architecture design. In Proceedings of the 45th international ACM SIGZIR conference on research and development in information retrieval, pp. 2680–2685.
Liu, H., Zhang, Z., Cui, P., Zhang, Y., Cui, Q., Liu, J., & Zhu, W. (2021). Signed graph neural network with latent groups. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pp. 1066–1075.
Lu, Y., Wang, X., Shi, C., Yu, P. S., & Ye, Y. (2019). Temporal network embedding with micro-and macro-dynamics. In ACM international conference on information and knowledge management, pp. 469–478.
Luo, Y., Huang, Z., Chen, H., Yang, Y., Yin, H., & Baktashmotlagh, M. (2021). Interpretable signed link prediction with signed infomax hyperbolic graph. IEEE Transactions on Knowledge and Data Engineering. https://doi.org/10.1109/TKDE.2021.3139035
Nguyen, G. H., Lee, J. B., Rossi, R. A., Ahmed, N. K., Koh, E., & Kim, S. (2018). Continuous-time dynamic network embeddings. In International world wide web conferences (www), pp. 969–976.
Pareja, A., Domeniconi, G., Chen, J., Ma, T., Suzumura, T., Kanezashi, H. & Leiserson, C. (2020). Evolvegcn: Evolving graph convolutional networks for dynamic graphs. In AAAI conference on artificial intelligence (AAAI), pp. 5363–5370.
Poli, M., Massaroli, S., Park, J., Yamashita, A., Asama, H., & Park, J. (2019). Graph neural ordinary differential equations. arXiv preprint arXiv:1911.07532.
Raghavendra, M., Sharma, K., Kumar, S., et al. (2022). Signed link representation in continuous-time dynamic signed networks. arXiv preprint arXiv:2207.03408.
Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., & Bronstein, M. (2020). Temporal graph networks for deep learning on dynamic graphs. arXiv preprint arXiv:2006.10637.
Shu, L., Du, E., Chang, Y., Chen, C., Zheng, Z., Xing, X., & Shen, S. (2021). Sgcl: Contrastive representation learning for signed graphs. In ACM international conference on information and knowledge management, pp. 1671–1680.
Van de Bunt, G. G., Van Duijn, M. A., & Snijders, T. A. (1999). Friendship networks through time: An actor-oriented dynamic statistical network model. Computational & Mathematical Organization Theory, 5(2), 167–192.
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., & Bengio, Y. (2017). Graph attention networks. arXiv preprint arXiv:1710.10903.
Wang, G., Ying, R., Huang, J., & Leskovec, J. (2020). Direct multi-hop attention based graph neural network. arXiv preprint arXiv:2009.14332.
Wang, S., Tang, J., Aggarwal, C. C., Chang, Y., & Liu, H. (2017). Signed network embedding in social media. In N. V. Chawla., & W. Wang (Eds.), International conference on data mining (pp. 327–335). SIAM.
Wang, Z., Li, Q., & Yu, D. (2022). TPGNN: Learning high-order information in dynamic graphs via temporal propagation. arXiv preprint arXiv:2210.01171.
Wen, Z., & Fang, Y. (2022). Trend: Temporal event and node dynamics for graph representation learning. In Proceedings of the ACM web conference, pp. 1159–1169.
Xhonneux, L.-P., Qu, M., & Tang, J. (2020). Continuous graph neural networks. In International conference on machine learning, pp. 10432–10441.
Xu, D., Ruan, C., Korpeoglu, E., Kumar, S., & Achan, K. (2020). Inductive representation learning on temporal graphs. arXiv preprint arXiv:2002.07962.
Xue, G., Zhong, M., Li, J., Chen, J., Zhai, C., & Kong, R. (2022). Dynamic network embedding survey. Neurocomputing, 472, 212–223.
Yang, M., Meng, Z., & King, I. (2020). Featurenorm: L2 feature normalization for dynamic graph embedding. In International conference on data mining, pp. 731–740.
Yu, W., Cheng, W., Aggarwal, C.C., Zhang, K., Chen, H., & Wang, W. (2018). Netwalk: A flexible deep embedding approach for anomaly detection in dynamic networks. In Acm knowledge discovery and data mining (SIGKDD), pp. 2672–2681.
Zhang, M., Wu, S., Yu, X., Liu, Q., & Wang, L. (2022). Dynamic graph neural networks for sequential recommendation. IEEE Transactions on Knowledge and Data Engineering, 35, 4741–4753.
Zhang, Y., Gao, S., Pei, J., & Huang, H. (2022). Improving social network embedding via new second-order continuous graph neural networks. In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining, pp. 2515–2523.
Zhang, Y., Xiong, Y., Li, D., Shan, C., Ren, K., & Zhu, Y. (2021). Cope: Modeling continuous propagation and evolution on interaction graph. In ACM international conference on information and knowledge management, pp. 2627–2636.
Zhu, D., Cui, P., Zhang, Z., Pei, J., & Zhu, W. (2018). High-order proximity preserved embedding for dynamic networks. IEEE Transactions on Knowledge and Data Engineering (TKDE), 30(11), 2134–2144.
Acknowledgements
We would like to thank the anonymous reviewers and our shepherd for their detailed and valuable comments. This work was supported by the National Natural Science Foundation of China (No. U1936213) and CNKLSTISS.
Funding
This work is funded in part by the National Natural Science Foundation of China Projects No. U1936213, and also supported by CNKLSTISS.
Author information
Authors and Affiliations
Contributions
All authors contributed to conceptualization, investigation and Methodology. Writing and visualization are preformed by H.T.S and P.T. Software is preformed by H.T.S, P.T, Y.L. The reviewing and editing are performed by Y.X, H.F.W, Y.Z and J.X.
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare no conflicts of interest regarding this paper.
Ethics approval
Not Applicable.
Consent to participate
Not Applicable.
Consent for publication
Not Applicable.
Additional information
Editors: Bingxue Zhang, Feida Zhu, Bin Yang, João Gama.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sun, H., Tian, P., Xiong, Y. et al. DynamiSE: dynamic signed network embedding for link prediction. Mach Learn 113, 4037–4053 (2024). https://doi.org/10.1007/s10994-023-06473-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10994-023-06473-z