Dynamic graph summarization: a tensor decomposition approach

Abstract

Due to the scale and complexity of todays’ social networks, it becomes infeasible to mine them with traditional approaches. A possible solution to reduce such scale and complexity is to produce a compact (lossy) version of the network that represents its major properties. This task is known as graph summarization, which is the subject of this research. Our focus is on time-evolving graphs, a more complex scenario where the dynamics of the network also should be taken into account. We address this problem using tensor decomposition, which enables us to capture the multi-way structure of the time-evolving network. This property is unique and is impossible to obtain with other approaches such as matrix factorization. Experimental evaluation on five real world networks implies promising results demonstrating that tensor decomposition is quite useful for summarizing dynamic networks.

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Acknowledgements

This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, and by National Funds through the FCT - Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013. Sofia Fernandes also acknowledges the support of FCT via the PhD scholarship PD/BD/114189/2016. The authors would also like to acknowledge the SocioPatterns collaboration for making the Infectious Patterns dataset available.

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Correspondence to Sofia Fernandes.

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Appendix

Appendix

The results of the signed Wilcoxon rank tests are shown in Table 7. We did not apply the tests on Friends&Family and DBLP datasets, when using a window length of 6, because the number of available windows was extremely small (3 and 4, respectively).

Table 7 p Values of the signed Wilcoxon rank tests involving tenClustS, with respect to: reconstruction error (top table), compression cost (middle table) and running time (bottom table)

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Fernandes, S., Fanaee-T, H. & Gama, J. Dynamic graph summarization: a tensor decomposition approach. Data Min Knowl Disc 32, 1397–1420 (2018). https://doi.org/10.1007/s10618-018-0583-9

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Keywords

  • Graph summarization
  • Time-evolving networks
  • Tensor decomposition