Abstract
In this paper, we introduce spatiotemporal graph \( k \)-means (STG\(k\)M), a novel, unsupervised method to cluster vertices within a dynamic network. Drawing inspiration from traditional \( k \)-means, STG\(k\)M finds both short-term dynamic clusters and a “long-lived” partitioning of vertices within a network whose topology is evolving over time. We provide an exposition of the algorithm, illuminate its operation on synthetic data, and apply it to detect political parties from a dynamic network of voting data in the United States House of Representatives. One of the main advantages of STGkM is that it has only one required parameter, namely \( k \); we therefore include an analysis of the range of this parameter and guidance on selecting its optimal value. We also give certain theoretical guarantees about the correctness of our algorithm.
Both authors contributed equally to this work.
See https://github.com/dynestic/stgkm for the associated code for this project.
We would like to acknowledge J. Nathan Kutz (U. of Washington) for his support.
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Notes
- 1.
Our approach is perhaps more analogous to \( k \)-medoids, but in a network context, the distinction between \( k \)-means and \( k \)-medoids is not obvious.
- 2.
If no weight functions are provided or if the weight functions only output natural numbers, then \( \delta \) will assign only natural numbers.
- 3.
To see why, observe that \( k \)-medoids is \( \textsf{NP} \)-hard [20].
- 4.
In the worst case, e.g. when the graph is complete at every time step, optimizing this objective is still \( \textsf{NP} \)-hard, but in practice, it makes STG\(k\)M tractable.
References
Becker, R., et al.: Giant components in random temporal graphs. arXiv preprint arXiv:2205.14888 (2022)
Bergamini, E., Meyerhenke, H.: Approximating betweenness centrality in fully dynamic networks. Internet Math. 12(5), 281–314 (2016)
Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)
Chakrabarti, D., Kumar, R., Tomkins, A.: Evolutionary clustering. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 554–560 (2006)
Chi, Y., Song, X., Zhou, D., Hino, K., Tseng, B.L.: Evolutionary spectral clustering by incorporating temporal smoothness. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 153–162 (2007)
Cleveland, J., et al.: Introducing tropical geometric approaches to delay tolerant networking optimization. In: 2022 IEEE Aerospace Conference (AERO), pp. 1–11 (2022)
Dabke, D.V., Dorabiala, O.: Spatiotemporal graph k-means. In: Proceedings of the Communities in Networks ComNets @ NetSci 2023 (2023)
Dabke, D.V., Karntikoon, K., Aluru, C., Singh, M., Chazelle, B.: Network-augmented compartmental models to track asymptomatic disease spread. Bioinform. Adv. 3, vbad082 (2023)
DiTursi, D.J., Ghosh, G., Bogdanov, P.: Local community detection in dynamic networks. In: 2017 IEEE International Conference on Data Mining (ICDM), pp. 847–852 (2017)
Dorabiala, O., Webster, J., Kutz, N., Aravkin, A.: Spatiotemporal k-means. arXiv preprint arXiv:2211.05337 (2022)
Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3–5), 75–174 (2010)
Görke, R., Maillard, P., Schumm, A., Staudt, C., Wagner, D.: Dynamic graph clustering combining modularity and smoothness. J. Exp. Algorithmics 18, 1–1 (2013)
Gurukar, S., Ranu, S., Ravindran, B.: Commit: a scalable approach to mining communication motifs from dynamic networks. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, SIGMOD 2015, pp. 475–489. Association for Computing Machinery, New York (2015)
Habiba, C.T., Tanya, Y.: Berger-Wolf. Betweenness centrality measure in dynamic networks, Technical Report 19, DIMACS (2007)
Hylton, A., et al.: A survey of mathematical structures for lunar networks. In: 2022 IEEE Aerospace Conference (AERO), pp. 1–17 (2022)
Kodinariya, T.M., Makwana, P.R., et al.: Review on determining number of cluster in k-means clustering. Int. J. 1(6), 90–95 (2013)
Latapy, M., Viard, T., Magnien, C.: Stream graphs and link streams for the modeling of interactions over time. Soc. Netw. Anal. Min. 8(1), 61 (2018)
Lerman, K., Ghosh, R., Kang, J.H.: Centrality metric for dynamic networks. In: Proceedings of the Eighth Workshop on Mining and Learning with Graphs, MLG 2010, pp. 70—77. Association for Computing Machinery, New York (2010)
Lin, Y.-R., Chi, Y., Zhu, S., Sundaram, H., Tseng, B.L.: FacetNet: a framework for analyzing communities and their evolutions in dynamic networks. In: Proceedings of the 17th International Conference on World Wide Web, pp. 685–694 (2008)
Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)
Reda, K., Tantipathananandh, C., Johnson, A., Leigh, J., Berger-Wolf, T.: Visualizing the evolution of community structures in dynamic social networks. In: Computer Graphics Forum, vol. 30, pp. 1061–1070. Wiley Online Library (2011)
Rossetti, G., Cazabet, R.: Community discovery in dynamic networks: a survey. ACM Comput. Surv. 51(2), 1–37 (2018)
Ruan, B., Gan, J., Wu, H., Wirth, A.: Dynamic structural clustering on graphs. In: Proceedings of the 2021 International Conference on Management of Data, pp. 1491–1503 (2021)
Yao, Y., Joe-Wong, C.: Interpretable clustering on dynamic graphs with recurrent graph neural networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 4608–4616 (2021)
Yen, C.-C., Yeh, M.-Y., Chen, M.-S.: An efficient approach to updating closeness centrality and average path length in dynamic networks. In: 2013 IEEE 13th International Conference on Data Mining, pp. 867–876 (2013)
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Dabke, D.V., Dorabiala, O. (2024). A Novel Method for Vertex Clustering in Dynamic Networks. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1142. Springer, Cham. https://doi.org/10.1007/978-3-031-53499-7_36
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