Abstract
Graph embedding is a transformation of vertices of a graph into a set of vectors. A good embedding should capture the graph topology, vertex-to-vertex relationship, and other relevant information about the graph, its subgraphs, and vertices. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representations of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts.
In the recent paper [1], we propose a “divergence score” that can be assigned to embeddings to help distinguish good ones from bad ones. This general framework provides a tool for an unsupervised graph embedding comparison. The complexity of the original algorithm was quadratic in the number of vertices. It was enough to show that the proposed method is feasible and has practical potential (proof-of-concept). In this paper, we improve the complexity of the original framework and design a scalable approximation algorithm. Moreover, we perform some detailed quality and speed benchmarks.
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References
Kamiński, B., Prałat, P., Théberge, F.: An unsupervised framework for comparing graph embeddings. J. Complex Networks, in press. 27 p
Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Bianconi, G.: Interdisciplinary and physics challenges of network theory. EPL 111(5), 56001 (2015)
Janssen, J.: Spatial models for virtual networks. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 201–210. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13962-8_23
Poulin, V., Théberge, F.: Ensemble clustering for graphs. In: Aiello, L.M., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L.M. (eds.) COMPLEX NETWORKS 2018. SCI, vol. 812, pp. 231–243. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05411-3_19
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)
McInnes, L., Healy, J., Melville, J.: UMAP: uniform manifold approximation and projection for dimension reduction. pre-print arXiv:1802.03426 (2018)
Chung, F.R.K., Lu, L.: Complex Graphs and Networks. American Mathematical Society, Boston (2006)
Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99, 7821–7826 (2002)
Leskovec, J., Krevl, A.: SNAP datasets: Stanford large network dataset collection. http://snap.stanford.edu/data
Kamiński, B., Prałat, P., Théberge, F.: Artificial benchmark for community detection (ABCD) – fast random graph model with community structure, pre-print arXiv:2002.00843 (2020)
Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)
Kamiński, B., Poulin, V., Prałat, P., Szufel, P., Théberge, F.: Clustering via Hypergraph Modularity. PLoS ONE 14(11), e0224307 (2019)
Antelmi, A., et al.: Analyzing, exploring, and visualizing complex networks via hypergraphs using SimpleHypergraphs.jl. Internet Math. (2020). 32 p
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Kamiński, B., Prałat, P., Théberge, F. (2020). A Scalable Unsupervised Framework for Comparing Graph Embeddings. In: Kamiński, B., Prałat, P., Szufel, P. (eds) Algorithms and Models for the Web Graph. WAW 2020. Lecture Notes in Computer Science(), vol 12091. Springer, Cham. https://doi.org/10.1007/978-3-030-48478-1_4
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DOI: https://doi.org/10.1007/978-3-030-48478-1_4
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