Abstract
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about the graph, its subgraphs or nodes themselves. A practical challenge with using embeddings is that there are many available variants to choose from. Selecting a small set of most promising embeddings from the long list of possible options for a given task is challenging and often requires domain expertise. Embeddings can be categorized into two main types: classical embeddings and structural embeddings. Classical embeddings focus on learning both local and global proximity of nodes, while structural embeddings learn information specifically about the local structure of nodes’ neighbourhood. For classical node embeddings there exists a framework which helps data scientists to identify (in an unsupervised way) a few embeddings that are worth further investigation. Unfortunately, no such framework exists for structural embeddings. In this paper we propose a framework for unsupervised ranking of structural graph embeddings. The proposed framework, apart from assigning an aggregate quality score for a structural embedding, additionally gives a data scientist insights into properties of this embedding. It produces information which predefined node features the embedding learns, how well it learns them, and which dimensions in the embedded space represent the predefined node features. Using this information the user gets a level of explainability to an otherwise complex black-box embedding algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aggarwal, M., Murty, M.N.: Machine Learning in Social Networks: Embedding Nodes, Edges, Communities, and Graphs. Springer, Singapore (2021). https://doi.org/10.1007/978-981-33-4022-0
Ahmed, N.K., et al.: Learning role-based graph embeddings. arXiv preprint arXiv:1802.02896 (2018)
Akoglu, L., Tong, H., Koutra, D.: Graph based anomaly detection and description: a survey. Data Min. Knowl. Disc. 29(3), 626–688 (2015)
Chami, I., Abu-El-Haija, S., Perozzi, B., Ré, C., Murphy, K.: Machine learning on graphs: a model and comprehensive taxonomy. arXiv preprint arXiv:2005.03675, p. 1 (2020)
Dehghan, A., Kamiński, B., Prałat, P.: Node structural representation learning using local signature matrix embedding [LSME] (2022, work in progress)
Dehghan-Kooshkghazi, A., Kamiński, B., Kraiński, Ł., Prałat, P., Théberge, F.: Evaluating node embeddings of complex networks. J. Complex Netw. 10(4), cnac030 (2022)
Donnat, C., Zitnik, M., Hallac, D., Leskovec, J.: Learning structural node embeddings via diffusion wavelets. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1320–1329 (2018)
Everett, M.G., Borgatti, S.P.: Unpacking Burt’s constraint measure. Soc. Netw. 62, 50–57 (2020)
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, pp. 855–864 (2016)
Hamilton, W.L., Ying, R., Leskovec, J.: Representation learning on graphs: methods and applications. arXiv preprint arXiv:1709.05584 (2017)
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
Henderson, K., et al.: RolX: structural role extraction & mining in large graphs. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1231–1239 (2012)
Kamiński, B., Kraiński, Ł, Prałat, P., Théberge, F.: A multi-purposed unsupervised framework for comparing embeddings of undirected and directed graphs. Netw. Sci. 10, 323–346 (2022)
Kamiński, B., Prałat, P., Théberge, F.: A scalable unsupervised framework for comparing graph embeddings. In: Kamiński, B., Prałat, P., Szufel, P. (eds.) WAW 2020. LNCS, vol. 12091, pp. 52–67. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48478-1_4
Kamiński, B., Prałat, P., Théberge, F.: An unsupervised framework for comparing graph embeddings. J. Complex Netw. 8(5), cnz043 (2020)
Kamiński, B., Prałat, P., Théberge, F.: Mining Complex Networks. Chapman and Hall/CRC, London (2021)
Mikolov, T., Chen, K., Corrado, G., Dean, J.: Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781 (2013)
Neville, J., Jensen, D.: Iterative classification in relational data. In: Proceedings of the AAAI-2000 Workshop on Learning Statistical Models from Relational Data, pp. 13–20 (2000)
Pankratz, B., Kamiński, B., Prałat, P.: Community detection supported by node embeddings. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds.) Complex Networks and Their Applications XI. Studies in Computational Intelligence, vol. 1078, pp. 221–232. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-21131-7_17
Perozzi, B., Al-Rfou, R., Skiena, S.: DeepWalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701–710 (2014)
Ribeiro, L.F., Saverese, P.H., Figueiredo, D.R.: struc2vec: learning node representations from structural identity. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 385–394 (2017)
Stolman, A., Levy, C., Seshadhri, C., Sharma, A.: Classic graph structural features outperform factorization-based graph embedding methods on community labeling. In: Proceedings of the 2022 SIAM International Conference on Data Mining (SDM), pp. 388–396. SIAM (2022)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Dehghan, A. et al. (2023). Unsupervised Framework for Evaluating Structural Node Embeddings of Graphs. In: Dewar, M., Prałat, P., Szufel, P., Théberge, F., Wrzosek, M. (eds) Algorithms and Models for the Web Graph. WAW 2023. Lecture Notes in Computer Science, vol 13894. Springer, Cham. https://doi.org/10.1007/978-3-031-32296-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-32296-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-32295-2
Online ISBN: 978-3-031-32296-9
eBook Packages: Computer ScienceComputer Science (R0)